Hugging Face's logo

Datasets:
PINNBench
/
pinnbench

Tasks:
Other
Modalities:
Image
Tabular
Text
Languages:
English
Size:
< 1K
Tags:
physics-informed-neural-networks
pinn
pde
benchmark
evaluation
routing
License:
Dataset card Data Studio Files
xet
 Community
1
EvalData commited on
Commit
c3f7558
·
verified ·
1 Parent(s): bd14b51

Add full experiments/results/ (paper_a + paper_c + rq* + paper_combined; ~397 MB)

Browse files
This view is limited to 50 files because it contains too many changes.   See raw diff
Files changed (50) hide show
  1. .gitattributes +1 -0
  2. results/paper_a/advdiff1d/results.json +0 -0
  3. results/paper_a/advdiff1d_highpe/results.json +0 -0
  4. results/paper_a/allencahn1d/results.json +0 -0
  5. results/paper_a/allencahn1d_sharp/results.json +0 -0
  6. results/paper_a/bandit_evaluation/results.json +770 -0
  7. results/paper_a/burgers1d/results.json +0 -0
  8. results/paper_a/burgers1d_lownu/results.json +0 -0
  9. results/paper_a/burgers1d_verylow/results.json +0 -0
  10. results/paper_a/heat1d/results.json +3 -0
  11. results/paper_a/holdout_validation/results.json +702 -0
  12. results/paper_a/kdv1d/results.json +0 -0
  13. results/paper_a/meta_router_evaluation/results.json +1253 -0
  14. results/paper_a/navier_stokes2d/results.json +0 -0
  15. results/paper_a/ntk_proxy/ntk_proxy_results.json +387 -0
  16. results/paper_a/reaction_diffusion1d/results.json +0 -0
  17. results/paper_a/reaction_diffusion1d_stiff/results.json +0 -0
  18. results/paper_a/regret_bound_validation.json +834 -0
  19. results/paper_a/routing_evaluation_full/results.json +753 -0
  20. results/paper_a/scaling_ablation/results.json +247 -0
  21. results/paper_a/wave2d/results.json +0 -0
  22. results/paper_c/ablation_statistics/results.json +554 -0
  23. results/paper_c/advdiff1d_ablation/results.json +0 -0
  24. results/paper_c/allencahn1d_standard_ablation/results.json +0 -0
  25. results/paper_c/allencahn_sharp_ablation/results.json +0 -0
  26. results/paper_c/burgers1d_ablation/results.json +0 -0
  27. results/paper_c/burgers1d_verylow_ablation/results.json +0 -0
  28. results/paper_c/causal_weight_evolution/causal_weight_evolution.json +2082 -0
  29. results/paper_c/gradient_flow_advdiff1d/fig_gradient_alignment.pdf +0 -0
  30. results/paper_c/gradient_flow_advdiff1d/gradient_flow_results.json +1039 -0
  31. results/paper_c/gradient_flow_allencahn/fig_gradient_alignment.pdf +0 -0
  32. results/paper_c/gradient_flow_allencahn/gradient_flow_results.json +1039 -0
  33. results/paper_c/gradient_flow_heat1d/fig_gradient_alignment.pdf +0 -0
  34. results/paper_c/gradient_flow_heat1d/gradient_flow_results.json +1039 -0
  35. results/paper_c/gradient_flow_kdv1d/fig_gradient_alignment.pdf +0 -0
  36. results/paper_c/gradient_flow_kdv1d/gradient_flow_results.json +1039 -0
  37. results/paper_c/heat1d_ablation/results.json +0 -0
  38. results/paper_c/kdv1d_ablation/results.json +0 -0
  39. results/paper_c/navier_stokes2d_ablation/results.json +0 -0
  40. results/paper_c/pinn_only_ablation_heat1d/results.json +0 -0
  41. results/paper_c/reaction_diffusion_stiff_ablation/results.json +0 -0
  42. results/paper_c/temporal_error_analysis/fig_temporal_error.pdf +0 -0
  43. results/paper_c/temporal_error_analysis/fig_temporal_error.png +3 -0
  44. results/paper_c/temporal_error_analysis/results.json +988 -0
  45. results/paper_c/wang_comparison/advdiff1d_results.json +0 -0
  46. results/paper_c/wang_comparison/allencahn1d_sharp_results.json +0 -0
  47. results/paper_c/wang_comparison/heat1d_results.json +0 -0
  48. results/paper_c/wang_comparison/kdv1d.log +10 -0
  49. results/paper_c/wang_comparison/kdv1d_results.json +0 -0
  50. results/paper_combined/adaptive_epsilon/fig_epsilon_trajectories.pdf +0 -0
.gitattributes CHANGED
@@ -58,3 +58,4 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
58
  # Video files - compressed
59
  *.mp4 filter=lfs diff=lfs merge=lfs -text
60
  *.webm filter=lfs diff=lfs merge=lfs -text
 
 
58
  # Video files - compressed
59
  *.mp4 filter=lfs diff=lfs merge=lfs -text
60
  *.webm filter=lfs diff=lfs merge=lfs -text
61
+ results/paper_a/heat1d/results.json filter=lfs diff=lfs merge=lfs -text
results/paper_a/advdiff1d/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_a/advdiff1d_highpe/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_a/allencahn1d/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_a/allencahn1d_sharp/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_a/bandit_evaluation/results.json ADDED
@@ -0,0 +1,770 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "config": {
3
+ "target_metric": "relative_l2_error",
4
+ "window_size": 50,
5
+ "probe_epochs": 50,
6
+ "total_epochs": 500,
7
+ "linucb_alphas": [
8
+ 0.1,
9
+ 0.5,
10
+ 1.0,
11
+ 2.0
12
+ ],
13
+ "n_samples": 220,
14
+ "n_pdes": 6,
15
+ "pdes": [
16
+ "advdiff1d",
17
+ "advdiff1d_highpe",
18
+ "allencahn1d",
19
+ "heat1d",
20
+ "kdv1d",
21
+ "wave2d"
22
+ ]
23
+ },
24
+ "selectors": {
25
+ "random_forest": {
26
+ "mean_regret": 0.0012462233814100425,
27
+ "max_regret": 0.00378037542104721,
28
+ "selection_accuracy": 0.6666666666666666,
29
+ "mean_budget_ratio": 0.355,
30
+ "mean_budget_savings": 0.645,
31
+ "fallback_rate": 0.0
32
+ },
33
+ "physics_final": {
34
+ "mean_regret": 0.1132673015197118,
35
+ "max_regret": 0.3662658512592316,
36
+ "selection_accuracy": 0.5,
37
+ "mean_budget_ratio": 0.355,
38
+ "mean_budget_savings": 0.645,
39
+ "fallback_rate": 0.0
40
+ },
41
+ "successive_halving": {
42
+ "mean_regret": 0.0025319281810273725,
43
+ "max_regret": 0.010100016370415686,
44
+ "selection_accuracy": 0.5,
45
+ "mean_budget_ratio": 0.16040000000000001,
46
+ "mean_budget_savings": 0.8395999999999999,
47
+ "fallback_rate": 0.0
48
+ },
49
+ "linucb_alpha0.1": {
50
+ "mean_regret": 0.059513779636472475,
51
+ "max_regret": 0.18926255106925963,
52
+ "selection_accuracy": 0.3333333333333333,
53
+ "mean_budget_ratio": 0.355,
54
+ "mean_budget_savings": 0.645,
55
+ "fallback_rate": 0.0
56
+ },
57
+ "linucb_alpha0.5": {
58
+ "mean_regret": 0.059513779636472475,
59
+ "max_regret": 0.18926255106925963,
60
+ "selection_accuracy": 0.3333333333333333,
61
+ "mean_budget_ratio": 0.355,
62
+ "mean_budget_savings": 0.645,
63
+ "fallback_rate": 0.0
64
+ },
65
+ "linucb_alpha1.0": {
66
+ "mean_regret": 0.059513779636472475,
67
+ "max_regret": 0.18926255106925963,
68
+ "selection_accuracy": 0.3333333333333333,
69
+ "mean_budget_ratio": 0.355,
70
+ "mean_budget_savings": 0.645,
71
+ "fallback_rate": 0.0
72
+ },
73
+ "linucb_alpha2.0": {
74
+ "mean_regret": 0.059513779636472475,
75
+ "max_regret": 0.18926255106925963,
76
+ "selection_accuracy": 0.3333333333333333,
77
+ "mean_budget_ratio": 0.355,
78
+ "mean_budget_savings": 0.645,
79
+ "fallback_rate": 0.0
80
+ }
81
+ },
82
+ "fold_details": {
83
+ "random_forest": [
84
+ {
85
+ "selector": "random_forest",
86
+ "held_out_group": "advdiff1d",
87
+ "selected_policy": "hybrid_no_gate",
88
+ "actual_best_policy": "hybrid_no_gate",
89
+ "selected_target": 0.010851731896400452,
90
+ "oracle_target": 0.010851731896400452,
91
+ "regret": 0.0,
92
+ "correct": 1.0,
93
+ "num_policies": 4,
94
+ "probe_epochs": 50,
95
+ "total_epochs": 500,
96
+ "budget_ratio": 0.325,
97
+ "budget_savings": 0.675,
98
+ "fallback_used": false
99
+ },
100
+ {
101
+ "selector": "random_forest",
102
+ "held_out_group": "advdiff1d_highpe",
103
+ "selected_policy": "hybrid_full",
104
+ "actual_best_policy": "hybrid_full",
105
+ "selected_target": 0.6212037026882171,
106
+ "oracle_target": 0.6212037026882171,
107
+ "regret": 0.0,
108
+ "correct": 1.0,
109
+ "num_policies": 3,
110
+ "probe_epochs": 50,
111
+ "total_epochs": 500,
112
+ "budget_ratio": 0.4,
113
+ "budget_savings": 0.6,
114
+ "fallback_used": false
115
+ },
116
+ {
117
+ "selector": "random_forest",
118
+ "held_out_group": "allencahn1d",
119
+ "selected_policy": "hybrid_full_lambda0.1",
120
+ "actual_best_policy": "hybrid_full",
121
+ "selected_target": 0.02434600070118904,
122
+ "oracle_target": 0.020649035833775996,
123
+ "regret": 0.0036969648674130447,
124
+ "correct": 0.0,
125
+ "num_policies": 4,
126
+ "probe_epochs": 50,
127
+ "total_epochs": 500,
128
+ "budget_ratio": 0.325,
129
+ "budget_savings": 0.675,
130
+ "fallback_used": false
131
+ },
132
+ {
133
+ "selector": "random_forest",
134
+ "held_out_group": "heat1d",
135
+ "selected_policy": "hybrid_full",
136
+ "actual_best_policy": "hybrid_no_gate",
137
+ "selected_target": 0.019640809297561644,
138
+ "oracle_target": 0.015860433876514434,
139
+ "regret": 0.00378037542104721,
140
+ "correct": 0.0,
141
+ "num_policies": 5,
142
+ "probe_epochs": 50,
143
+ "total_epochs": 500,
144
+ "budget_ratio": 0.28,
145
+ "budget_savings": 0.72,
146
+ "fallback_used": false
147
+ },
148
+ {
149
+ "selector": "random_forest",
150
+ "held_out_group": "kdv1d",
151
+ "selected_policy": "hybrid_no_gate",
152
+ "actual_best_policy": "hybrid_no_gate",
153
+ "selected_target": 0.003019273583777249,
154
+ "oracle_target": 0.003019273583777249,
155
+ "regret": 0.0,
156
+ "correct": 1.0,
157
+ "num_policies": 3,
158
+ "probe_epochs": 50,
159
+ "total_epochs": 500,
160
+ "budget_ratio": 0.4,
161
+ "budget_savings": 0.6,
162
+ "fallback_used": false
163
+ },
164
+ {
165
+ "selector": "random_forest",
166
+ "held_out_group": "wave2d",
167
+ "selected_policy": "hybrid_full",
168
+ "actual_best_policy": "hybrid_full",
169
+ "selected_target": 0.35113765448331835,
170
+ "oracle_target": 0.35113765448331835,
171
+ "regret": 0.0,
172
+ "correct": 1.0,
173
+ "num_policies": 3,
174
+ "probe_epochs": 50,
175
+ "total_epochs": 500,
176
+ "budget_ratio": 0.4,
177
+ "budget_savings": 0.6,
178
+ "fallback_used": false
179
+ }
180
+ ],
181
+ "physics_final": [
182
+ {
183
+ "selector": "physics_final",
184
+ "held_out_group": "advdiff1d",
185
+ "selected_policy": "hybrid_no_gate",
186
+ "actual_best_policy": "hybrid_no_gate",
187
+ "selected_target": 0.010851731896400452,
188
+ "oracle_target": 0.010851731896400452,
189
+ "regret": 0.0,
190
+ "correct": 1.0,
191
+ "num_policies": 4,
192
+ "probe_epochs": 50,
193
+ "total_epochs": 500,
194
+ "budget_ratio": 0.325,
195
+ "budget_savings": 0.675,
196
+ "fallback_used": false
197
+ },
198
+ {
199
+ "selector": "physics_final",
200
+ "held_out_group": "advdiff1d_highpe",
201
+ "selected_policy": "pinn_only",
202
+ "actual_best_policy": "hybrid_full",
203
+ "selected_target": 0.9874695539474487,
204
+ "oracle_target": 0.6212037026882171,
205
+ "regret": 0.3662658512592316,
206
+ "correct": 0.0,
207
+ "num_policies": 3,
208
+ "probe_epochs": 50,
209
+ "total_epochs": 500,
210
+ "budget_ratio": 0.4,
211
+ "budget_savings": 0.6,
212
+ "fallback_used": false
213
+ },
214
+ {
215
+ "selector": "physics_final",
216
+ "held_out_group": "allencahn1d",
217
+ "selected_policy": "hybrid_full",
218
+ "actual_best_policy": "hybrid_full",
219
+ "selected_target": 0.020649035833775996,
220
+ "oracle_target": 0.020649035833775996,
221
+ "regret": 0.0,
222
+ "correct": 1.0,
223
+ "num_policies": 4,
224
+ "probe_epochs": 50,
225
+ "total_epochs": 500,
226
+ "budget_ratio": 0.325,
227
+ "budget_savings": 0.675,
228
+ "fallback_used": false
229
+ },
230
+ {
231
+ "selector": "physics_final",
232
+ "held_out_group": "heat1d",
233
+ "selected_policy": "hybrid_full",
234
+ "actual_best_policy": "hybrid_no_gate",
235
+ "selected_target": 0.019640809297561644,
236
+ "oracle_target": 0.015860433876514434,
237
+ "regret": 0.00378037542104721,
238
+ "correct": 0.0,
239
+ "num_policies": 5,
240
+ "probe_epochs": 50,
241
+ "total_epochs": 500,
242
+ "budget_ratio": 0.28,
243
+ "budget_savings": 0.72,
244
+ "fallback_used": false
245
+ },
246
+ {
247
+ "selector": "physics_final",
248
+ "held_out_group": "kdv1d",
249
+ "selected_policy": "hybrid_no_gate",
250
+ "actual_best_policy": "hybrid_no_gate",
251
+ "selected_target": 0.003019273583777249,
252
+ "oracle_target": 0.003019273583777249,
253
+ "regret": 0.0,
254
+ "correct": 1.0,
255
+ "num_policies": 3,
256
+ "probe_epochs": 50,
257
+ "total_epochs": 500,
258
+ "budget_ratio": 0.4,
259
+ "budget_savings": 0.6,
260
+ "fallback_used": false
261
+ },
262
+ {
263
+ "selector": "physics_final",
264
+ "held_out_group": "wave2d",
265
+ "selected_policy": "pinn_only",
266
+ "actual_best_policy": "hybrid_full",
267
+ "selected_target": 0.6606952369213104,
268
+ "oracle_target": 0.35113765448331835,
269
+ "regret": 0.30955758243799203,
270
+ "correct": 0.0,
271
+ "num_policies": 3,
272
+ "probe_epochs": 50,
273
+ "total_epochs": 500,
274
+ "budget_ratio": 0.4,
275
+ "budget_savings": 0.6,
276
+ "fallback_used": false
277
+ }
278
+ ],
279
+ "successive_halving": [
280
+ {
281
+ "selector": "successive_halving",
282
+ "held_out_group": "advdiff1d",
283
+ "selected_policy": "hybrid_full_lambda0.1",
284
+ "actual_best_policy": "hybrid_no_gate",
285
+ "selected_target": 0.020951748266816138,
286
+ "oracle_target": 0.010851731896400452,
287
+ "regret": 0.010100016370415686,
288
+ "correct": 0.0,
289
+ "num_policies": 4,
290
+ "probe_epochs": 50,
291
+ "total_epochs": 500,
292
+ "budget_ratio": 0.18599999999999994,
293
+ "budget_savings": 0.8140000000000001,
294
+ "fallback_used": false
295
+ },
296
+ {
297
+ "selector": "successive_halving",
298
+ "held_out_group": "advdiff1d_highpe",
299
+ "selected_policy": "hybrid_full",
300
+ "actual_best_policy": "hybrid_full",
301
+ "selected_target": 0.6212037026882171,
302
+ "oracle_target": 0.6212037026882171,
303
+ "regret": 0.0,
304
+ "correct": 1.0,
305
+ "num_policies": 3,
306
+ "probe_epochs": 50,
307
+ "total_epochs": 500,
308
+ "budget_ratio": 0.16600000000000004,
309
+ "budget_savings": 0.834,
310
+ "fallback_used": false
311
+ },
312
+ {
313
+ "selector": "successive_halving",
314
+ "held_out_group": "allencahn1d",
315
+ "selected_policy": "hybrid_full_lambda0.1",
316
+ "actual_best_policy": "hybrid_full",
317
+ "selected_target": 0.02434600070118904,
318
+ "oracle_target": 0.020649035833775996,
319
+ "regret": 0.0036969648674130447,
320
+ "correct": 0.0,
321
+ "num_policies": 4,
322
+ "probe_epochs": 50,
323
+ "total_epochs": 500,
324
+ "budget_ratio": 0.18599999999999994,
325
+ "budget_savings": 0.8140000000000001,
326
+ "fallback_used": false
327
+ },
328
+ {
329
+ "selector": "successive_halving",
330
+ "held_out_group": "heat1d",
331
+ "selected_policy": "hybrid_full_lambda0.1",
332
+ "actual_best_policy": "hybrid_no_gate",
333
+ "selected_target": 0.01725502172484994,
334
+ "oracle_target": 0.015860433876514434,
335
+ "regret": 0.0013945878483355052,
336
+ "correct": 0.0,
337
+ "num_policies": 5,
338
+ "probe_epochs": 50,
339
+ "total_epochs": 500,
340
+ "budget_ratio": 0.09240000000000004,
341
+ "budget_savings": 0.9076,
342
+ "fallback_used": false
343
+ },
344
+ {
345
+ "selector": "successive_halving",
346
+ "held_out_group": "kdv1d",
347
+ "selected_policy": "hybrid_no_gate",
348
+ "actual_best_policy": "hybrid_no_gate",
349
+ "selected_target": 0.003019273583777249,
350
+ "oracle_target": 0.003019273583777249,
351
+ "regret": 0.0,
352
+ "correct": 1.0,
353
+ "num_policies": 3,
354
+ "probe_epochs": 50,
355
+ "total_epochs": 500,
356
+ "budget_ratio": 0.16600000000000004,
357
+ "budget_savings": 0.834,
358
+ "fallback_used": false
359
+ },
360
+ {
361
+ "selector": "successive_halving",
362
+ "held_out_group": "wave2d",
363
+ "selected_policy": "hybrid_full",
364
+ "actual_best_policy": "hybrid_full",
365
+ "selected_target": 0.35113765448331835,
366
+ "oracle_target": 0.35113765448331835,
367
+ "regret": 0.0,
368
+ "correct": 1.0,
369
+ "num_policies": 3,
370
+ "probe_epochs": 50,
371
+ "total_epochs": 500,
372
+ "budget_ratio": 0.16600000000000004,
373
+ "budget_savings": 0.834,
374
+ "fallback_used": false
375
+ }
376
+ ],
377
+ "linucb_alpha0.1": [
378
+ {
379
+ "selector": "linucb_alpha0.1",
380
+ "held_out_group": "advdiff1d",
381
+ "selected_policy": "pinn_only",
382
+ "actual_best_policy": "hybrid_no_gate",
383
+ "selected_target": 0.20011428296566008,
384
+ "oracle_target": 0.010851731896400452,
385
+ "regret": 0.18926255106925963,
386
+ "correct": 0.0,
387
+ "num_policies": 4,
388
+ "probe_epochs": 50,
389
+ "total_epochs": 500,
390
+ "budget_ratio": 0.325,
391
+ "budget_savings": 0.675,
392
+ "fallback_used": false
393
+ },
394
+ {
395
+ "selector": "linucb_alpha0.1",
396
+ "held_out_group": "advdiff1d_highpe",
397
+ "selected_policy": "hybrid_no_gate",
398
+ "actual_best_policy": "hybrid_full",
399
+ "selected_target": 0.6937585055828095,
400
+ "oracle_target": 0.6212037026882171,
401
+ "regret": 0.07255480289459237,
402
+ "correct": 0.0,
403
+ "num_policies": 3,
404
+ "probe_epochs": 50,
405
+ "total_epochs": 500,
406
+ "budget_ratio": 0.4,
407
+ "budget_savings": 0.6,
408
+ "fallback_used": false
409
+ },
410
+ {
411
+ "selector": "linucb_alpha0.1",
412
+ "held_out_group": "allencahn1d",
413
+ "selected_policy": "hybrid_full_lambda0.1",
414
+ "actual_best_policy": "hybrid_full",
415
+ "selected_target": 0.02434600070118904,
416
+ "oracle_target": 0.020649035833775996,
417
+ "regret": 0.0036969648674130447,
418
+ "correct": 0.0,
419
+ "num_policies": 4,
420
+ "probe_epochs": 50,
421
+ "total_epochs": 500,
422
+ "budget_ratio": 0.325,
423
+ "budget_savings": 0.675,
424
+ "fallback_used": false
425
+ },
426
+ {
427
+ "selector": "linucb_alpha0.1",
428
+ "held_out_group": "heat1d",
429
+ "selected_policy": "pinn_only",
430
+ "actual_best_policy": "hybrid_no_gate",
431
+ "selected_target": 0.10742879286408424,
432
+ "oracle_target": 0.015860433876514434,
433
+ "regret": 0.0915683589875698,
434
+ "correct": 0.0,
435
+ "num_policies": 5,
436
+ "probe_epochs": 50,
437
+ "total_epochs": 500,
438
+ "budget_ratio": 0.28,
439
+ "budget_savings": 0.72,
440
+ "fallback_used": false
441
+ },
442
+ {
443
+ "selector": "linucb_alpha0.1",
444
+ "held_out_group": "kdv1d",
445
+ "selected_policy": "hybrid_no_gate",
446
+ "actual_best_policy": "hybrid_no_gate",
447
+ "selected_target": 0.003019273583777249,
448
+ "oracle_target": 0.003019273583777249,
449
+ "regret": 0.0,
450
+ "correct": 1.0,
451
+ "num_policies": 3,
452
+ "probe_epochs": 50,
453
+ "total_epochs": 500,
454
+ "budget_ratio": 0.4,
455
+ "budget_savings": 0.6,
456
+ "fallback_used": false
457
+ },
458
+ {
459
+ "selector": "linucb_alpha0.1",
460
+ "held_out_group": "wave2d",
461
+ "selected_policy": "hybrid_full",
462
+ "actual_best_policy": "hybrid_full",
463
+ "selected_target": 0.35113765448331835,
464
+ "oracle_target": 0.35113765448331835,
465
+ "regret": 0.0,
466
+ "correct": 1.0,
467
+ "num_policies": 3,
468
+ "probe_epochs": 50,
469
+ "total_epochs": 500,
470
+ "budget_ratio": 0.4,
471
+ "budget_savings": 0.6,
472
+ "fallback_used": false
473
+ }
474
+ ],
475
+ "linucb_alpha0.5": [
476
+ {
477
+ "selector": "linucb_alpha0.5",
478
+ "held_out_group": "advdiff1d",
479
+ "selected_policy": "pinn_only",
480
+ "actual_best_policy": "hybrid_no_gate",
481
+ "selected_target": 0.20011428296566008,
482
+ "oracle_target": 0.010851731896400452,
483
+ "regret": 0.18926255106925963,
484
+ "correct": 0.0,
485
+ "num_policies": 4,
486
+ "probe_epochs": 50,
487
+ "total_epochs": 500,
488
+ "budget_ratio": 0.325,
489
+ "budget_savings": 0.675,
490
+ "fallback_used": false
491
+ },
492
+ {
493
+ "selector": "linucb_alpha0.5",
494
+ "held_out_group": "advdiff1d_highpe",
495
+ "selected_policy": "hybrid_no_gate",
496
+ "actual_best_policy": "hybrid_full",
497
+ "selected_target": 0.6937585055828095,
498
+ "oracle_target": 0.6212037026882171,
499
+ "regret": 0.07255480289459237,
500
+ "correct": 0.0,
501
+ "num_policies": 3,
502
+ "probe_epochs": 50,
503
+ "total_epochs": 500,
504
+ "budget_ratio": 0.4,
505
+ "budget_savings": 0.6,
506
+ "fallback_used": false
507
+ },
508
+ {
509
+ "selector": "linucb_alpha0.5",
510
+ "held_out_group": "allencahn1d",
511
+ "selected_policy": "hybrid_full_lambda0.1",
512
+ "actual_best_policy": "hybrid_full",
513
+ "selected_target": 0.02434600070118904,
514
+ "oracle_target": 0.020649035833775996,
515
+ "regret": 0.0036969648674130447,
516
+ "correct": 0.0,
517
+ "num_policies": 4,
518
+ "probe_epochs": 50,
519
+ "total_epochs": 500,
520
+ "budget_ratio": 0.325,
521
+ "budget_savings": 0.675,
522
+ "fallback_used": false
523
+ },
524
+ {
525
+ "selector": "linucb_alpha0.5",
526
+ "held_out_group": "heat1d",
527
+ "selected_policy": "pinn_only",
528
+ "actual_best_policy": "hybrid_no_gate",
529
+ "selected_target": 0.10742879286408424,
530
+ "oracle_target": 0.015860433876514434,
531
+ "regret": 0.0915683589875698,
532
+ "correct": 0.0,
533
+ "num_policies": 5,
534
+ "probe_epochs": 50,
535
+ "total_epochs": 500,
536
+ "budget_ratio": 0.28,
537
+ "budget_savings": 0.72,
538
+ "fallback_used": false
539
+ },
540
+ {
541
+ "selector": "linucb_alpha0.5",
542
+ "held_out_group": "kdv1d",
543
+ "selected_policy": "hybrid_no_gate",
544
+ "actual_best_policy": "hybrid_no_gate",
545
+ "selected_target": 0.003019273583777249,
546
+ "oracle_target": 0.003019273583777249,
547
+ "regret": 0.0,
548
+ "correct": 1.0,
549
+ "num_policies": 3,
550
+ "probe_epochs": 50,
551
+ "total_epochs": 500,
552
+ "budget_ratio": 0.4,
553
+ "budget_savings": 0.6,
554
+ "fallback_used": false
555
+ },
556
+ {
557
+ "selector": "linucb_alpha0.5",
558
+ "held_out_group": "wave2d",
559
+ "selected_policy": "hybrid_full",
560
+ "actual_best_policy": "hybrid_full",
561
+ "selected_target": 0.35113765448331835,
562
+ "oracle_target": 0.35113765448331835,
563
+ "regret": 0.0,
564
+ "correct": 1.0,
565
+ "num_policies": 3,
566
+ "probe_epochs": 50,
567
+ "total_epochs": 500,
568
+ "budget_ratio": 0.4,
569
+ "budget_savings": 0.6,
570
+ "fallback_used": false
571
+ }
572
+ ],
573
+ "linucb_alpha1.0": [
574
+ {
575
+ "selector": "linucb_alpha1.0",
576
+ "held_out_group": "advdiff1d",
577
+ "selected_policy": "pinn_only",
578
+ "actual_best_policy": "hybrid_no_gate",
579
+ "selected_target": 0.20011428296566008,
580
+ "oracle_target": 0.010851731896400452,
581
+ "regret": 0.18926255106925963,
582
+ "correct": 0.0,
583
+ "num_policies": 4,
584
+ "probe_epochs": 50,
585
+ "total_epochs": 500,
586
+ "budget_ratio": 0.325,
587
+ "budget_savings": 0.675,
588
+ "fallback_used": false
589
+ },
590
+ {
591
+ "selector": "linucb_alpha1.0",
592
+ "held_out_group": "advdiff1d_highpe",
593
+ "selected_policy": "hybrid_no_gate",
594
+ "actual_best_policy": "hybrid_full",
595
+ "selected_target": 0.6937585055828095,
596
+ "oracle_target": 0.6212037026882171,
597
+ "regret": 0.07255480289459237,
598
+ "correct": 0.0,
599
+ "num_policies": 3,
600
+ "probe_epochs": 50,
601
+ "total_epochs": 500,
602
+ "budget_ratio": 0.4,
603
+ "budget_savings": 0.6,
604
+ "fallback_used": false
605
+ },
606
+ {
607
+ "selector": "linucb_alpha1.0",
608
+ "held_out_group": "allencahn1d",
609
+ "selected_policy": "hybrid_full_lambda0.1",
610
+ "actual_best_policy": "hybrid_full",
611
+ "selected_target": 0.02434600070118904,
612
+ "oracle_target": 0.020649035833775996,
613
+ "regret": 0.0036969648674130447,
614
+ "correct": 0.0,
615
+ "num_policies": 4,
616
+ "probe_epochs": 50,
617
+ "total_epochs": 500,
618
+ "budget_ratio": 0.325,
619
+ "budget_savings": 0.675,
620
+ "fallback_used": false
621
+ },
622
+ {
623
+ "selector": "linucb_alpha1.0",
624
+ "held_out_group": "heat1d",
625
+ "selected_policy": "pinn_only",
626
+ "actual_best_policy": "hybrid_no_gate",
627
+ "selected_target": 0.10742879286408424,
628
+ "oracle_target": 0.015860433876514434,
629
+ "regret": 0.0915683589875698,
630
+ "correct": 0.0,
631
+ "num_policies": 5,
632
+ "probe_epochs": 50,
633
+ "total_epochs": 500,
634
+ "budget_ratio": 0.28,
635
+ "budget_savings": 0.72,
636
+ "fallback_used": false
637
+ },
638
+ {
639
+ "selector": "linucb_alpha1.0",
640
+ "held_out_group": "kdv1d",
641
+ "selected_policy": "hybrid_no_gate",
642
+ "actual_best_policy": "hybrid_no_gate",
643
+ "selected_target": 0.003019273583777249,
644
+ "oracle_target": 0.003019273583777249,
645
+ "regret": 0.0,
646
+ "correct": 1.0,
647
+ "num_policies": 3,
648
+ "probe_epochs": 50,
649
+ "total_epochs": 500,
650
+ "budget_ratio": 0.4,
651
+ "budget_savings": 0.6,
652
+ "fallback_used": false
653
+ },
654
+ {
655
+ "selector": "linucb_alpha1.0",
656
+ "held_out_group": "wave2d",
657
+ "selected_policy": "hybrid_full",
658
+ "actual_best_policy": "hybrid_full",
659
+ "selected_target": 0.35113765448331835,
660
+ "oracle_target": 0.35113765448331835,
661
+ "regret": 0.0,
662
+ "correct": 1.0,
663
+ "num_policies": 3,
664
+ "probe_epochs": 50,
665
+ "total_epochs": 500,
666
+ "budget_ratio": 0.4,
667
+ "budget_savings": 0.6,
668
+ "fallback_used": false
669
+ }
670
+ ],
671
+ "linucb_alpha2.0": [
672
+ {
673
+ "selector": "linucb_alpha2.0",
674
+ "held_out_group": "advdiff1d",
675
+ "selected_policy": "pinn_only",
676
+ "actual_best_policy": "hybrid_no_gate",
677
+ "selected_target": 0.20011428296566008,
678
+ "oracle_target": 0.010851731896400452,
679
+ "regret": 0.18926255106925963,
680
+ "correct": 0.0,
681
+ "num_policies": 4,
682
+ "probe_epochs": 50,
683
+ "total_epochs": 500,
684
+ "budget_ratio": 0.325,
685
+ "budget_savings": 0.675,
686
+ "fallback_used": false
687
+ },
688
+ {
689
+ "selector": "linucb_alpha2.0",
690
+ "held_out_group": "advdiff1d_highpe",
691
+ "selected_policy": "hybrid_no_gate",
692
+ "actual_best_policy": "hybrid_full",
693
+ "selected_target": 0.6937585055828095,
694
+ "oracle_target": 0.6212037026882171,
695
+ "regret": 0.07255480289459237,
696
+ "correct": 0.0,
697
+ "num_policies": 3,
698
+ "probe_epochs": 50,
699
+ "total_epochs": 500,
700
+ "budget_ratio": 0.4,
701
+ "budget_savings": 0.6,
702
+ "fallback_used": false
703
+ },
704
+ {
705
+ "selector": "linucb_alpha2.0",
706
+ "held_out_group": "allencahn1d",
707
+ "selected_policy": "hybrid_full_lambda0.1",
708
+ "actual_best_policy": "hybrid_full",
709
+ "selected_target": 0.02434600070118904,
710
+ "oracle_target": 0.020649035833775996,
711
+ "regret": 0.0036969648674130447,
712
+ "correct": 0.0,
713
+ "num_policies": 4,
714
+ "probe_epochs": 50,
715
+ "total_epochs": 500,
716
+ "budget_ratio": 0.325,
717
+ "budget_savings": 0.675,
718
+ "fallback_used": false
719
+ },
720
+ {
721
+ "selector": "linucb_alpha2.0",
722
+ "held_out_group": "heat1d",
723
+ "selected_policy": "pinn_only",
724
+ "actual_best_policy": "hybrid_no_gate",
725
+ "selected_target": 0.10742879286408424,
726
+ "oracle_target": 0.015860433876514434,
727
+ "regret": 0.0915683589875698,
728
+ "correct": 0.0,
729
+ "num_policies": 5,
730
+ "probe_epochs": 50,
731
+ "total_epochs": 500,
732
+ "budget_ratio": 0.28,
733
+ "budget_savings": 0.72,
734
+ "fallback_used": false
735
+ },
736
+ {
737
+ "selector": "linucb_alpha2.0",
738
+ "held_out_group": "kdv1d",
739
+ "selected_policy": "hybrid_no_gate",
740
+ "actual_best_policy": "hybrid_no_gate",
741
+ "selected_target": 0.003019273583777249,
742
+ "oracle_target": 0.003019273583777249,
743
+ "regret": 0.0,
744
+ "correct": 1.0,
745
+ "num_policies": 3,
746
+ "probe_epochs": 50,
747
+ "total_epochs": 500,
748
+ "budget_ratio": 0.4,
749
+ "budget_savings": 0.6,
750
+ "fallback_used": false
751
+ },
752
+ {
753
+ "selector": "linucb_alpha2.0",
754
+ "held_out_group": "wave2d",
755
+ "selected_policy": "hybrid_full",
756
+ "actual_best_policy": "hybrid_full",
757
+ "selected_target": 0.35113765448331835,
758
+ "oracle_target": 0.35113765448331835,
759
+ "regret": 0.0,
760
+ "correct": 1.0,
761
+ "num_policies": 3,
762
+ "probe_epochs": 50,
763
+ "total_epochs": 500,
764
+ "budget_ratio": 0.4,
765
+ "budget_savings": 0.6,
766
+ "fallback_used": false
767
+ }
768
+ ]
769
+ }
770
+ }
results/paper_a/burgers1d/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_a/burgers1d_lownu/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_a/burgers1d_verylow/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_a/heat1d/results.json ADDED
@@ -0,0 +1,3 @@
 
 
 
 
1
+ version https://git-lfs.github.com/spec/v1
2
+ oid sha256:438892e5825f9204c19cd96e506b0bc4802acb0ebc58fa3c4a7ea49ff1a95cb2
3
+ size 12363893
results/paper_a/holdout_validation/results.json ADDED
@@ -0,0 +1,702 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "experiment": "holdout_validation",
3
+ "window_size": 50,
4
+ "train_pdes": [
5
+ "heat1d",
6
+ "burgers1d",
7
+ "advdiff1d",
8
+ "kdv1d",
9
+ "allencahn1d",
10
+ "wave2d",
11
+ "burgers1d_lownu",
12
+ "advdiff1d_highpe",
13
+ "reaction_diffusion1d",
14
+ "reaction_diffusion1d_stiff"
15
+ ],
16
+ "test_pdes": [
17
+ "allencahn1d_sharp",
18
+ "burgers1d_verylow",
19
+ "navier_stokes2d"
20
+ ],
21
+ "part1_holdout_generalization": {
22
+ "pde_residual_norm": {
23
+ "n_train_pdes": 10,
24
+ "n_test_pdes": 3,
25
+ "n_train_samples": 360,
26
+ "n_test_samples": 90,
27
+ "train_pdes": [
28
+ "advdiff1d",
29
+ "advdiff1d_highpe",
30
+ "allencahn1d",
31
+ "burgers1d",
32
+ "burgers1d_lownu",
33
+ "heat1d",
34
+ "kdv1d",
35
+ "reaction_diffusion1d",
36
+ "reaction_diffusion1d_stiff",
37
+ "wave2d"
38
+ ],
39
+ "test_pdes": [
40
+ "allencahn1d_sharp",
41
+ "burgers1d_verylow",
42
+ "navier_stokes2d"
43
+ ],
44
+ "rf_accuracy": 0.6666666666666666,
45
+ "rf_mean_regret": 0.001819628197699785,
46
+ "physics_final_accuracy": 0.6666666666666666,
47
+ "physics_final_mean_regret": 0.001819628197699785,
48
+ "random_mean_regret": 0.029225271671182582,
49
+ "per_pde": [
50
+ {
51
+ "pde": "allencahn1d_sharp",
52
+ "n_samples": 30,
53
+ "n_policies": 3,
54
+ "policies": [
55
+ "hybrid_no_gate",
56
+ "hybrid_full",
57
+ "pinn_only"
58
+ ],
59
+ "actual_best_policy": "hybrid_full",
60
+ "oracle_target": 0.04590511210262775,
61
+ "rf_predicted_best": "hybrid_full",
62
+ "rf_selected_target": 0.04590511210262775,
63
+ "rf_regret": 0.0,
64
+ "rf_correct": true,
65
+ "physics_final_best": "hybrid_full",
66
+ "physics_final_target": 0.04590511210262775,
67
+ "physics_final_regret": 0.0,
68
+ "physics_final_correct": true,
69
+ "random_accuracy": 0.3333333333333333,
70
+ "random_expected_target": 0.0978225680689017,
71
+ "random_regret": 0.05191745596627395,
72
+ "actual_policy_means": {
73
+ "pinn_only": 0.1924288809299469,
74
+ "hybrid_no_gate": 0.05513371117413044,
75
+ "hybrid_full": 0.04590511210262775
76
+ }
77
+ },
78
+ {
79
+ "pde": "burgers1d_verylow",
80
+ "n_samples": 30,
81
+ "n_policies": 3,
82
+ "policies": [
83
+ "hybrid_no_gate",
84
+ "hybrid_full",
85
+ "pinn_only"
86
+ ],
87
+ "actual_best_policy": "hybrid_no_gate",
88
+ "oracle_target": 0.023859372083097696,
89
+ "rf_predicted_best": "hybrid_full",
90
+ "rf_selected_target": 0.02931825667619705,
91
+ "rf_regret": 0.005458884593099355,
92
+ "rf_correct": false,
93
+ "physics_final_best": "hybrid_full",
94
+ "physics_final_target": 0.02931825667619705,
95
+ "physics_final_regret": 0.005458884593099355,
96
+ "physics_final_correct": false,
97
+ "random_accuracy": 0.3333333333333333,
98
+ "random_expected_target": 0.056313403975218536,
99
+ "random_regret": 0.032454031892120844,
100
+ "actual_policy_means": {
101
+ "pinn_only": 0.11576258316636086,
102
+ "hybrid_no_gate": 0.023859372083097696,
103
+ "hybrid_full": 0.02931825667619705
104
+ }
105
+ },
106
+ {
107
+ "pde": "navier_stokes2d",
108
+ "n_samples": 30,
109
+ "n_policies": 3,
110
+ "policies": [
111
+ "hybrid_no_gate",
112
+ "hybrid_full",
113
+ "pinn_only"
114
+ ],
115
+ "actual_best_policy": "hybrid_full",
116
+ "oracle_target": 0.06746206581592559,
117
+ "rf_predicted_best": "hybrid_full",
118
+ "rf_selected_target": 0.06746206581592559,
119
+ "rf_regret": 0.0,
120
+ "rf_correct": true,
121
+ "physics_final_best": "hybrid_full",
122
+ "physics_final_target": 0.06746206581592559,
123
+ "physics_final_regret": 0.0,
124
+ "physics_final_correct": true,
125
+ "random_accuracy": 0.3333333333333333,
126
+ "random_expected_target": 0.07076639297107855,
127
+ "random_regret": 0.0033043271551529557,
128
+ "actual_policy_means": {
129
+ "pinn_only": 0.07310397885739803,
130
+ "hybrid_no_gate": 0.07173313423991204,
131
+ "hybrid_full": 0.06746206581592559
132
+ }
133
+ }
134
+ ]
135
+ },
136
+ "relative_l2_error": {
137
+ "n_train_pdes": 6,
138
+ "n_test_pdes": 2,
139
+ "n_train_samples": 220,
140
+ "n_test_samples": 60,
141
+ "train_pdes": [
142
+ "advdiff1d",
143
+ "advdiff1d_highpe",
144
+ "allencahn1d",
145
+ "heat1d",
146
+ "kdv1d",
147
+ "wave2d"
148
+ ],
149
+ "test_pdes": [
150
+ "allencahn1d_sharp",
151
+ "navier_stokes2d"
152
+ ],
153
+ "rf_accuracy": 1.0,
154
+ "rf_mean_regret": 0.0,
155
+ "physics_final_accuracy": 1.0,
156
+ "physics_final_mean_regret": 0.0,
157
+ "random_mean_regret": 0.0465408985192577,
158
+ "per_pde": [
159
+ {
160
+ "pde": "allencahn1d_sharp",
161
+ "n_samples": 30,
162
+ "n_policies": 3,
163
+ "policies": [
164
+ "hybrid_no_gate",
165
+ "hybrid_full",
166
+ "pinn_only"
167
+ ],
168
+ "actual_best_policy": "hybrid_full",
169
+ "oracle_target": 0.07737095616757869,
170
+ "rf_predicted_best": "hybrid_full",
171
+ "rf_selected_target": 0.07737095616757869,
172
+ "rf_regret": 0.0,
173
+ "rf_correct": true,
174
+ "physics_final_best": "hybrid_full",
175
+ "physics_final_target": 0.07737095616757869,
176
+ "physics_final_regret": 0.0,
177
+ "physics_final_correct": true,
178
+ "random_accuracy": 0.3333333333333333,
179
+ "random_expected_target": 0.16369764544069765,
180
+ "random_regret": 0.08632668927311896,
181
+ "actual_policy_means": {
182
+ "pinn_only": 0.32362509369850156,
183
+ "hybrid_no_gate": 0.09009688645601273,
184
+ "hybrid_full": 0.07737095616757869
185
+ }
186
+ },
187
+ {
188
+ "pde": "navier_stokes2d",
189
+ "n_samples": 30,
190
+ "n_policies": 3,
191
+ "policies": [
192
+ "hybrid_no_gate",
193
+ "hybrid_full",
194
+ "pinn_only"
195
+ ],
196
+ "actual_best_policy": "hybrid_full",
197
+ "oracle_target": 0.04342896416783333,
198
+ "rf_predicted_best": "hybrid_full",
199
+ "rf_selected_target": 0.04342896416783333,
200
+ "rf_regret": 0.0,
201
+ "rf_correct": true,
202
+ "physics_final_best": "hybrid_full",
203
+ "physics_final_target": 0.04342896416783333,
204
+ "physics_final_regret": 0.0,
205
+ "physics_final_correct": true,
206
+ "random_accuracy": 0.3333333333333333,
207
+ "random_expected_target": 0.05018407193322977,
208
+ "random_regret": 0.006755107765396437,
209
+ "actual_policy_means": {
210
+ "pinn_only": 0.05322579741477966,
211
+ "hybrid_no_gate": 0.0538974542170763,
212
+ "hybrid_full": 0.04342896416783333
213
+ }
214
+ }
215
+ ]
216
+ }
217
+ },
218
+ "part2_l2_feature_ablation": {
219
+ "residual": {
220
+ "metric": "pde_residual_norm",
221
+ "n_pdes": 13,
222
+ "n_samples": 450,
223
+ "full_rf_accuracy": 0.5384615384615384,
224
+ "ablation": {
225
+ "top-3": {
226
+ "k": 3,
227
+ "rf": 0.8461538461538461,
228
+ "physics_final": 0.6923076923076923,
229
+ "random": 0.2974358974358975,
230
+ "features_used": [
231
+ "physics_loss_min",
232
+ "physics_loss_final",
233
+ "bc_loss_std"
234
+ ]
235
+ },
236
+ "top-5": {
237
+ "k": 5,
238
+ "rf": 0.8461538461538461,
239
+ "physics_final": 0.6923076923076923,
240
+ "random": 0.2974358974358975,
241
+ "features_used": [
242
+ "physics_loss_min",
243
+ "physics_loss_final",
244
+ "bc_loss_std",
245
+ "physics_loss_std",
246
+ "physics_loss_slope"
247
+ ]
248
+ },
249
+ "top-10": {
250
+ "k": 10,
251
+ "rf": 0.6153846153846154,
252
+ "physics_final": 0.6923076923076923,
253
+ "random": 0.2974358974358975,
254
+ "features_used": [
255
+ "physics_loss_min",
256
+ "physics_loss_final",
257
+ "bc_loss_std",
258
+ "physics_loss_std",
259
+ "physics_loss_slope",
260
+ "physics_loss_initial",
261
+ "total_initial",
262
+ "bc_loss_slope",
263
+ "bc_loss_final",
264
+ "total_final"
265
+ ]
266
+ },
267
+ "top-20": {
268
+ "k": 20,
269
+ "rf": 0.5384615384615384,
270
+ "physics_final": 0.6923076923076923,
271
+ "random": 0.2974358974358975,
272
+ "features_used": [
273
+ "physics_loss_min",
274
+ "physics_loss_final",
275
+ "bc_loss_std",
276
+ "physics_loss_std",
277
+ "physics_loss_slope",
278
+ "physics_loss_initial",
279
+ "total_initial",
280
+ "bc_loss_slope",
281
+ "bc_loss_final",
282
+ "total_final"
283
+ ]
284
+ },
285
+ "all (38)": {
286
+ "k": 38,
287
+ "rf": 0.5384615384615384,
288
+ "physics_final": 0.6923076923076923,
289
+ "random": 0.2974358974358975,
290
+ "features_used": [
291
+ "physics_loss_min",
292
+ "physics_loss_final",
293
+ "bc_loss_std",
294
+ "physics_loss_std",
295
+ "physics_loss_slope",
296
+ "physics_loss_initial",
297
+ "total_initial",
298
+ "bc_loss_slope",
299
+ "bc_loss_final",
300
+ "total_final"
301
+ ]
302
+ }
303
+ },
304
+ "feature_ranking": [
305
+ [
306
+ "physics_loss_min",
307
+ 0.3623012555047965
308
+ ],
309
+ [
310
+ "physics_loss_final",
311
+ 0.33159566681309627
312
+ ],
313
+ [
314
+ "bc_loss_std",
315
+ 0.05063331929638993
316
+ ],
317
+ [
318
+ "physics_loss_std",
319
+ 0.02747991868435747
320
+ ],
321
+ [
322
+ "physics_loss_slope",
323
+ 0.026580226535040195
324
+ ],
325
+ [
326
+ "physics_loss_initial",
327
+ 0.020241320526920206
328
+ ],
329
+ [
330
+ "total_initial",
331
+ 0.02001709140360812
332
+ ],
333
+ [
334
+ "bc_loss_slope",
335
+ 0.018834257844603262
336
+ ],
337
+ [
338
+ "bc_loss_final",
339
+ 0.018285388225605364
340
+ ],
341
+ [
342
+ "total_final",
343
+ 0.016326180805806646
344
+ ],
345
+ [
346
+ "physics_loss_mean",
347
+ 0.014815368185680716
348
+ ],
349
+ [
350
+ "bc_loss_initial",
351
+ 0.014615685759944848
352
+ ],
353
+ [
354
+ "total_mean",
355
+ 0.01389767528136862
356
+ ],
357
+ [
358
+ "bc_loss_total_ratio_final",
359
+ 0.013187378435613444
360
+ ],
361
+ [
362
+ "physics_loss_data_loss_ratio_final",
363
+ 0.009477214840722866
364
+ ],
365
+ [
366
+ "total_slope",
367
+ 0.006345500721262421
368
+ ],
369
+ [
370
+ "total_std",
371
+ 0.006033857725854835
372
+ ],
373
+ [
374
+ "total_ratio",
375
+ 0.004897099204002061
376
+ ],
377
+ [
378
+ "physics_loss_ratio",
379
+ 0.004471167446524188
380
+ ],
381
+ [
382
+ "total_min",
383
+ 0.0037297244174898103
384
+ ],
385
+ [
386
+ "bc_loss_min",
387
+ 0.0034589363084648805
388
+ ],
389
+ [
390
+ "bc_loss_mean",
391
+ 0.003401367135643378
392
+ ],
393
+ [
394
+ "bc_loss_ratio",
395
+ 0.0020124285497619965
396
+ ],
397
+ [
398
+ "physics_loss_total_ratio_final",
399
+ 0.00181757608014534
400
+ ],
401
+ [
402
+ "data_loss_min",
403
+ 0.0012159032072611385
404
+ ],
405
+ [
406
+ "data_loss_mean",
407
+ 0.0007131651167296514
408
+ ],
409
+ [
410
+ "data_loss_slope",
411
+ 0.0006702616311346256
412
+ ],
413
+ [
414
+ "data_loss_std",
415
+ 0.0005446426916860314
416
+ ],
417
+ [
418
+ "data_loss_final",
419
+ 0.0005178710113609916
420
+ ],
421
+ [
422
+ "data_loss_initial",
423
+ 0.0005026486636808899
424
+ ],
425
+ [
426
+ "data_loss_ratio",
427
+ 0.0003466222831037818
428
+ ],
429
+ [
430
+ "lambda_physics_std",
431
+ 0.0002282075127743612
432
+ ],
433
+ [
434
+ "lambda_physics_slope",
435
+ 0.00021166359160170722
436
+ ],
437
+ [
438
+ "lambda_physics_mean",
439
+ 0.0001657760287639902
440
+ ],
441
+ [
442
+ "lambda_physics_final",
443
+ 0.00016493223507971284
444
+ ],
445
+ [
446
+ "lambda_physics_min",
447
+ 0.00013255777500960112
448
+ ],
449
+ [
450
+ "lambda_physics_initial",
451
+ 0.00013014251911010443
452
+ ],
453
+ [
454
+ "lambda_physics_ratio",
455
+ 0.0
456
+ ]
457
+ ],
458
+ "n_total_features": 38
459
+ },
460
+ "l2": {
461
+ "metric": "relative_l2_error",
462
+ "n_pdes": 8,
463
+ "n_samples": 280,
464
+ "full_rf_accuracy": 0.625,
465
+ "ablation": {
466
+ "top-3": {
467
+ "k": 3,
468
+ "rf": 0.5,
469
+ "physics_final": 0.625,
470
+ "random": 0.29583333333333334,
471
+ "features_used": [
472
+ "physics_loss_total_ratio_final",
473
+ "physics_loss_data_loss_ratio_final",
474
+ "data_loss_min"
475
+ ]
476
+ },
477
+ "top-5": {
478
+ "k": 5,
479
+ "rf": 0.625,
480
+ "physics_final": 0.625,
481
+ "random": 0.29583333333333334,
482
+ "features_used": [
483
+ "physics_loss_total_ratio_final",
484
+ "physics_loss_data_loss_ratio_final",
485
+ "data_loss_min",
486
+ "total_min",
487
+ "data_loss_mean"
488
+ ]
489
+ },
490
+ "top-10": {
491
+ "k": 10,
492
+ "rf": 0.625,
493
+ "physics_final": 0.625,
494
+ "random": 0.29583333333333334,
495
+ "features_used": [
496
+ "physics_loss_total_ratio_final",
497
+ "physics_loss_data_loss_ratio_final",
498
+ "data_loss_min",
499
+ "total_min",
500
+ "data_loss_mean",
501
+ "data_loss_initial",
502
+ "total_mean",
503
+ "bc_loss_min",
504
+ "total_initial",
505
+ "bc_loss_final"
506
+ ]
507
+ },
508
+ "top-20": {
509
+ "k": 20,
510
+ "rf": 0.625,
511
+ "physics_final": 0.625,
512
+ "random": 0.29583333333333334,
513
+ "features_used": [
514
+ "physics_loss_total_ratio_final",
515
+ "physics_loss_data_loss_ratio_final",
516
+ "data_loss_min",
517
+ "total_min",
518
+ "data_loss_mean",
519
+ "data_loss_initial",
520
+ "total_mean",
521
+ "bc_loss_min",
522
+ "total_initial",
523
+ "bc_loss_final"
524
+ ]
525
+ },
526
+ "all (38)": {
527
+ "k": 38,
528
+ "rf": 0.625,
529
+ "physics_final": 0.625,
530
+ "random": 0.29583333333333334,
531
+ "features_used": [
532
+ "physics_loss_total_ratio_final",
533
+ "physics_loss_data_loss_ratio_final",
534
+ "data_loss_min",
535
+ "total_min",
536
+ "data_loss_mean",
537
+ "data_loss_initial",
538
+ "total_mean",
539
+ "bc_loss_min",
540
+ "total_initial",
541
+ "bc_loss_final"
542
+ ]
543
+ }
544
+ },
545
+ "feature_ranking": [
546
+ [
547
+ "physics_loss_total_ratio_final",
548
+ 0.46307502912899595
549
+ ],
550
+ [
551
+ "physics_loss_data_loss_ratio_final",
552
+ 0.21859438971778222
553
+ ],
554
+ [
555
+ "data_loss_min",
556
+ 0.07512897680713243
557
+ ],
558
+ [
559
+ "total_min",
560
+ 0.06978056857872457
561
+ ],
562
+ [
563
+ "data_loss_mean",
564
+ 0.049577625560856785
565
+ ],
566
+ [
567
+ "data_loss_initial",
568
+ 0.017668074363382216
569
+ ],
570
+ [
571
+ "total_mean",
572
+ 0.016484834855444566
573
+ ],
574
+ [
575
+ "bc_loss_min",
576
+ 0.012895396054234206
577
+ ],
578
+ [
579
+ "total_initial",
580
+ 0.011884998124870936
581
+ ],
582
+ [
583
+ "bc_loss_final",
584
+ 0.010074951449517484
585
+ ],
586
+ [
587
+ "total_final",
588
+ 0.009563021577642803
589
+ ],
590
+ [
591
+ "bc_loss_initial",
592
+ 0.0077863227988129915
593
+ ],
594
+ [
595
+ "data_loss_final",
596
+ 0.007150614652495824
597
+ ],
598
+ [
599
+ "bc_loss_mean",
600
+ 0.005738841920714108
601
+ ],
602
+ [
603
+ "physics_loss_min",
604
+ 0.00417219610162485
605
+ ],
606
+ [
607
+ "physics_loss_final",
608
+ 0.003431928163884786
609
+ ],
610
+ [
611
+ "physics_loss_mean",
612
+ 0.0031030097562497173
613
+ ],
614
+ [
615
+ "physics_loss_initial",
616
+ 0.0023604019548904088
617
+ ],
618
+ [
619
+ "bc_loss_total_ratio_final",
620
+ 0.0023569667681061024
621
+ ],
622
+ [
623
+ "physics_loss_ratio",
624
+ 0.0020724597562313683
625
+ ],
626
+ [
627
+ "total_std",
628
+ 0.0013371056474261317
629
+ ],
630
+ [
631
+ "bc_loss_std",
632
+ 0.001170519112332939
633
+ ],
634
+ [
635
+ "physics_loss_std",
636
+ 0.0011013896327805596
637
+ ],
638
+ [
639
+ "data_loss_std",
640
+ 0.0007393697636941699
641
+ ],
642
+ [
643
+ "bc_loss_ratio",
644
+ 0.0006660261091597417
645
+ ],
646
+ [
647
+ "data_loss_slope",
648
+ 0.0004738666160729259
649
+ ],
650
+ [
651
+ "total_slope",
652
+ 0.0004287855836827564
653
+ ],
654
+ [
655
+ "physics_loss_slope",
656
+ 0.0004248234625378218
657
+ ],
658
+ [
659
+ "total_ratio",
660
+ 0.0002551663725321127
661
+ ],
662
+ [
663
+ "data_loss_ratio",
664
+ 0.0002535710829956696
665
+ ],
666
+ [
667
+ "bc_loss_slope",
668
+ 0.0002482194524354902
669
+ ],
670
+ [
671
+ "lambda_physics_initial",
672
+ 2.636326820555117e-07
673
+ ],
674
+ [
675
+ "lambda_physics_slope",
676
+ 1.0549733722757491e-07
677
+ ],
678
+ [
679
+ "lambda_physics_mean",
680
+ 9.200182765946776e-08
681
+ ],
682
+ [
683
+ "lambda_physics_std",
684
+ 3.985147798887366e-08
685
+ ],
686
+ [
687
+ "lambda_physics_final",
688
+ 2.7716915067622034e-08
689
+ ],
690
+ [
691
+ "lambda_physics_min",
692
+ 2.0372515332048705e-08
693
+ ],
694
+ [
695
+ "lambda_physics_ratio",
696
+ 0.0
697
+ ]
698
+ ],
699
+ "n_total_features": 38
700
+ }
701
+ }
702
+ }
results/paper_a/kdv1d/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_a/meta_router_evaluation/results.json ADDED
@@ -0,0 +1,1253 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "experiment": "meta_router_evaluation",
3
+ "target_metric": "pde_residual_norm",
4
+ "window_size": 50,
5
+ "n_samples": 450,
6
+ "n_pdes": 13,
7
+ "pdes": [
8
+ "advdiff1d",
9
+ "advdiff1d_highpe",
10
+ "allencahn1d",
11
+ "allencahn1d_sharp",
12
+ "burgers1d",
13
+ "burgers1d_lownu",
14
+ "burgers1d_verylow",
15
+ "heat1d",
16
+ "kdv1d",
17
+ "navier_stokes2d",
18
+ "reaction_diffusion1d",
19
+ "reaction_diffusion1d_stiff",
20
+ "wave2d"
21
+ ],
22
+ "results": {
23
+ "MetaRouter": {
24
+ "accuracy": 0.46153846153846156,
25
+ "mean_regret": 0.5625658956074548,
26
+ "n_folds": 13
27
+ },
28
+ "MetaRouter-full": {
29
+ "accuracy": 0.3076923076923077,
30
+ "mean_regret": 0.5691396832678329,
31
+ "n_folds": 13
32
+ },
33
+ "GBR+PDE": {
34
+ "accuracy": 0.8461538461538461,
35
+ "mean_regret": 0.03969063347551661,
36
+ "n_folds": 13
37
+ },
38
+ "GBR+PDE-all": {
39
+ "accuracy": 0.6153846153846154,
40
+ "mean_regret": 0.20517151767694322,
41
+ "n_folds": 13
42
+ },
43
+ "RF+PDE": {
44
+ "accuracy": 0.6153846153846154,
45
+ "mean_regret": 0.19254935969008685,
46
+ "n_folds": 13
47
+ },
48
+ "RF+PDE-top5": {
49
+ "accuracy": 0.8461538461538461,
50
+ "mean_regret": 0.03969063347551661,
51
+ "n_folds": 13
52
+ },
53
+ "RF": {
54
+ "accuracy": 0.5384615384615384,
55
+ "mean_regret": 0.2076880548309419,
56
+ "n_folds": 13
57
+ },
58
+ "RF-top3": {
59
+ "accuracy": 0.6153846153846154,
60
+ "mean_regret": 0.09405681615213303,
61
+ "n_folds": 13
62
+ },
63
+ "physics_final": {
64
+ "accuracy": 0.6923076923076923,
65
+ "mean_regret": 0.06928714987159462,
66
+ "n_folds": 13
67
+ },
68
+ "random": {
69
+ "accuracy": 0.2974358974358975,
70
+ "mean_regret": 1.0081220969383358,
71
+ "n_folds": 13
72
+ }
73
+ },
74
+ "fold_details": {
75
+ "MetaRouter": [
76
+ {
77
+ "held_out": "advdiff1d",
78
+ "oracle_policy": "hybrid_no_gate",
79
+ "oracle_val": 0.012432838091626763,
80
+ "predicted_policy": "hybrid_full",
81
+ "selected_val": 0.01605730839073658,
82
+ "correct": false,
83
+ "regret": 0.291523968413199
84
+ },
85
+ {
86
+ "held_out": "advdiff1d_highpe",
87
+ "oracle_policy": "pinn_only",
88
+ "oracle_val": 0.04680136069655418,
89
+ "predicted_policy": "pinn_only",
90
+ "selected_val": 0.04680136069655418,
91
+ "correct": true,
92
+ "regret": 0.0
93
+ },
94
+ {
95
+ "held_out": "allencahn1d",
96
+ "oracle_policy": "hybrid_full",
97
+ "oracle_val": 0.02884605899453163,
98
+ "predicted_policy": "hybrid_full",
99
+ "selected_val": 0.02884605899453163,
100
+ "correct": true,
101
+ "regret": 0.0
102
+ },
103
+ {
104
+ "held_out": "allencahn1d_sharp",
105
+ "oracle_policy": "hybrid_full",
106
+ "oracle_val": 0.04590511210262775,
107
+ "predicted_policy": "hybrid_no_gate",
108
+ "selected_val": 0.05513371117413044,
109
+ "correct": false,
110
+ "regret": 0.2010364129134632
111
+ },
112
+ {
113
+ "held_out": "burgers1d",
114
+ "oracle_policy": "hybrid_full",
115
+ "oracle_val": 0.0796903658658266,
116
+ "predicted_policy": "hybrid_full",
117
+ "selected_val": 0.0796903658658266,
118
+ "correct": true,
119
+ "regret": 0.0
120
+ },
121
+ {
122
+ "held_out": "burgers1d_lownu",
123
+ "oracle_policy": "hybrid_no_gate",
124
+ "oracle_val": 0.18069636225700378,
125
+ "predicted_policy": "hybrid_full_lambda0.1",
126
+ "selected_val": 0.2907987028360367,
127
+ "correct": false,
128
+ "regret": 0.6093223969967628
129
+ },
130
+ {
131
+ "held_out": "burgers1d_verylow",
132
+ "oracle_policy": "hybrid_no_gate",
133
+ "oracle_val": 0.023859372083097696,
134
+ "predicted_policy": "pinn_only",
135
+ "selected_val": 0.11576258316636086,
136
+ "correct": false,
137
+ "regret": 3.8518704835643454
138
+ },
139
+ {
140
+ "held_out": "heat1d",
141
+ "oracle_policy": "hybrid_full",
142
+ "oracle_val": 0.010440931282937526,
143
+ "predicted_policy": "hybrid_no_gate",
144
+ "selected_val": 0.01985112838447094,
145
+ "correct": false,
146
+ "regret": 0.901279478480188
147
+ },
148
+ {
149
+ "held_out": "kdv1d",
150
+ "oracle_policy": "hybrid_no_gate",
151
+ "oracle_val": 0.008130461303517222,
152
+ "predicted_policy": "hybrid_no_gate",
153
+ "selected_val": 0.008130461303517222,
154
+ "correct": true,
155
+ "regret": 0.0
156
+ },
157
+ {
158
+ "held_out": "navier_stokes2d",
159
+ "oracle_policy": "hybrid_full",
160
+ "oracle_val": 0.06746206581592559,
161
+ "predicted_policy": "hybrid_full",
162
+ "selected_val": 0.06746206581592559,
163
+ "correct": true,
164
+ "regret": 0.0
165
+ },
166
+ {
167
+ "held_out": "reaction_diffusion1d",
168
+ "oracle_policy": "hybrid_full",
169
+ "oracle_val": 0.022279974073171616,
170
+ "predicted_policy": "hybrid_full",
171
+ "selected_val": 0.022279974073171616,
172
+ "correct": true,
173
+ "regret": 0.0
174
+ },
175
+ {
176
+ "held_out": "reaction_diffusion1d_stiff",
177
+ "oracle_policy": "hybrid_full",
178
+ "oracle_val": 0.04314509090036154,
179
+ "predicted_policy": "hybrid_no_gate",
180
+ "selected_val": 0.055535674653947355,
181
+ "correct": false,
182
+ "regret": 0.28718409197932615
183
+ },
184
+ {
185
+ "held_out": "wave2d",
186
+ "oracle_policy": "pinn_only",
187
+ "oracle_val": 0.028174721263349058,
188
+ "predicted_policy": "hybrid_no_gate",
189
+ "selected_val": 0.06117125898599625,
190
+ "correct": false,
191
+ "regret": 1.171139810549628
192
+ }
193
+ ],
194
+ "MetaRouter-full": [
195
+ {
196
+ "held_out": "advdiff1d",
197
+ "oracle_policy": "hybrid_no_gate",
198
+ "oracle_val": 0.012432838091626763,
199
+ "predicted_policy": "hybrid_full",
200
+ "selected_val": 0.01605730839073658,
201
+ "correct": false,
202
+ "regret": 0.291523968413199
203
+ },
204
+ {
205
+ "held_out": "advdiff1d_highpe",
206
+ "oracle_policy": "pinn_only",
207
+ "oracle_val": 0.04680136069655418,
208
+ "predicted_policy": "hybrid_full",
209
+ "selected_val": 0.054425609111785886,
210
+ "correct": false,
211
+ "regret": 0.16290655446248703
212
+ },
213
+ {
214
+ "held_out": "allencahn1d",
215
+ "oracle_policy": "hybrid_full",
216
+ "oracle_val": 0.02884605899453163,
217
+ "predicted_policy": "hybrid_no_gate",
218
+ "selected_val": 0.04240037016570568,
219
+ "correct": false,
220
+ "regret": 0.4698843323361277
221
+ },
222
+ {
223
+ "held_out": "allencahn1d_sharp",
224
+ "oracle_policy": "hybrid_full",
225
+ "oracle_val": 0.04590511210262775,
226
+ "predicted_policy": "hybrid_full",
227
+ "selected_val": 0.04590511210262775,
228
+ "correct": true,
229
+ "regret": 0.0
230
+ },
231
+ {
232
+ "held_out": "burgers1d",
233
+ "oracle_policy": "hybrid_full",
234
+ "oracle_val": 0.0796903658658266,
235
+ "predicted_policy": "hybrid_full_lambda0.1",
236
+ "selected_val": 0.17034928128123283,
237
+ "correct": false,
238
+ "regret": 1.1376395933235794
239
+ },
240
+ {
241
+ "held_out": "burgers1d_lownu",
242
+ "oracle_policy": "hybrid_no_gate",
243
+ "oracle_val": 0.18069636225700378,
244
+ "predicted_policy": "hybrid_no_gate",
245
+ "selected_val": 0.18069636225700378,
246
+ "correct": true,
247
+ "regret": 0.0
248
+ },
249
+ {
250
+ "held_out": "burgers1d_verylow",
251
+ "oracle_policy": "hybrid_no_gate",
252
+ "oracle_val": 0.023859372083097696,
253
+ "predicted_policy": "pinn_only",
254
+ "selected_val": 0.11576258316636086,
255
+ "correct": false,
256
+ "regret": 3.8518704835643454
257
+ },
258
+ {
259
+ "held_out": "heat1d",
260
+ "oracle_policy": "hybrid_full",
261
+ "oracle_val": 0.010440931282937526,
262
+ "predicted_policy": "hybrid_no_gate",
263
+ "selected_val": 0.01985112838447094,
264
+ "correct": false,
265
+ "regret": 0.901279478480188
266
+ },
267
+ {
268
+ "held_out": "kdv1d",
269
+ "oracle_policy": "hybrid_no_gate",
270
+ "oracle_val": 0.008130461303517222,
271
+ "predicted_policy": "hybrid_no_gate",
272
+ "selected_val": 0.008130461303517222,
273
+ "correct": true,
274
+ "regret": 0.0
275
+ },
276
+ {
277
+ "held_out": "navier_stokes2d",
278
+ "oracle_policy": "hybrid_full",
279
+ "oracle_val": 0.06746206581592559,
280
+ "predicted_policy": "pinn_only",
281
+ "selected_val": 0.07310397885739803,
282
+ "correct": false,
283
+ "regret": 0.08363089646360286
284
+ },
285
+ {
286
+ "held_out": "reaction_diffusion1d",
287
+ "oracle_policy": "hybrid_full",
288
+ "oracle_val": 0.022279974073171616,
289
+ "predicted_policy": "hybrid_no_gate",
290
+ "selected_val": 0.02702330220490694,
291
+ "correct": false,
292
+ "regret": 0.21289648345897288
293
+ },
294
+ {
295
+ "held_out": "reaction_diffusion1d_stiff",
296
+ "oracle_policy": "hybrid_full",
297
+ "oracle_val": 0.04314509090036154,
298
+ "predicted_policy": "hybrid_no_gate",
299
+ "selected_val": 0.055535674653947355,
300
+ "correct": false,
301
+ "regret": 0.28718409197932615
302
+ },
303
+ {
304
+ "held_out": "wave2d",
305
+ "oracle_policy": "pinn_only",
306
+ "oracle_val": 0.028174721263349058,
307
+ "predicted_policy": "pinn_only",
308
+ "selected_val": 0.028174721263349058,
309
+ "correct": true,
310
+ "regret": 0.0
311
+ }
312
+ ],
313
+ "GBR+PDE": [
314
+ {
315
+ "held_out": "advdiff1d",
316
+ "oracle_policy": "hybrid_no_gate",
317
+ "oracle_val": 0.012432838091626763,
318
+ "predicted_policy": "hybrid_no_gate",
319
+ "selected_val": 0.012432838091626763,
320
+ "correct": true,
321
+ "regret": 0.0
322
+ },
323
+ {
324
+ "held_out": "advdiff1d_highpe",
325
+ "oracle_policy": "pinn_only",
326
+ "oracle_val": 0.04680136069655418,
327
+ "predicted_policy": "pinn_only",
328
+ "selected_val": 0.04680136069655418,
329
+ "correct": true,
330
+ "regret": 0.0
331
+ },
332
+ {
333
+ "held_out": "allencahn1d",
334
+ "oracle_policy": "hybrid_full",
335
+ "oracle_val": 0.02884605899453163,
336
+ "predicted_policy": "hybrid_full",
337
+ "selected_val": 0.02884605899453163,
338
+ "correct": true,
339
+ "regret": 0.0
340
+ },
341
+ {
342
+ "held_out": "allencahn1d_sharp",
343
+ "oracle_policy": "hybrid_full",
344
+ "oracle_val": 0.04590511210262775,
345
+ "predicted_policy": "hybrid_full",
346
+ "selected_val": 0.04590511210262775,
347
+ "correct": true,
348
+ "regret": 0.0
349
+ },
350
+ {
351
+ "held_out": "burgers1d",
352
+ "oracle_policy": "hybrid_full",
353
+ "oracle_val": 0.0796903658658266,
354
+ "predicted_policy": "hybrid_full",
355
+ "selected_val": 0.0796903658658266,
356
+ "correct": true,
357
+ "regret": 0.0
358
+ },
359
+ {
360
+ "held_out": "burgers1d_lownu",
361
+ "oracle_policy": "hybrid_no_gate",
362
+ "oracle_val": 0.18069636225700378,
363
+ "predicted_policy": "hybrid_no_gate",
364
+ "selected_val": 0.18069636225700378,
365
+ "correct": true,
366
+ "regret": 0.0
367
+ },
368
+ {
369
+ "held_out": "burgers1d_verylow",
370
+ "oracle_policy": "hybrid_no_gate",
371
+ "oracle_val": 0.023859372083097696,
372
+ "predicted_policy": "hybrid_full",
373
+ "selected_val": 0.02931825667619705,
374
+ "correct": false,
375
+ "regret": 0.22879414320238978
376
+ },
377
+ {
378
+ "held_out": "heat1d",
379
+ "oracle_policy": "hybrid_full",
380
+ "oracle_val": 0.010440931282937526,
381
+ "predicted_policy": "hybrid_full",
382
+ "selected_val": 0.010440931282937526,
383
+ "correct": true,
384
+ "regret": 0.0
385
+ },
386
+ {
387
+ "held_out": "kdv1d",
388
+ "oracle_policy": "hybrid_no_gate",
389
+ "oracle_val": 0.008130461303517222,
390
+ "predicted_policy": "hybrid_no_gate",
391
+ "selected_val": 0.008130461303517222,
392
+ "correct": true,
393
+ "regret": 0.0
394
+ },
395
+ {
396
+ "held_out": "navier_stokes2d",
397
+ "oracle_policy": "hybrid_full",
398
+ "oracle_val": 0.06746206581592559,
399
+ "predicted_policy": "hybrid_full",
400
+ "selected_val": 0.06746206581592559,
401
+ "correct": true,
402
+ "regret": 0.0
403
+ },
404
+ {
405
+ "held_out": "reaction_diffusion1d",
406
+ "oracle_policy": "hybrid_full",
407
+ "oracle_val": 0.022279974073171616,
408
+ "predicted_policy": "hybrid_full",
409
+ "selected_val": 0.022279974073171616,
410
+ "correct": true,
411
+ "regret": 0.0
412
+ },
413
+ {
414
+ "held_out": "reaction_diffusion1d_stiff",
415
+ "oracle_policy": "hybrid_full",
416
+ "oracle_val": 0.04314509090036154,
417
+ "predicted_policy": "hybrid_no_gate",
418
+ "selected_val": 0.055535674653947355,
419
+ "correct": false,
420
+ "regret": 0.28718409197932615
421
+ },
422
+ {
423
+ "held_out": "wave2d",
424
+ "oracle_policy": "pinn_only",
425
+ "oracle_val": 0.028174721263349058,
426
+ "predicted_policy": "pinn_only",
427
+ "selected_val": 0.028174721263349058,
428
+ "correct": true,
429
+ "regret": 0.0
430
+ }
431
+ ],
432
+ "GBR+PDE-all": [
433
+ {
434
+ "held_out": "advdiff1d",
435
+ "oracle_policy": "hybrid_no_gate",
436
+ "oracle_val": 0.012432838091626763,
437
+ "predicted_policy": "hybrid_no_gate",
438
+ "selected_val": 0.012432838091626763,
439
+ "correct": true,
440
+ "regret": 0.0
441
+ },
442
+ {
443
+ "held_out": "advdiff1d_highpe",
444
+ "oracle_policy": "pinn_only",
445
+ "oracle_val": 0.04680136069655418,
446
+ "predicted_policy": "hybrid_full",
447
+ "selected_val": 0.054425609111785886,
448
+ "correct": false,
449
+ "regret": 0.16290655446248703
450
+ },
451
+ {
452
+ "held_out": "allencahn1d",
453
+ "oracle_policy": "hybrid_full",
454
+ "oracle_val": 0.02884605899453163,
455
+ "predicted_policy": "hybrid_full",
456
+ "selected_val": 0.02884605899453163,
457
+ "correct": true,
458
+ "regret": 0.0
459
+ },
460
+ {
461
+ "held_out": "allencahn1d_sharp",
462
+ "oracle_policy": "hybrid_full",
463
+ "oracle_val": 0.04590511210262775,
464
+ "predicted_policy": "hybrid_full",
465
+ "selected_val": 0.04590511210262775,
466
+ "correct": true,
467
+ "regret": 0.0
468
+ },
469
+ {
470
+ "held_out": "burgers1d",
471
+ "oracle_policy": "hybrid_full",
472
+ "oracle_val": 0.0796903658658266,
473
+ "predicted_policy": "hybrid_full",
474
+ "selected_val": 0.0796903658658266,
475
+ "correct": true,
476
+ "regret": 0.0
477
+ },
478
+ {
479
+ "held_out": "burgers1d_lownu",
480
+ "oracle_policy": "hybrid_no_gate",
481
+ "oracle_val": 0.18069636225700378,
482
+ "predicted_policy": "hybrid_no_gate",
483
+ "selected_val": 0.18069636225700378,
484
+ "correct": true,
485
+ "regret": 0.0
486
+ },
487
+ {
488
+ "held_out": "burgers1d_verylow",
489
+ "oracle_policy": "hybrid_no_gate",
490
+ "oracle_val": 0.023859372083097696,
491
+ "predicted_policy": "hybrid_full",
492
+ "selected_val": 0.02931825667619705,
493
+ "correct": false,
494
+ "regret": 0.22879414320238978
495
+ },
496
+ {
497
+ "held_out": "heat1d",
498
+ "oracle_policy": "hybrid_full",
499
+ "oracle_val": 0.010440931282937526,
500
+ "predicted_policy": "hybrid_full",
501
+ "selected_val": 0.010440931282937526,
502
+ "correct": true,
503
+ "regret": 0.0
504
+ },
505
+ {
506
+ "held_out": "kdv1d",
507
+ "oracle_policy": "hybrid_no_gate",
508
+ "oracle_val": 0.008130461303517222,
509
+ "predicted_policy": "hybrid_full",
510
+ "selected_val": 0.013440604414790868,
511
+ "correct": false,
512
+ "regret": 0.6531170757772979
513
+ },
514
+ {
515
+ "held_out": "navier_stokes2d",
516
+ "oracle_policy": "hybrid_full",
517
+ "oracle_val": 0.06746206581592559,
518
+ "predicted_policy": "hybrid_full",
519
+ "selected_val": 0.06746206581592559,
520
+ "correct": true,
521
+ "regret": 0.0
522
+ },
523
+ {
524
+ "held_out": "reaction_diffusion1d",
525
+ "oracle_policy": "hybrid_full",
526
+ "oracle_val": 0.022279974073171616,
527
+ "predicted_policy": "hybrid_full",
528
+ "selected_val": 0.022279974073171616,
529
+ "correct": true,
530
+ "regret": 0.0
531
+ },
532
+ {
533
+ "held_out": "reaction_diffusion1d_stiff",
534
+ "oracle_policy": "hybrid_full",
535
+ "oracle_val": 0.04314509090036154,
536
+ "predicted_policy": "hybrid_no_gate",
537
+ "selected_val": 0.055535674653947355,
538
+ "correct": false,
539
+ "regret": 0.28718409197932615
540
+ },
541
+ {
542
+ "held_out": "wave2d",
543
+ "oracle_policy": "pinn_only",
544
+ "oracle_val": 0.028174721263349058,
545
+ "predicted_policy": "hybrid_full",
546
+ "selected_val": 0.06579439416527748,
547
+ "correct": false,
548
+ "regret": 1.3352278643787607
549
+ }
550
+ ],
551
+ "RF+PDE": [
552
+ {
553
+ "held_out": "advdiff1d",
554
+ "oracle_policy": "hybrid_no_gate",
555
+ "oracle_val": 0.012432838091626763,
556
+ "predicted_policy": "hybrid_no_gate",
557
+ "selected_val": 0.012432838091626763,
558
+ "correct": true,
559
+ "regret": 0.0
560
+ },
561
+ {
562
+ "held_out": "advdiff1d_highpe",
563
+ "oracle_policy": "pinn_only",
564
+ "oracle_val": 0.04680136069655418,
565
+ "predicted_policy": "hybrid_full",
566
+ "selected_val": 0.054425609111785886,
567
+ "correct": false,
568
+ "regret": 0.16290655446248703
569
+ },
570
+ {
571
+ "held_out": "allencahn1d",
572
+ "oracle_policy": "hybrid_full",
573
+ "oracle_val": 0.02884605899453163,
574
+ "predicted_policy": "hybrid_full",
575
+ "selected_val": 0.02884605899453163,
576
+ "correct": true,
577
+ "regret": 0.0
578
+ },
579
+ {
580
+ "held_out": "allencahn1d_sharp",
581
+ "oracle_policy": "hybrid_full",
582
+ "oracle_val": 0.04590511210262775,
583
+ "predicted_policy": "hybrid_full",
584
+ "selected_val": 0.04590511210262775,
585
+ "correct": true,
586
+ "regret": 0.0
587
+ },
588
+ {
589
+ "held_out": "burgers1d",
590
+ "oracle_policy": "hybrid_full",
591
+ "oracle_val": 0.0796903658658266,
592
+ "predicted_policy": "hybrid_full",
593
+ "selected_val": 0.0796903658658266,
594
+ "correct": true,
595
+ "regret": 0.0
596
+ },
597
+ {
598
+ "held_out": "burgers1d_lownu",
599
+ "oracle_policy": "hybrid_no_gate",
600
+ "oracle_val": 0.18069636225700378,
601
+ "predicted_policy": "hybrid_no_gate",
602
+ "selected_val": 0.18069636225700378,
603
+ "correct": true,
604
+ "regret": 0.0
605
+ },
606
+ {
607
+ "held_out": "burgers1d_verylow",
608
+ "oracle_policy": "hybrid_no_gate",
609
+ "oracle_val": 0.023859372083097696,
610
+ "predicted_policy": "hybrid_full",
611
+ "selected_val": 0.02931825667619705,
612
+ "correct": false,
613
+ "regret": 0.22879414320238978
614
+ },
615
+ {
616
+ "held_out": "heat1d",
617
+ "oracle_policy": "hybrid_full",
618
+ "oracle_val": 0.010440931282937526,
619
+ "predicted_policy": "hybrid_full",
620
+ "selected_val": 0.010440931282937526,
621
+ "correct": true,
622
+ "regret": 0.0
623
+ },
624
+ {
625
+ "held_out": "kdv1d",
626
+ "oracle_policy": "hybrid_no_gate",
627
+ "oracle_val": 0.008130461303517222,
628
+ "predicted_policy": "hybrid_full",
629
+ "selected_val": 0.013440604414790868,
630
+ "correct": false,
631
+ "regret": 0.6531170757772979
632
+ },
633
+ {
634
+ "held_out": "navier_stokes2d",
635
+ "oracle_policy": "hybrid_full",
636
+ "oracle_val": 0.06746206581592559,
637
+ "predicted_policy": "hybrid_full",
638
+ "selected_val": 0.06746206581592559,
639
+ "correct": true,
640
+ "regret": 0.0
641
+ },
642
+ {
643
+ "held_out": "reaction_diffusion1d",
644
+ "oracle_policy": "hybrid_full",
645
+ "oracle_val": 0.022279974073171616,
646
+ "predicted_policy": "hybrid_full",
647
+ "selected_val": 0.022279974073171616,
648
+ "correct": true,
649
+ "regret": 0.0
650
+ },
651
+ {
652
+ "held_out": "reaction_diffusion1d_stiff",
653
+ "oracle_policy": "hybrid_full",
654
+ "oracle_val": 0.04314509090036154,
655
+ "predicted_policy": "hybrid_no_gate",
656
+ "selected_val": 0.055535674653947355,
657
+ "correct": false,
658
+ "regret": 0.28718409197932615
659
+ },
660
+ {
661
+ "held_out": "wave2d",
662
+ "oracle_policy": "pinn_only",
663
+ "oracle_val": 0.028174721263349058,
664
+ "predicted_policy": "hybrid_no_gate",
665
+ "selected_val": 0.06117125898599625,
666
+ "correct": false,
667
+ "regret": 1.171139810549628
668
+ }
669
+ ],
670
+ "RF+PDE-top5": [
671
+ {
672
+ "held_out": "advdiff1d",
673
+ "oracle_policy": "hybrid_no_gate",
674
+ "oracle_val": 0.012432838091626763,
675
+ "predicted_policy": "hybrid_no_gate",
676
+ "selected_val": 0.012432838091626763,
677
+ "correct": true,
678
+ "regret": 0.0
679
+ },
680
+ {
681
+ "held_out": "advdiff1d_highpe",
682
+ "oracle_policy": "pinn_only",
683
+ "oracle_val": 0.04680136069655418,
684
+ "predicted_policy": "pinn_only",
685
+ "selected_val": 0.04680136069655418,
686
+ "correct": true,
687
+ "regret": 0.0
688
+ },
689
+ {
690
+ "held_out": "allencahn1d",
691
+ "oracle_policy": "hybrid_full",
692
+ "oracle_val": 0.02884605899453163,
693
+ "predicted_policy": "hybrid_full",
694
+ "selected_val": 0.02884605899453163,
695
+ "correct": true,
696
+ "regret": 0.0
697
+ },
698
+ {
699
+ "held_out": "allencahn1d_sharp",
700
+ "oracle_policy": "hybrid_full",
701
+ "oracle_val": 0.04590511210262775,
702
+ "predicted_policy": "hybrid_full",
703
+ "selected_val": 0.04590511210262775,
704
+ "correct": true,
705
+ "regret": 0.0
706
+ },
707
+ {
708
+ "held_out": "burgers1d",
709
+ "oracle_policy": "hybrid_full",
710
+ "oracle_val": 0.0796903658658266,
711
+ "predicted_policy": "hybrid_full",
712
+ "selected_val": 0.0796903658658266,
713
+ "correct": true,
714
+ "regret": 0.0
715
+ },
716
+ {
717
+ "held_out": "burgers1d_lownu",
718
+ "oracle_policy": "hybrid_no_gate",
719
+ "oracle_val": 0.18069636225700378,
720
+ "predicted_policy": "hybrid_no_gate",
721
+ "selected_val": 0.18069636225700378,
722
+ "correct": true,
723
+ "regret": 0.0
724
+ },
725
+ {
726
+ "held_out": "burgers1d_verylow",
727
+ "oracle_policy": "hybrid_no_gate",
728
+ "oracle_val": 0.023859372083097696,
729
+ "predicted_policy": "hybrid_full",
730
+ "selected_val": 0.02931825667619705,
731
+ "correct": false,
732
+ "regret": 0.22879414320238978
733
+ },
734
+ {
735
+ "held_out": "heat1d",
736
+ "oracle_policy": "hybrid_full",
737
+ "oracle_val": 0.010440931282937526,
738
+ "predicted_policy": "hybrid_full",
739
+ "selected_val": 0.010440931282937526,
740
+ "correct": true,
741
+ "regret": 0.0
742
+ },
743
+ {
744
+ "held_out": "kdv1d",
745
+ "oracle_policy": "hybrid_no_gate",
746
+ "oracle_val": 0.008130461303517222,
747
+ "predicted_policy": "hybrid_no_gate",
748
+ "selected_val": 0.008130461303517222,
749
+ "correct": true,
750
+ "regret": 0.0
751
+ },
752
+ {
753
+ "held_out": "navier_stokes2d",
754
+ "oracle_policy": "hybrid_full",
755
+ "oracle_val": 0.06746206581592559,
756
+ "predicted_policy": "hybrid_full",
757
+ "selected_val": 0.06746206581592559,
758
+ "correct": true,
759
+ "regret": 0.0
760
+ },
761
+ {
762
+ "held_out": "reaction_diffusion1d",
763
+ "oracle_policy": "hybrid_full",
764
+ "oracle_val": 0.022279974073171616,
765
+ "predicted_policy": "hybrid_full",
766
+ "selected_val": 0.022279974073171616,
767
+ "correct": true,
768
+ "regret": 0.0
769
+ },
770
+ {
771
+ "held_out": "reaction_diffusion1d_stiff",
772
+ "oracle_policy": "hybrid_full",
773
+ "oracle_val": 0.04314509090036154,
774
+ "predicted_policy": "hybrid_no_gate",
775
+ "selected_val": 0.055535674653947355,
776
+ "correct": false,
777
+ "regret": 0.28718409197932615
778
+ },
779
+ {
780
+ "held_out": "wave2d",
781
+ "oracle_policy": "pinn_only",
782
+ "oracle_val": 0.028174721263349058,
783
+ "predicted_policy": "pinn_only",
784
+ "selected_val": 0.028174721263349058,
785
+ "correct": true,
786
+ "regret": 0.0
787
+ }
788
+ ],
789
+ "RF": [
790
+ {
791
+ "held_out": "advdiff1d",
792
+ "oracle_policy": "hybrid_no_gate",
793
+ "oracle_val": 0.012432838091626763,
794
+ "predicted_policy": "hybrid_no_gate",
795
+ "selected_val": 0.012432838091626763,
796
+ "correct": true,
797
+ "regret": 0.0
798
+ },
799
+ {
800
+ "held_out": "advdiff1d_highpe",
801
+ "oracle_policy": "pinn_only",
802
+ "oracle_val": 0.04680136069655418,
803
+ "predicted_policy": "hybrid_full",
804
+ "selected_val": 0.054425609111785886,
805
+ "correct": false,
806
+ "regret": 0.16290655446248703
807
+ },
808
+ {
809
+ "held_out": "allencahn1d",
810
+ "oracle_policy": "hybrid_full",
811
+ "oracle_val": 0.02884605899453163,
812
+ "predicted_policy": "hybrid_full",
813
+ "selected_val": 0.02884605899453163,
814
+ "correct": true,
815
+ "regret": 0.0
816
+ },
817
+ {
818
+ "held_out": "allencahn1d_sharp",
819
+ "oracle_policy": "hybrid_full",
820
+ "oracle_val": 0.04590511210262775,
821
+ "predicted_policy": "hybrid_full",
822
+ "selected_val": 0.04590511210262775,
823
+ "correct": true,
824
+ "regret": 0.0
825
+ },
826
+ {
827
+ "held_out": "burgers1d",
828
+ "oracle_policy": "hybrid_full",
829
+ "oracle_val": 0.0796903658658266,
830
+ "predicted_policy": "hybrid_no_gate",
831
+ "selected_val": 0.09537367187440396,
832
+ "correct": false,
833
+ "regret": 0.19680303683111566
834
+ },
835
+ {
836
+ "held_out": "burgers1d_lownu",
837
+ "oracle_policy": "hybrid_no_gate",
838
+ "oracle_val": 0.18069636225700378,
839
+ "predicted_policy": "hybrid_no_gate",
840
+ "selected_val": 0.18069636225700378,
841
+ "correct": true,
842
+ "regret": 0.0
843
+ },
844
+ {
845
+ "held_out": "burgers1d_verylow",
846
+ "oracle_policy": "hybrid_no_gate",
847
+ "oracle_val": 0.023859372083097696,
848
+ "predicted_policy": "hybrid_full",
849
+ "selected_val": 0.02931825667619705,
850
+ "correct": false,
851
+ "regret": 0.22879414320238978
852
+ },
853
+ {
854
+ "held_out": "heat1d",
855
+ "oracle_policy": "hybrid_full",
856
+ "oracle_val": 0.010440931282937526,
857
+ "predicted_policy": "hybrid_full",
858
+ "selected_val": 0.010440931282937526,
859
+ "correct": true,
860
+ "regret": 0.0
861
+ },
862
+ {
863
+ "held_out": "kdv1d",
864
+ "oracle_policy": "hybrid_no_gate",
865
+ "oracle_val": 0.008130461303517222,
866
+ "predicted_policy": "hybrid_full",
867
+ "selected_val": 0.013440604414790868,
868
+ "correct": false,
869
+ "regret": 0.6531170757772979
870
+ },
871
+ {
872
+ "held_out": "navier_stokes2d",
873
+ "oracle_policy": "hybrid_full",
874
+ "oracle_val": 0.06746206581592559,
875
+ "predicted_policy": "hybrid_full",
876
+ "selected_val": 0.06746206581592559,
877
+ "correct": true,
878
+ "regret": 0.0
879
+ },
880
+ {
881
+ "held_out": "reaction_diffusion1d",
882
+ "oracle_policy": "hybrid_full",
883
+ "oracle_val": 0.022279974073171616,
884
+ "predicted_policy": "hybrid_full",
885
+ "selected_val": 0.022279974073171616,
886
+ "correct": true,
887
+ "regret": 0.0
888
+ },
889
+ {
890
+ "held_out": "reaction_diffusion1d_stiff",
891
+ "oracle_policy": "hybrid_full",
892
+ "oracle_val": 0.04314509090036154,
893
+ "predicted_policy": "hybrid_no_gate",
894
+ "selected_val": 0.055535674653947355,
895
+ "correct": false,
896
+ "regret": 0.28718409197932615
897
+ },
898
+ {
899
+ "held_out": "wave2d",
900
+ "oracle_policy": "pinn_only",
901
+ "oracle_val": 0.028174721263349058,
902
+ "predicted_policy": "hybrid_no_gate",
903
+ "selected_val": 0.06117125898599625,
904
+ "correct": false,
905
+ "regret": 1.171139810549628
906
+ }
907
+ ],
908
+ "RF-top3": [
909
+ {
910
+ "held_out": "advdiff1d",
911
+ "oracle_policy": "hybrid_no_gate",
912
+ "oracle_val": 0.012432838091626763,
913
+ "predicted_policy": "hybrid_no_gate",
914
+ "selected_val": 0.012432838091626763,
915
+ "correct": true,
916
+ "regret": 0.0
917
+ },
918
+ {
919
+ "held_out": "advdiff1d_highpe",
920
+ "oracle_policy": "pinn_only",
921
+ "oracle_val": 0.04680136069655418,
922
+ "predicted_policy": "pinn_only",
923
+ "selected_val": 0.04680136069655418,
924
+ "correct": true,
925
+ "regret": 0.0
926
+ },
927
+ {
928
+ "held_out": "allencahn1d",
929
+ "oracle_policy": "hybrid_full",
930
+ "oracle_val": 0.02884605899453163,
931
+ "predicted_policy": "hybrid_full_lambda0.1",
932
+ "selected_val": 0.03741509392857552,
933
+ "correct": false,
934
+ "regret": 0.2970608545059249
935
+ },
936
+ {
937
+ "held_out": "allencahn1d_sharp",
938
+ "oracle_policy": "hybrid_full",
939
+ "oracle_val": 0.04590511210262775,
940
+ "predicted_policy": "hybrid_full",
941
+ "selected_val": 0.04590511210262775,
942
+ "correct": true,
943
+ "regret": 0.0
944
+ },
945
+ {
946
+ "held_out": "burgers1d",
947
+ "oracle_policy": "hybrid_full",
948
+ "oracle_val": 0.0796903658658266,
949
+ "predicted_policy": "hybrid_no_gate",
950
+ "selected_val": 0.09537367187440396,
951
+ "correct": false,
952
+ "regret": 0.19680303683111566
953
+ },
954
+ {
955
+ "held_out": "burgers1d_lownu",
956
+ "oracle_policy": "hybrid_no_gate",
957
+ "oracle_val": 0.18069636225700378,
958
+ "predicted_policy": "hybrid_no_gate",
959
+ "selected_val": 0.18069636225700378,
960
+ "correct": true,
961
+ "regret": 0.0
962
+ },
963
+ {
964
+ "held_out": "burgers1d_verylow",
965
+ "oracle_policy": "hybrid_no_gate",
966
+ "oracle_val": 0.023859372083097696,
967
+ "predicted_policy": "hybrid_full",
968
+ "selected_val": 0.02931825667619705,
969
+ "correct": false,
970
+ "regret": 0.22879414320238978
971
+ },
972
+ {
973
+ "held_out": "heat1d",
974
+ "oracle_policy": "hybrid_full",
975
+ "oracle_val": 0.010440931282937526,
976
+ "predicted_policy": "hybrid_full",
977
+ "selected_val": 0.010440931282937526,
978
+ "correct": true,
979
+ "regret": 0.0
980
+ },
981
+ {
982
+ "held_out": "kdv1d",
983
+ "oracle_policy": "hybrid_no_gate",
984
+ "oracle_val": 0.008130461303517222,
985
+ "predicted_policy": "hybrid_no_gate",
986
+ "selected_val": 0.008130461303517222,
987
+ "correct": true,
988
+ "regret": 0.0
989
+ },
990
+ {
991
+ "held_out": "navier_stokes2d",
992
+ "oracle_policy": "hybrid_full",
993
+ "oracle_val": 0.06746206581592559,
994
+ "predicted_policy": "hybrid_full",
995
+ "selected_val": 0.06746206581592559,
996
+ "correct": true,
997
+ "regret": 0.0
998
+ },
999
+ {
1000
+ "held_out": "reaction_diffusion1d",
1001
+ "oracle_policy": "hybrid_full",
1002
+ "oracle_val": 0.022279974073171616,
1003
+ "predicted_policy": "hybrid_no_gate",
1004
+ "selected_val": 0.02702330220490694,
1005
+ "correct": false,
1006
+ "regret": 0.21289648345897288
1007
+ },
1008
+ {
1009
+ "held_out": "reaction_diffusion1d_stiff",
1010
+ "oracle_policy": "hybrid_full",
1011
+ "oracle_val": 0.04314509090036154,
1012
+ "predicted_policy": "hybrid_no_gate",
1013
+ "selected_val": 0.055535674653947355,
1014
+ "correct": false,
1015
+ "regret": 0.28718409197932615
1016
+ },
1017
+ {
1018
+ "held_out": "wave2d",
1019
+ "oracle_policy": "pinn_only",
1020
+ "oracle_val": 0.028174721263349058,
1021
+ "predicted_policy": "pinn_only",
1022
+ "selected_val": 0.028174721263349058,
1023
+ "correct": true,
1024
+ "regret": 0.0
1025
+ }
1026
+ ],
1027
+ "physics_final": [
1028
+ {
1029
+ "held_out": "advdiff1d",
1030
+ "oracle_policy": "hybrid_no_gate",
1031
+ "oracle_val": 0.012432838091626763,
1032
+ "predicted_policy": "hybrid_no_gate",
1033
+ "selected_val": 0.012432838091626763,
1034
+ "correct": true,
1035
+ "regret": 0.0
1036
+ },
1037
+ {
1038
+ "held_out": "advdiff1d_highpe",
1039
+ "oracle_policy": "pinn_only",
1040
+ "oracle_val": 0.04680136069655418,
1041
+ "predicted_policy": "pinn_only",
1042
+ "selected_val": 0.04680136069655418,
1043
+ "correct": true,
1044
+ "regret": 0.0
1045
+ },
1046
+ {
1047
+ "held_out": "allencahn1d",
1048
+ "oracle_policy": "hybrid_full",
1049
+ "oracle_val": 0.02884605899453163,
1050
+ "predicted_policy": "hybrid_full",
1051
+ "selected_val": 0.02884605899453163,
1052
+ "correct": true,
1053
+ "regret": 0.0
1054
+ },
1055
+ {
1056
+ "held_out": "allencahn1d_sharp",
1057
+ "oracle_policy": "hybrid_full",
1058
+ "oracle_val": 0.04590511210262775,
1059
+ "predicted_policy": "hybrid_full",
1060
+ "selected_val": 0.04590511210262775,
1061
+ "correct": true,
1062
+ "regret": 0.0
1063
+ },
1064
+ {
1065
+ "held_out": "burgers1d",
1066
+ "oracle_policy": "hybrid_full",
1067
+ "oracle_val": 0.0796903658658266,
1068
+ "predicted_policy": "hybrid_no_gate",
1069
+ "selected_val": 0.09537367187440396,
1070
+ "correct": false,
1071
+ "regret": 0.19680303683111566
1072
+ },
1073
+ {
1074
+ "held_out": "burgers1d_lownu",
1075
+ "oracle_policy": "hybrid_no_gate",
1076
+ "oracle_val": 0.18069636225700378,
1077
+ "predicted_policy": "pinn_only",
1078
+ "selected_val": 0.2146585464477539,
1079
+ "correct": false,
1080
+ "regret": 0.18795167631789855
1081
+ },
1082
+ {
1083
+ "held_out": "burgers1d_verylow",
1084
+ "oracle_policy": "hybrid_no_gate",
1085
+ "oracle_val": 0.023859372083097696,
1086
+ "predicted_policy": "hybrid_full",
1087
+ "selected_val": 0.02931825667619705,
1088
+ "correct": false,
1089
+ "regret": 0.22879414320238978
1090
+ },
1091
+ {
1092
+ "held_out": "heat1d",
1093
+ "oracle_policy": "hybrid_full",
1094
+ "oracle_val": 0.010440931282937526,
1095
+ "predicted_policy": "hybrid_full",
1096
+ "selected_val": 0.010440931282937526,
1097
+ "correct": true,
1098
+ "regret": 0.0
1099
+ },
1100
+ {
1101
+ "held_out": "kdv1d",
1102
+ "oracle_policy": "hybrid_no_gate",
1103
+ "oracle_val": 0.008130461303517222,
1104
+ "predicted_policy": "hybrid_no_gate",
1105
+ "selected_val": 0.008130461303517222,
1106
+ "correct": true,
1107
+ "regret": 0.0
1108
+ },
1109
+ {
1110
+ "held_out": "navier_stokes2d",
1111
+ "oracle_policy": "hybrid_full",
1112
+ "oracle_val": 0.06746206581592559,
1113
+ "predicted_policy": "hybrid_full",
1114
+ "selected_val": 0.06746206581592559,
1115
+ "correct": true,
1116
+ "regret": 0.0
1117
+ },
1118
+ {
1119
+ "held_out": "reaction_diffusion1d",
1120
+ "oracle_policy": "hybrid_full",
1121
+ "oracle_val": 0.022279974073171616,
1122
+ "predicted_policy": "hybrid_full",
1123
+ "selected_val": 0.022279974073171616,
1124
+ "correct": true,
1125
+ "regret": 0.0
1126
+ },
1127
+ {
1128
+ "held_out": "reaction_diffusion1d_stiff",
1129
+ "oracle_policy": "hybrid_full",
1130
+ "oracle_val": 0.04314509090036154,
1131
+ "predicted_policy": "hybrid_no_gate",
1132
+ "selected_val": 0.055535674653947355,
1133
+ "correct": false,
1134
+ "regret": 0.28718409197932615
1135
+ },
1136
+ {
1137
+ "held_out": "wave2d",
1138
+ "oracle_policy": "pinn_only",
1139
+ "oracle_val": 0.028174721263349058,
1140
+ "predicted_policy": "pinn_only",
1141
+ "selected_val": 0.028174721263349058,
1142
+ "correct": true,
1143
+ "regret": 0.0
1144
+ }
1145
+ ],
1146
+ "random": [
1147
+ {
1148
+ "held_out": "advdiff1d",
1149
+ "oracle_policy": "hybrid_no_gate",
1150
+ "oracle_val": 0.012432838091626763,
1151
+ "predicted_policy": "random",
1152
+ "correct": false,
1153
+ "regret": 3.086635443457888
1154
+ },
1155
+ {
1156
+ "held_out": "advdiff1d_highpe",
1157
+ "oracle_policy": "pinn_only",
1158
+ "oracle_val": 0.04680136069655418,
1159
+ "predicted_policy": "random",
1160
+ "correct": false,
1161
+ "regret": 0.10666109555617673
1162
+ },
1163
+ {
1164
+ "held_out": "allencahn1d",
1165
+ "oracle_policy": "hybrid_full",
1166
+ "oracle_val": 0.02884605899453163,
1167
+ "predicted_policy": "random",
1168
+ "correct": false,
1169
+ "regret": 1.5809931256743726
1170
+ },
1171
+ {
1172
+ "held_out": "allencahn1d_sharp",
1173
+ "oracle_policy": "hybrid_full",
1174
+ "oracle_val": 0.04590511210262775,
1175
+ "predicted_policy": "random",
1176
+ "correct": false,
1177
+ "regret": 1.1309732966168278
1178
+ },
1179
+ {
1180
+ "held_out": "burgers1d",
1181
+ "oracle_policy": "hybrid_full",
1182
+ "oracle_val": 0.0796903658658266,
1183
+ "predicted_policy": "random",
1184
+ "correct": false,
1185
+ "regret": 0.7531077153184651
1186
+ },
1187
+ {
1188
+ "held_out": "burgers1d_lownu",
1189
+ "oracle_policy": "hybrid_no_gate",
1190
+ "oracle_val": 0.18069636225700378,
1191
+ "predicted_policy": "random",
1192
+ "correct": false,
1193
+ "regret": 0.2009210067852694
1194
+ },
1195
+ {
1196
+ "held_out": "burgers1d_verylow",
1197
+ "oracle_policy": "hybrid_no_gate",
1198
+ "oracle_val": 0.023859372083097696,
1199
+ "predicted_policy": "random",
1200
+ "correct": false,
1201
+ "regret": 1.3602215422555786
1202
+ },
1203
+ {
1204
+ "held_out": "heat1d",
1205
+ "oracle_policy": "hybrid_full",
1206
+ "oracle_val": 0.010440931282937526,
1207
+ "predicted_policy": "random",
1208
+ "correct": false,
1209
+ "regret": 0.8448917847067746
1210
+ },
1211
+ {
1212
+ "held_out": "kdv1d",
1213
+ "oracle_policy": "hybrid_no_gate",
1214
+ "oracle_val": 0.008130461303517222,
1215
+ "predicted_policy": "random",
1216
+ "correct": false,
1217
+ "regret": 0.2783199751204743
1218
+ },
1219
+ {
1220
+ "held_out": "navier_stokes2d",
1221
+ "oracle_policy": "hybrid_full",
1222
+ "oracle_val": 0.06746206581592559,
1223
+ "predicted_policy": "random",
1224
+ "correct": false,
1225
+ "regret": 0.048980521352088684
1226
+ },
1227
+ {
1228
+ "held_out": "reaction_diffusion1d",
1229
+ "oracle_policy": "hybrid_full",
1230
+ "oracle_val": 0.022279974073171616,
1231
+ "predicted_policy": "random",
1232
+ "correct": false,
1233
+ "regret": 0.6328201829150876
1234
+ },
1235
+ {
1236
+ "held_out": "reaction_diffusion1d_stiff",
1237
+ "oracle_policy": "hybrid_full",
1238
+ "oracle_val": 0.04314509090036154,
1239
+ "predicted_policy": "random",
1240
+ "correct": false,
1241
+ "regret": 2.2456056787965637
1242
+ },
1243
+ {
1244
+ "held_out": "wave2d",
1245
+ "oracle_policy": "pinn_only",
1246
+ "oracle_val": 0.028174721263349058,
1247
+ "predicted_policy": "random",
1248
+ "correct": false,
1249
+ "regret": 0.8354558916427964
1250
+ }
1251
+ ]
1252
+ }
1253
+ }
results/paper_a/navier_stokes2d/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_a/ntk_proxy/ntk_proxy_results.json ADDED
@@ -0,0 +1,387 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "experiment": "ntk_proxy_analysis",
3
+ "seed": 42,
4
+ "device": "cuda",
5
+ "checkpoint_epochs": [
6
+ 10,
7
+ 50,
8
+ 100,
9
+ 250,
10
+ 500
11
+ ],
12
+ "stage1_epochs": 200,
13
+ "stage2_epochs": 500,
14
+ "hyperparameters": {
15
+ "stage1_lr": 0.001,
16
+ "stage2_lr": 0.0001,
17
+ "num_collocation": 2000,
18
+ "num_boundary": 200,
19
+ "batch_size": 256,
20
+ "hidden_dims": [
21
+ 64,
22
+ 64,
23
+ 64,
24
+ 64
25
+ ]
26
+ },
27
+ "pde_results": {
28
+ "heat1d": {
29
+ "pde": "heat1d",
30
+ "policies": [
31
+ {
32
+ "policy": "pinn_only",
33
+ "checkpoints": [
34
+ {
35
+ "epoch": 10,
36
+ "cosine_similarity": 0.5123063325881958,
37
+ "grad_norm": 0.35270166397094727,
38
+ "physics_loss": 0.0161279384046793
39
+ },
40
+ {
41
+ "epoch": 50,
42
+ "cosine_similarity": 0.7218053936958313,
43
+ "grad_norm": 0.3855777382850647,
44
+ "physics_loss": 0.020037271082401276
45
+ },
46
+ {
47
+ "epoch": 100,
48
+ "cosine_similarity": 0.7810920476913452,
49
+ "grad_norm": 0.2590717375278473,
50
+ "physics_loss": 0.01733652874827385
51
+ },
52
+ {
53
+ "epoch": 250,
54
+ "cosine_similarity": 0.9147284030914307,
55
+ "grad_norm": 0.16760271787643433,
56
+ "physics_loss": 0.003061551135033369
57
+ },
58
+ {
59
+ "epoch": 500,
60
+ "cosine_similarity": 1.0000001192092896,
61
+ "grad_norm": 0.13323625922203064,
62
+ "physics_loss": 0.0020184325985610485
63
+ }
64
+ ],
65
+ "final_grad_norm": 0.13323625922203064,
66
+ "final_physics_loss": 0.0020184325985610485,
67
+ "wall_time_s": 10.88
68
+ },
69
+ {
70
+ "policy": "hybrid_no_gate",
71
+ "checkpoints": [
72
+ {
73
+ "epoch": 10,
74
+ "cosine_similarity": 0.23125199973583221,
75
+ "grad_norm": 0.8374547958374023,
76
+ "physics_loss": 0.006407200358808041
77
+ },
78
+ {
79
+ "epoch": 50,
80
+ "cosine_similarity": 0.8842431902885437,
81
+ "grad_norm": 0.46802008152008057,
82
+ "physics_loss": 0.004573889076709747
83
+ },
84
+ {
85
+ "epoch": 100,
86
+ "cosine_similarity": -0.012260548770427704,
87
+ "grad_norm": 0.15888354182243347,
88
+ "physics_loss": 0.0032701604068279266
89
+ },
90
+ {
91
+ "epoch": 250,
92
+ "cosine_similarity": 0.9806137084960938,
93
+ "grad_norm": 0.15144680440425873,
94
+ "physics_loss": 0.002012234879657626
95
+ },
96
+ {
97
+ "epoch": 500,
98
+ "cosine_similarity": 0.9999999403953552,
99
+ "grad_norm": 0.10894204676151276,
100
+ "physics_loss": 0.0011886653956025839
101
+ }
102
+ ],
103
+ "final_grad_norm": 0.10894204676151276,
104
+ "final_physics_loss": 0.0011886653956025839,
105
+ "wall_time_s": 48.07
106
+ },
107
+ {
108
+ "policy": "hybrid_full",
109
+ "checkpoints": [
110
+ {
111
+ "epoch": 10,
112
+ "cosine_similarity": 0.3531556725502014,
113
+ "grad_norm": 0.28320425748825073,
114
+ "physics_loss": 0.001380318426527083
115
+ },
116
+ {
117
+ "epoch": 50,
118
+ "cosine_similarity": -0.11546725034713745,
119
+ "grad_norm": 0.15716058015823364,
120
+ "physics_loss": 0.001077119610272348
121
+ },
122
+ {
123
+ "epoch": 100,
124
+ "cosine_similarity": 0.6970533132553101,
125
+ "grad_norm": 0.17671377956867218,
126
+ "physics_loss": 0.0008458818774670362
127
+ },
128
+ {
129
+ "epoch": 250,
130
+ "cosine_similarity": 0.8644483685493469,
131
+ "grad_norm": 0.12702320516109467,
132
+ "physics_loss": 0.000544607755728066
133
+ },
134
+ {
135
+ "epoch": 500,
136
+ "cosine_similarity": 1.0,
137
+ "grad_norm": 0.14420261979103088,
138
+ "physics_loss": 0.0003855630347970873
139
+ }
140
+ ],
141
+ "final_grad_norm": 0.14420261979103088,
142
+ "final_physics_loss": 0.0003855630347970873,
143
+ "wall_time_s": 71.79
144
+ }
145
+ ]
146
+ },
147
+ "advdiff1d": {
148
+ "pde": "advdiff1d",
149
+ "policies": [
150
+ {
151
+ "policy": "pinn_only",
152
+ "checkpoints": [
153
+ {
154
+ "epoch": 10,
155
+ "cosine_similarity": -0.20914365351200104,
156
+ "grad_norm": 0.08753504604101181,
157
+ "physics_loss": 0.004240971989929676
158
+ },
159
+ {
160
+ "epoch": 50,
161
+ "cosine_similarity": -0.27593693137168884,
162
+ "grad_norm": 0.1210208460688591,
163
+ "physics_loss": 0.006844665389508009
164
+ },
165
+ {
166
+ "epoch": 100,
167
+ "cosine_similarity": -0.2206527590751648,
168
+ "grad_norm": 0.1096719354391098,
169
+ "physics_loss": 0.008016401901841164
170
+ },
171
+ {
172
+ "epoch": 250,
173
+ "cosine_similarity": 0.8353182077407837,
174
+ "grad_norm": 0.08916417509317398,
175
+ "physics_loss": 0.011085241101682186
176
+ },
177
+ {
178
+ "epoch": 500,
179
+ "cosine_similarity": 1.0000001192092896,
180
+ "grad_norm": 0.15722805261611938,
181
+ "physics_loss": 0.016511257737874985
182
+ }
183
+ ],
184
+ "final_grad_norm": 0.15722805261611938,
185
+ "final_physics_loss": 0.016511257737874985,
186
+ "wall_time_s": 13.19
187
+ },
188
+ {
189
+ "policy": "hybrid_no_gate",
190
+ "checkpoints": [
191
+ {
192
+ "epoch": 10,
193
+ "cosine_similarity": 0.5577482581138611,
194
+ "grad_norm": 0.6671752333641052,
195
+ "physics_loss": 0.013618306256830692
196
+ },
197
+ {
198
+ "epoch": 50,
199
+ "cosine_similarity": 0.2423178106546402,
200
+ "grad_norm": 0.764694094657898,
201
+ "physics_loss": 0.018145769834518433
202
+ },
203
+ {
204
+ "epoch": 100,
205
+ "cosine_similarity": 0.370167076587677,
206
+ "grad_norm": 0.45893144607543945,
207
+ "physics_loss": 0.009508499875664711
208
+ },
209
+ {
210
+ "epoch": 250,
211
+ "cosine_similarity": 0.7516151070594788,
212
+ "grad_norm": 0.11427507549524307,
213
+ "physics_loss": 0.0024819588288664818
214
+ },
215
+ {
216
+ "epoch": 500,
217
+ "cosine_similarity": 1.0,
218
+ "grad_norm": 0.12031659483909607,
219
+ "physics_loss": 0.000861744221765548
220
+ }
221
+ ],
222
+ "final_grad_norm": 0.12031659483909607,
223
+ "final_physics_loss": 0.000861744221765548,
224
+ "wall_time_s": 63.3
225
+ },
226
+ {
227
+ "policy": "hybrid_full",
228
+ "checkpoints": [
229
+ {
230
+ "epoch": 10,
231
+ "cosine_similarity": 0.8210325837135315,
232
+ "grad_norm": 0.5265653133392334,
233
+ "physics_loss": 0.007059501484036446
234
+ },
235
+ {
236
+ "epoch": 50,
237
+ "cosine_similarity": 0.8384649753570557,
238
+ "grad_norm": 0.4237087666988373,
239
+ "physics_loss": 0.006733257323503494
240
+ },
241
+ {
242
+ "epoch": 100,
243
+ "cosine_similarity": 0.8409834504127502,
244
+ "grad_norm": 0.21392309665679932,
245
+ "physics_loss": 0.0048600430600345135
246
+ },
247
+ {
248
+ "epoch": 250,
249
+ "cosine_similarity": 0.950865626335144,
250
+ "grad_norm": 0.09507833421230316,
251
+ "physics_loss": 0.001611027866601944
252
+ },
253
+ {
254
+ "epoch": 500,
255
+ "cosine_similarity": 1.0,
256
+ "grad_norm": 0.0641392171382904,
257
+ "physics_loss": 0.0005810715956613421
258
+ }
259
+ ],
260
+ "final_grad_norm": 0.0641392171382904,
261
+ "final_physics_loss": 0.0005810715956613421,
262
+ "wall_time_s": 73.34
263
+ }
264
+ ]
265
+ },
266
+ "allencahn1d": {
267
+ "pde": "allencahn1d",
268
+ "policies": [
269
+ {
270
+ "policy": "pinn_only",
271
+ "checkpoints": [
272
+ {
273
+ "epoch": 10,
274
+ "cosine_similarity": 0.9683452844619751,
275
+ "grad_norm": 0.7039585113525391,
276
+ "physics_loss": 0.053616128861904144
277
+ },
278
+ {
279
+ "epoch": 50,
280
+ "cosine_similarity": 0.9780865907669067,
281
+ "grad_norm": 0.5625851154327393,
282
+ "physics_loss": 0.04948995262384415
283
+ },
284
+ {
285
+ "epoch": 100,
286
+ "cosine_similarity": 0.977483868598938,
287
+ "grad_norm": 0.7362470626831055,
288
+ "physics_loss": 0.05105339363217354
289
+ },
290
+ {
291
+ "epoch": 250,
292
+ "cosine_similarity": 0.9934762716293335,
293
+ "grad_norm": 0.6857259273529053,
294
+ "physics_loss": 0.04538419470191002
295
+ },
296
+ {
297
+ "epoch": 500,
298
+ "cosine_similarity": 0.9999998807907104,
299
+ "grad_norm": 0.6119616627693176,
300
+ "physics_loss": 0.040751706808805466
301
+ }
302
+ ],
303
+ "final_grad_norm": 0.6119616627693176,
304
+ "final_physics_loss": 0.040751706808805466,
305
+ "wall_time_s": 13.01
306
+ },
307
+ {
308
+ "policy": "hybrid_no_gate",
309
+ "checkpoints": [
310
+ {
311
+ "epoch": 10,
312
+ "cosine_similarity": 0.4528622031211853,
313
+ "grad_norm": 0.3615739941596985,
314
+ "physics_loss": 0.005752693396061659
315
+ },
316
+ {
317
+ "epoch": 50,
318
+ "cosine_similarity": 0.5630664825439453,
319
+ "grad_norm": 0.20084305107593536,
320
+ "physics_loss": 0.005717021878808737
321
+ },
322
+ {
323
+ "epoch": 100,
324
+ "cosine_similarity": 0.25144249200820923,
325
+ "grad_norm": 0.14814463257789612,
326
+ "physics_loss": 0.005410314071923494
327
+ },
328
+ {
329
+ "epoch": 250,
330
+ "cosine_similarity": 0.47346919775009155,
331
+ "grad_norm": 0.08782326430082321,
332
+ "physics_loss": 0.004057080019265413
333
+ },
334
+ {
335
+ "epoch": 500,
336
+ "cosine_similarity": 1.0,
337
+ "grad_norm": 0.1224752739071846,
338
+ "physics_loss": 0.0029592616483569145
339
+ }
340
+ ],
341
+ "final_grad_norm": 0.1224752739071846,
342
+ "final_physics_loss": 0.0029592616483569145,
343
+ "wall_time_s": 61.64
344
+ },
345
+ {
346
+ "policy": "hybrid_full",
347
+ "checkpoints": [
348
+ {
349
+ "epoch": 10,
350
+ "cosine_similarity": 0.9038909673690796,
351
+ "grad_norm": 0.4015835225582123,
352
+ "physics_loss": 0.005355903413146734
353
+ },
354
+ {
355
+ "epoch": 50,
356
+ "cosine_similarity": 0.5775554180145264,
357
+ "grad_norm": 0.11608213186264038,
358
+ "physics_loss": 0.004136783070862293
359
+ },
360
+ {
361
+ "epoch": 100,
362
+ "cosine_similarity": 0.44379544258117676,
363
+ "grad_norm": 0.12899824976921082,
364
+ "physics_loss": 0.0034300440456718206
365
+ },
366
+ {
367
+ "epoch": 250,
368
+ "cosine_similarity": 0.08809975534677505,
369
+ "grad_norm": 0.07462827861309052,
370
+ "physics_loss": 0.0016869273968040943
371
+ },
372
+ {
373
+ "epoch": 500,
374
+ "cosine_similarity": 1.0000001192092896,
375
+ "grad_norm": 0.059767451137304306,
376
+ "physics_loss": 0.0008711705449968576
377
+ }
378
+ ],
379
+ "final_grad_norm": 0.059767451137304306,
380
+ "final_physics_loss": 0.0008711705449968576,
381
+ "wall_time_s": 71.56
382
+ }
383
+ ]
384
+ }
385
+ },
386
+ "total_wall_time_s": 426.77
387
+ }
results/paper_a/reaction_diffusion1d/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_a/reaction_diffusion1d_stiff/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_a/regret_bound_validation.json ADDED
@@ -0,0 +1,834 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ [
2
+ {
3
+ "pde": "advdiff1d",
4
+ "k": 10,
5
+ "n_runs": 40,
6
+ "P": 4,
7
+ "rho_k": 0.9103189493433398,
8
+ "rho_p": 3.891390155414773e-16,
9
+ "sigma": 0.022464973775874583,
10
+ "delta_gap": 0.0001853690831921995,
11
+ "best_policy": "hybrid_no_gate",
12
+ "best_final": 0.00028148697165306655,
13
+ "theoretical_bound": 0.1572471513427463,
14
+ "observed_regret": 0.02441836497746408,
15
+ "bound_valid": true,
16
+ "tightness_ratio": 6.439708452546723
17
+ },
18
+ {
19
+ "pde": "advdiff1d_highpe",
20
+ "k": 10,
21
+ "n_runs": 30,
22
+ "P": 3,
23
+ "rho_k": 0.8740823136818686,
24
+ "rho_p": 2.8107238793162205e-10,
25
+ "sigma": 0.12057964683000501,
26
+ "delta_gap": 0.11614939272403713,
27
+ "best_policy": "hybrid_full",
28
+ "best_final": 0.32731066793203356,
29
+ "theoretical_bound": 0.8537302839918219,
30
+ "observed_regret": 0.007624248415231703,
31
+ "bound_valid": true,
32
+ "tightness_ratio": 111.97566468141854
33
+ },
34
+ {
35
+ "pde": "allencahn1d",
36
+ "k": 10,
37
+ "n_runs": 40,
38
+ "P": 4,
39
+ "rho_k": 0.9193245778611633,
40
+ "rho_p": 5.644924479224813e-17,
41
+ "sigma": 0.029143366107101137,
42
+ "delta_gap": 0.0005680945527274158,
43
+ "best_policy": "hybrid_full_lambda0.1",
44
+ "best_final": 0.002289587585255504,
45
+ "theoretical_bound": 0.20199531414316962,
46
+ "observed_regret": 0.008569034934043887,
47
+ "bound_valid": true,
48
+ "tightness_ratio": 23.572702842027542
49
+ },
50
+ {
51
+ "pde": "allencahn1d_sharp",
52
+ "k": 10,
53
+ "n_runs": 30,
54
+ "P": 3,
55
+ "rho_k": 0.8193548387096774,
56
+ "rho_p": 3.080263956770427e-08,
57
+ "sigma": 0.034466034464487795,
58
+ "delta_gap": 0.005231749545782802,
59
+ "best_policy": "hybrid_full",
60
+ "best_final": 0.01953851627185941,
61
+ "theoretical_bound": 0.26032645693366907,
62
+ "observed_regret": 0.0,
63
+ "bound_valid": true,
64
+ "tightness_ratio": "nan"
65
+ },
66
+ {
67
+ "pde": "burgers1d",
68
+ "k": 10,
69
+ "n_runs": 40,
70
+ "P": 4,
71
+ "rho_k": 0.9245778611632272,
72
+ "rho_p": 1.6454119814147836e-17,
73
+ "sigma": 0.010022084871966699,
74
+ "delta_gap": 0.007069513935130091,
75
+ "best_policy": "hybrid_full_lambda0.1",
76
+ "best_final": 0.009187573171220719,
77
+ "theoretical_bound": 0.06906929767061686,
78
+ "observed_regret": 0.09065891541540623,
79
+ "bound_valid": false,
80
+ "tightness_ratio": 0.7618588569489932
81
+ },
82
+ {
83
+ "pde": "burgers1d_lownu",
84
+ "k": 10,
85
+ "n_runs": 40,
86
+ "P": 4,
87
+ "rho_k": 0.8996247654784242,
88
+ "rho_p": 3.0074620473653184e-15,
89
+ "sigma": 0.003608960733921553,
90
+ "delta_gap": 0.06115469709038735,
91
+ "best_policy": "hybrid_full_lambda0.1",
92
+ "best_final": 0.02386377230286598,
93
+ "theoretical_bound": 0.025561786797310495,
94
+ "observed_regret": 0.11010234057903293,
95
+ "bound_valid": false,
96
+ "tightness_ratio": 0.23216388192003878
97
+ },
98
+ {
99
+ "pde": "burgers1d_verylow",
100
+ "k": 10,
101
+ "n_runs": 30,
102
+ "P": 3,
103
+ "rho_k": 0.8540600667408231,
104
+ "rho_p": 1.9495880671149297e-09,
105
+ "sigma": 0.0013540111052718852,
106
+ "delta_gap": 0.0003611462539993228,
107
+ "best_policy": "hybrid_no_gate",
108
+ "best_final": 0.001121796341612935,
109
+ "theoretical_bound": 0.009811441590545075,
110
+ "observed_regret": 0.005458884593099355,
111
+ "bound_valid": true,
112
+ "tightness_ratio": 1.7973344963086126
113
+ },
114
+ {
115
+ "pde": "heat1d",
116
+ "k": 10,
117
+ "n_runs": 50,
118
+ "P": 5,
119
+ "rho_k": 0.8257863145258102,
120
+ "rho_p": 1.581241574889372e-13,
121
+ "sigma": 0.00250671472741047,
122
+ "delta_gap": 5.250379908829927e-05,
123
+ "best_policy": "hybrid_full_lambda0.1",
124
+ "best_final": 7.408647652482614e-05,
125
+ "theoretical_bound": 0.019762924398410663,
126
+ "observed_regret": 0.006860199850052597,
127
+ "bound_valid": true,
128
+ "tightness_ratio": 2.8808088438209483
129
+ },
130
+ {
131
+ "pde": "kdv1d",
132
+ "k": 10,
133
+ "n_runs": 30,
134
+ "P": 3,
135
+ "rho_k": 0.17196885428253617,
136
+ "rho_p": 0.36351678056146086,
137
+ "sigma": 0.0015815526141963413,
138
+ "delta_gap": 7.576095486001578e-05,
139
+ "best_policy": "hybrid_no_gate",
140
+ "best_final": 0.00012927247917104978,
141
+ "theoretical_bound": 0.05691580188173457,
142
+ "observed_regret": 0.0,
143
+ "bound_valid": true,
144
+ "tightness_ratio": "nan"
145
+ },
146
+ {
147
+ "pde": "navier_stokes2d",
148
+ "k": 10,
149
+ "n_runs": 30,
150
+ "P": 3,
151
+ "rho_k": 0.9025583982202448,
152
+ "rho_p": 9.309452223851787e-12,
153
+ "sigma": 0.04313304866906295,
154
+ "delta_gap": 0.005380900483578442,
155
+ "best_policy": "hybrid_full",
156
+ "best_final": 0.01304085785523057,
157
+ "theoretical_bound": 0.29575619907436884,
158
+ "observed_regret": 0.0,
159
+ "bound_valid": true,
160
+ "tightness_ratio": "nan"
161
+ },
162
+ {
163
+ "pde": "reaction_diffusion1d",
164
+ "k": 10,
165
+ "n_runs": 30,
166
+ "P": 3,
167
+ "rho_k": 0.9083426028921023,
168
+ "rho_p": 4.099665581377395e-12,
169
+ "sigma": 0.003334135792020918,
170
+ "delta_gap": 0.0011453424813225863,
171
+ "best_policy": "hybrid_full",
172
+ "best_final": 0.0014936716062948108,
173
+ "theoretical_bound": 0.022716039349835227,
174
+ "observed_regret": 0.0,
175
+ "bound_valid": true,
176
+ "tightness_ratio": "nan"
177
+ },
178
+ {
179
+ "pde": "reaction_diffusion1d_stiff",
180
+ "k": 10,
181
+ "n_runs": 30,
182
+ "P": 3,
183
+ "rho_k": 0.9230255839822022,
184
+ "rho_p": 3.9032710919140186e-13,
185
+ "sigma": 0.13241552021257275,
186
+ "delta_gap": 0.04085545371053741,
187
+ "best_policy": "hybrid_full",
188
+ "best_final": 0.00922477392014116,
189
+ "theoretical_bound": 0.887818447499421,
190
+ "observed_regret": 0.012390583753585815,
191
+ "bound_valid": true,
192
+ "tightness_ratio": 71.65267312304698
193
+ },
194
+ {
195
+ "pde": "wave2d",
196
+ "k": 10,
197
+ "n_runs": 30,
198
+ "P": 3,
199
+ "rho_k": 0.7988876529477197,
200
+ "rho_p": 1.2087143085790022e-07,
201
+ "sigma": 0.011832335910120917,
202
+ "delta_gap": 0.004747881554067135,
203
+ "best_policy": "hybrid_full",
204
+ "best_final": 0.05684403423219919,
205
+ "theoretical_bound": 0.0916608317535386,
206
+ "observed_regret": 0.03761967290192842,
207
+ "bound_valid": true,
208
+ "tightness_ratio": 2.4365132571059642
209
+ },
210
+ {
211
+ "pde": "advdiff1d",
212
+ "k": 20,
213
+ "n_runs": 40,
214
+ "P": 4,
215
+ "rho_k": 0.9011257035647281,
216
+ "rho_p": 2.2893736752275754e-15,
217
+ "sigma": 0.02229197366751224,
218
+ "delta_gap": 0.0001853690831921995,
219
+ "best_policy": "hybrid_no_gate",
220
+ "best_final": 0.00028148697165306655,
221
+ "theoretical_bound": 0.15762808433024159,
222
+ "observed_regret": "nan",
223
+ "bound_valid": null,
224
+ "tightness_ratio": "nan"
225
+ },
226
+ {
227
+ "pde": "advdiff1d_highpe",
228
+ "k": 20,
229
+ "n_runs": 30,
230
+ "P": 3,
231
+ "rho_k": 0.875417130144605,
232
+ "rho_p": 2.4419795381046267e-10,
233
+ "sigma": 0.12143176814759983,
234
+ "delta_gap": 0.11614939272403713,
235
+ "best_policy": "hybrid_full",
236
+ "best_final": 0.32731066793203356,
237
+ "theoretical_bound": 0.8584525412345448,
238
+ "observed_regret": "nan",
239
+ "bound_valid": null,
240
+ "tightness_ratio": "nan"
241
+ },
242
+ {
243
+ "pde": "allencahn1d",
244
+ "k": 20,
245
+ "n_runs": 40,
246
+ "P": 4,
247
+ "rho_k": 0.9136960600375236,
248
+ "rho_p": 1.9339013588751176e-16,
249
+ "sigma": 0.028887198672256142,
250
+ "delta_gap": 0.0005680945527274158,
251
+ "best_policy": "hybrid_full_lambda0.1",
252
+ "best_final": 0.002289587585255504,
253
+ "theoretical_bound": 0.20145318123869294,
254
+ "observed_regret": "nan",
255
+ "bound_valid": null,
256
+ "tightness_ratio": "nan"
257
+ },
258
+ {
259
+ "pde": "allencahn1d_sharp",
260
+ "k": 20,
261
+ "n_runs": 30,
262
+ "P": 3,
263
+ "rho_k": 0.7975528364849833,
264
+ "rho_p": 1.31428054345191e-07,
265
+ "sigma": 0.0345805850864292,
266
+ "delta_gap": 0.005231749545782802,
267
+ "best_policy": "hybrid_full",
268
+ "best_final": 0.01953851627185941,
269
+ "theoretical_bound": 0.26833164035554646,
270
+ "observed_regret": "nan",
271
+ "bound_valid": null,
272
+ "tightness_ratio": "nan"
273
+ },
274
+ {
275
+ "pde": "burgers1d",
276
+ "k": 20,
277
+ "n_runs": 40,
278
+ "P": 4,
279
+ "rho_k": 0.9258911819887431,
280
+ "rho_p": 1.1922634701584218e-17,
281
+ "sigma": 0.008975368488461956,
282
+ "delta_gap": 0.007069513935130091,
283
+ "best_policy": "hybrid_full_lambda0.1",
284
+ "best_final": 0.009187573171220719,
285
+ "theoretical_bound": 0.06176789392539404,
286
+ "observed_regret": "nan",
287
+ "bound_valid": null,
288
+ "tightness_ratio": "nan"
289
+ },
290
+ {
291
+ "pde": "burgers1d_lownu",
292
+ "k": 20,
293
+ "n_runs": 40,
294
+ "P": 4,
295
+ "rho_k": 0.9536585365853661,
296
+ "rho_p": 2.0336377845454515e-21,
297
+ "sigma": 0.0036507141578925846,
298
+ "delta_gap": 0.06115469709038735,
299
+ "best_policy": "hybrid_full_lambda0.1",
300
+ "best_final": 0.02386377230286598,
301
+ "theoretical_bound": 0.024392447739840197,
302
+ "observed_regret": "nan",
303
+ "bound_valid": null,
304
+ "tightness_ratio": "nan"
305
+ },
306
+ {
307
+ "pde": "burgers1d_verylow",
308
+ "k": 20,
309
+ "n_runs": 30,
310
+ "P": 3,
311
+ "rho_k": 0.8589543937708565,
312
+ "rho_p": 1.2482452471230543e-09,
313
+ "sigma": 0.0012963669100295742,
314
+ "delta_gap": 0.0003611462539993228,
315
+ "best_policy": "hybrid_no_gate",
316
+ "best_final": 0.001121796341612935,
317
+ "theoretical_bound": 0.009340214370156575,
318
+ "observed_regret": "nan",
319
+ "bound_valid": null,
320
+ "tightness_ratio": "nan"
321
+ },
322
+ {
323
+ "pde": "heat1d",
324
+ "k": 20,
325
+ "n_runs": 50,
326
+ "P": 5,
327
+ "rho_k": 0.8676590636254502,
328
+ "rho_p": 3.5457120985631706e-16,
329
+ "sigma": 0.002427723915153419,
330
+ "delta_gap": 5.250379908829927e-05,
331
+ "best_policy": "hybrid_full_lambda0.1",
332
+ "best_final": 7.408647652482614e-05,
333
+ "theoretical_bound": 0.018216467637202898,
334
+ "observed_regret": "nan",
335
+ "bound_valid": null,
336
+ "tightness_ratio": "nan"
337
+ },
338
+ {
339
+ "pde": "kdv1d",
340
+ "k": 20,
341
+ "n_runs": 30,
342
+ "P": 3,
343
+ "rho_k": 0.23648498331479423,
344
+ "rho_p": 0.20832630526821463,
345
+ "sigma": 0.0011290283725704283,
346
+ "delta_gap": 7.576095486001578e-05,
347
+ "best_policy": "hybrid_no_gate",
348
+ "best_final": 0.00012927247917104978,
349
+ "theoretical_bound": 0.02954610928923126,
350
+ "observed_regret": "nan",
351
+ "bound_valid": null,
352
+ "tightness_ratio": "nan"
353
+ },
354
+ {
355
+ "pde": "navier_stokes2d",
356
+ "k": 20,
357
+ "n_runs": 30,
358
+ "P": 3,
359
+ "rho_k": 0.9065628476084538,
360
+ "rho_p": 5.306270459748493e-12,
361
+ "sigma": 0.04190586954704436,
362
+ "delta_gap": 0.005380900483578442,
363
+ "best_policy": "hybrid_full",
364
+ "best_final": 0.01304085785523057,
365
+ "theoretical_bound": 0.28607239516139726,
366
+ "observed_regret": "nan",
367
+ "bound_valid": null,
368
+ "tightness_ratio": "nan"
369
+ },
370
+ {
371
+ "pde": "reaction_diffusion1d",
372
+ "k": 20,
373
+ "n_runs": 30,
374
+ "P": 3,
375
+ "rho_k": 0.9012235817575083,
376
+ "rho_p": 1.1167932235809832e-11,
377
+ "sigma": 0.0032664115314064196,
378
+ "delta_gap": 0.0011453424813225863,
379
+ "best_policy": "hybrid_full",
380
+ "best_final": 0.0014936716062948108,
381
+ "theoretical_bound": 0.02243041792455206,
382
+ "observed_regret": "nan",
383
+ "bound_valid": null,
384
+ "tightness_ratio": "nan"
385
+ },
386
+ {
387
+ "pde": "reaction_diffusion1d_stiff",
388
+ "k": 20,
389
+ "n_runs": 30,
390
+ "P": 3,
391
+ "rho_k": 0.9234705228031145,
392
+ "rho_p": 3.6090657942872133e-13,
393
+ "sigma": 0.1305173029775927,
394
+ "delta_gap": 0.04085545371053741,
395
+ "best_policy": "hybrid_full",
396
+ "best_final": 0.00922477392014116,
397
+ "theoretical_bound": 0.8746696676678738,
398
+ "observed_regret": "nan",
399
+ "bound_valid": null,
400
+ "tightness_ratio": "nan"
401
+ },
402
+ {
403
+ "pde": "wave2d",
404
+ "k": 20,
405
+ "n_runs": 30,
406
+ "P": 3,
407
+ "rho_k": 0.8082313681868742,
408
+ "rho_p": 6.606913699199893e-08,
409
+ "sigma": 0.011859093693580609,
410
+ "delta_gap": 0.004747881554067135,
411
+ "best_policy": "hybrid_full",
412
+ "best_final": 0.05684403423219919,
413
+ "theoretical_bound": 0.09080605550676685,
414
+ "observed_regret": "nan",
415
+ "bound_valid": null,
416
+ "tightness_ratio": "nan"
417
+ },
418
+ {
419
+ "pde": "advdiff1d",
420
+ "k": 50,
421
+ "n_runs": 40,
422
+ "P": 4,
423
+ "rho_k": 0.905065666041276,
424
+ "rho_p": 1.0951572654152202e-15,
425
+ "sigma": 0.022165220904614247,
426
+ "delta_gap": 0.0001853690831921995,
427
+ "best_policy": "hybrid_no_gate",
428
+ "best_final": 0.00028148697165306655,
429
+ "theoretical_bound": 0.15604951659196986,
430
+ "observed_regret": 0.02441836497746408,
431
+ "bound_valid": true,
432
+ "tightness_ratio": 6.390661976589723
433
+ },
434
+ {
435
+ "pde": "advdiff1d_highpe",
436
+ "k": 50,
437
+ "n_runs": 30,
438
+ "P": 3,
439
+ "rho_k": 0.8869855394883204,
440
+ "rho_p": 6.719839067389329e-11,
441
+ "sigma": 0.12231016894946704,
442
+ "delta_gap": 0.11614939272403713,
443
+ "best_policy": "hybrid_full",
444
+ "best_final": 0.32731066793203356,
445
+ "theoretical_bound": 0.8533850667490278,
446
+ "observed_regret": 0.007624248415231703,
447
+ "bound_valid": true,
448
+ "tightness_ratio": 111.93038582585234
449
+ },
450
+ {
451
+ "pde": "allencahn1d",
452
+ "k": 50,
453
+ "n_runs": 40,
454
+ "P": 4,
455
+ "rho_k": 0.9290806754221389,
456
+ "rho_p": 5.316399370726143e-18,
457
+ "sigma": 0.027345515664390047,
458
+ "delta_gap": 0.0005680945527274158,
459
+ "best_policy": "hybrid_full_lambda0.1",
460
+ "best_final": 0.002289587585255504,
461
+ "theoretical_bound": 0.18754398691968574,
462
+ "observed_regret": 0.008569034934043887,
463
+ "bound_valid": true,
464
+ "tightness_ratio": 21.886243709264498
465
+ },
466
+ {
467
+ "pde": "allencahn1d_sharp",
468
+ "k": 50,
469
+ "n_runs": 30,
470
+ "P": 3,
471
+ "rho_k": 0.8589543937708565,
472
+ "rho_p": 1.2482452471230543e-09,
473
+ "sigma": 0.03299010374381597,
474
+ "delta_gap": 0.005231749545782802,
475
+ "best_policy": "hybrid_full",
476
+ "best_final": 0.01953851627185941,
477
+ "theoretical_bound": 0.23769091811662843,
478
+ "observed_regret": 0.0,
479
+ "bound_valid": true,
480
+ "tightness_ratio": "nan"
481
+ },
482
+ {
483
+ "pde": "burgers1d",
484
+ "k": 50,
485
+ "n_runs": 40,
486
+ "P": 4,
487
+ "rho_k": 0.8962476547842403,
488
+ "rho_p": 5.471521038483582e-15,
489
+ "sigma": 0.007925677449576417,
490
+ "delta_gap": 0.007069513935130091,
491
+ "best_policy": "hybrid_full_lambda0.1",
492
+ "best_final": 0.009187573171220719,
493
+ "theoretical_bound": 0.05634804016162036,
494
+ "observed_regret": 0.09065891541540623,
495
+ "bound_valid": false,
496
+ "tightness_ratio": 0.6215388735176153
497
+ },
498
+ {
499
+ "pde": "burgers1d_lownu",
500
+ "k": 50,
501
+ "n_runs": 40,
502
+ "P": 4,
503
+ "rho_k": 0.9626641651031896,
504
+ "rho_p": 3.6251617446369516e-23,
505
+ "sigma": 0.0032811516581506585,
506
+ "delta_gap": 0.06115469709038735,
507
+ "best_policy": "hybrid_full_lambda0.1",
508
+ "best_final": 0.02386377230286598,
509
+ "theoretical_bound": 0.021718106204466375,
510
+ "observed_regret": 0.11010234057903293,
511
+ "bound_valid": false,
512
+ "tightness_ratio": 0.19725381032092437
513
+ },
514
+ {
515
+ "pde": "burgers1d_verylow",
516
+ "k": 50,
517
+ "n_runs": 30,
518
+ "P": 3,
519
+ "rho_k": 0.8576195773081201,
520
+ "rho_p": 1.411952190491733e-09,
521
+ "sigma": 0.0012683814665875542,
522
+ "delta_gap": 0.0003611462539993228,
523
+ "best_policy": "hybrid_no_gate",
524
+ "best_final": 0.001121796341612935,
525
+ "theoretical_bound": 0.009152805081200317,
526
+ "observed_regret": 0.005458884593099355,
527
+ "bound_valid": true,
528
+ "tightness_ratio": 1.6766804509423947
529
+ },
530
+ {
531
+ "pde": "heat1d",
532
+ "k": 50,
533
+ "n_runs": 50,
534
+ "P": 5,
535
+ "rho_k": 0.927202881152461,
536
+ "rho_p": 4.1636610640680994e-22,
537
+ "sigma": 0.002304168916182272,
538
+ "delta_gap": 5.250379908829927e-05,
539
+ "best_policy": "hybrid_full_lambda0.1",
540
+ "best_final": 7.408647652482614e-05,
541
+ "theoretical_bound": 0.016179068695232668,
542
+ "observed_regret": 0.006860199850052597,
543
+ "bound_valid": true,
544
+ "tightness_ratio": 2.3583961180239705
545
+ },
546
+ {
547
+ "pde": "kdv1d",
548
+ "k": 50,
549
+ "n_runs": 30,
550
+ "P": 3,
551
+ "rho_k": 0.3637374860956618,
552
+ "rho_p": 0.04816715069766343,
553
+ "sigma": 0.0006950684853321834,
554
+ "delta_gap": 7.576095486001578e-05,
555
+ "best_policy": "hybrid_no_gate",
556
+ "best_final": 0.00012927247917104978,
557
+ "theoretical_bound": 0.011826018373714081,
558
+ "observed_regret": 0.0,
559
+ "bound_valid": true,
560
+ "tightness_ratio": "nan"
561
+ },
562
+ {
563
+ "pde": "navier_stokes2d",
564
+ "k": 50,
565
+ "n_runs": 30,
566
+ "P": 3,
567
+ "rho_k": 0.9127919911012237,
568
+ "rho_p": 2.1008509030159187e-12,
569
+ "sigma": 0.04071414035228751,
570
+ "delta_gap": 0.005380900483578442,
571
+ "best_policy": "hybrid_full",
572
+ "best_final": 0.01304085785523057,
573
+ "theoretical_bound": 0.2760402811036355,
574
+ "observed_regret": 0.0,
575
+ "bound_valid": true,
576
+ "tightness_ratio": "nan"
577
+ },
578
+ {
579
+ "pde": "reaction_diffusion1d",
580
+ "k": 50,
581
+ "n_runs": 30,
582
+ "P": 3,
583
+ "rho_k": 0.9065628476084538,
584
+ "rho_p": 5.306270459748493e-12,
585
+ "sigma": 0.0032956333912934695,
586
+ "delta_gap": 0.0011453424813225863,
587
+ "best_policy": "hybrid_full",
588
+ "best_final": 0.0014936716062948108,
589
+ "theoretical_bound": 0.02249779680058438,
590
+ "observed_regret": 0.0,
591
+ "bound_valid": true,
592
+ "tightness_ratio": "nan"
593
+ },
594
+ {
595
+ "pde": "reaction_diffusion1d_stiff",
596
+ "k": 50,
597
+ "n_runs": 30,
598
+ "P": 3,
599
+ "rho_k": 0.9101223581757508,
600
+ "rho_p": 3.150726046667502e-12,
601
+ "sigma": 0.12335024039319076,
602
+ "delta_gap": 0.04085545371053741,
603
+ "best_policy": "hybrid_full",
604
+ "best_final": 0.00922477392014116,
605
+ "theoretical_bound": 0.8387629321606067,
606
+ "observed_regret": 0.012390583753585815,
607
+ "bound_valid": true,
608
+ "tightness_ratio": 67.69357673869644
609
+ },
610
+ {
611
+ "pde": "wave2d",
612
+ "k": 50,
613
+ "n_runs": 30,
614
+ "P": 3,
615
+ "rho_k": 0.8166852057842046,
616
+ "rho_p": 3.7165684629364216e-08,
617
+ "sigma": 0.011718187469546603,
618
+ "delta_gap": 0.004747881554067135,
619
+ "best_policy": "hybrid_full",
620
+ "best_final": 0.05684403423219919,
621
+ "theoretical_bound": 0.08879832334311501,
622
+ "observed_regret": 0.03761967290192842,
623
+ "bound_valid": true,
624
+ "tightness_ratio": 2.3604225261236422
625
+ },
626
+ {
627
+ "pde": "advdiff1d",
628
+ "k": 100,
629
+ "n_runs": 40,
630
+ "P": 4,
631
+ "rho_k": 0.8964352720450284,
632
+ "rho_p": 5.295464186840909e-15,
633
+ "sigma": 0.02189957329494627,
634
+ "delta_gap": 0.0001853690831921995,
635
+ "best_policy": "hybrid_no_gate",
636
+ "best_final": 0.00028148697165306655,
637
+ "theoretical_bound": 0.15566363591615967,
638
+ "observed_regret": 0.02441836497746408,
639
+ "bound_valid": true,
640
+ "tightness_ratio": 6.374859089043143
641
+ },
642
+ {
643
+ "pde": "advdiff1d_highpe",
644
+ "k": 100,
645
+ "n_runs": 30,
646
+ "P": 3,
647
+ "rho_k": 0.8909899888765294,
648
+ "rho_p": 4.1600981493953806e-11,
649
+ "sigma": 0.12311220941484934,
650
+ "delta_gap": 0.11614939272403713,
651
+ "best_policy": "hybrid_full",
652
+ "best_final": 0.32731066793203356,
653
+ "theoretical_bound": 0.8551204911198952,
654
+ "observed_regret": 0.007624248415231703,
655
+ "bound_valid": true,
656
+ "tightness_ratio": 112.15800490072408
657
+ },
658
+ {
659
+ "pde": "allencahn1d",
660
+ "k": 100,
661
+ "n_runs": 40,
662
+ "P": 4,
663
+ "rho_k": 0.9431519699812384,
664
+ "rho_p": 9.005186401051422e-20,
665
+ "sigma": 0.026132665526246074,
666
+ "delta_gap": 0.0005680945527274158,
667
+ "best_policy": "hybrid_full_lambda0.1",
668
+ "best_final": 0.002289587585255504,
669
+ "theoretical_bound": 0.1765519373425457,
670
+ "observed_regret": 0.008569034934043887,
671
+ "bound_valid": true,
672
+ "tightness_ratio": 20.603479703545514
673
+ },
674
+ {
675
+ "pde": "allencahn1d_sharp",
676
+ "k": 100,
677
+ "n_runs": 30,
678
+ "P": 3,
679
+ "rho_k": 0.892769744160178,
680
+ "rho_p": 3.3414889757212515e-11,
681
+ "sigma": 0.03181190565831704,
682
+ "delta_gap": 0.005231749545782802,
683
+ "best_policy": "hybrid_full",
684
+ "best_final": 0.01953851627185941,
685
+ "theoretical_bound": 0.22052063512657386,
686
+ "observed_regret": 0.0,
687
+ "bound_valid": true,
688
+ "tightness_ratio": "nan"
689
+ },
690
+ {
691
+ "pde": "burgers1d",
692
+ "k": 100,
693
+ "n_runs": 40,
694
+ "P": 4,
695
+ "rho_k": 0.8621013133208256,
696
+ "rho_p": 8.946656480449566e-13,
697
+ "sigma": 0.008354963613784586,
698
+ "delta_gap": 0.007069513935130091,
699
+ "best_policy": "hybrid_full_lambda0.1",
700
+ "best_final": 0.009187573171220719,
701
+ "theoretical_bound": 0.06175280793151373,
702
+ "observed_regret": 0.09065891541540623,
703
+ "bound_valid": false,
704
+ "tightness_ratio": 0.6811553794633163
705
+ },
706
+ {
707
+ "pde": "burgers1d_lownu",
708
+ "k": 100,
709
+ "n_runs": 40,
710
+ "P": 4,
711
+ "rho_k": 0.9579737335834897,
712
+ "rho_p": 3.2968190254705303e-22,
713
+ "sigma": 0.0031201223969531833,
714
+ "delta_gap": 0.06115469709038735,
715
+ "best_policy": "hybrid_full_lambda0.1",
716
+ "best_final": 0.02386377230286598,
717
+ "theoretical_bound": 0.020753363042205635,
718
+ "observed_regret": 0.11010234057903293,
719
+ "bound_valid": false,
720
+ "tightness_ratio": 0.18849157005257844
721
+ },
722
+ {
723
+ "pde": "burgers1d_verylow",
724
+ "k": 100,
725
+ "n_runs": 30,
726
+ "P": 3,
727
+ "rho_k": 0.8981090100111234,
728
+ "rho_p": 1.690998550927341e-11,
729
+ "sigma": 0.0014157718666192164,
730
+ "delta_gap": 0.0003611462539993228,
731
+ "best_policy": "hybrid_no_gate",
732
+ "best_final": 0.001121796341612935,
733
+ "theoretical_bound": 0.009755807833727884,
734
+ "observed_regret": 0.005458884593099355,
735
+ "bound_valid": true,
736
+ "tightness_ratio": 1.7871430815848943
737
+ },
738
+ {
739
+ "pde": "heat1d",
740
+ "k": 100,
741
+ "n_runs": 50,
742
+ "P": 5,
743
+ "rho_k": 0.9571668667466987,
744
+ "rho_p": 1.7340572844083043e-27,
745
+ "sigma": 0.002182051040054992,
746
+ "delta_gap": 5.250379908829927e-05,
747
+ "best_policy": "hybrid_full_lambda0.1",
748
+ "best_final": 7.408647652482614e-05,
749
+ "theoretical_bound": 0.01484195895037289,
750
+ "observed_regret": 0.006860199850052597,
751
+ "bound_valid": true,
752
+ "tightness_ratio": 2.1634878392440853
753
+ },
754
+ {
755
+ "pde": "kdv1d",
756
+ "k": 100,
757
+ "n_runs": 30,
758
+ "P": 3,
759
+ "rho_k": 0.4909899888765294,
760
+ "rho_p": 0.005868586082908786,
761
+ "sigma": 0.0005308789908296335,
762
+ "delta_gap": 7.576095486001578e-05,
763
+ "best_policy": "hybrid_no_gate",
764
+ "best_final": 0.00012927247917104978,
765
+ "theoretical_bound": 0.0066914758383352525,
766
+ "observed_regret": 0.0,
767
+ "bound_valid": true,
768
+ "tightness_ratio": "nan"
769
+ },
770
+ {
771
+ "pde": "navier_stokes2d",
772
+ "k": 100,
773
+ "n_runs": 30,
774
+ "P": 3,
775
+ "rho_k": 0.9181312569521689,
776
+ "rho_p": 8.971614810575495e-13,
777
+ "sigma": 0.03871602162835968,
778
+ "delta_gap": 0.005380900483578442,
779
+ "best_policy": "hybrid_full",
780
+ "best_final": 0.01304085785523057,
781
+ "theoretical_bound": 0.2609666216643705,
782
+ "observed_regret": 0.0,
783
+ "bound_valid": true,
784
+ "tightness_ratio": "nan"
785
+ },
786
+ {
787
+ "pde": "reaction_diffusion1d",
788
+ "k": 100,
789
+ "n_runs": 30,
790
+ "P": 3,
791
+ "rho_k": 0.9056729699666296,
792
+ "rho_p": 6.025259751322178e-12,
793
+ "sigma": 0.0033334687376606153,
794
+ "delta_gap": 0.0011453424813225863,
795
+ "best_policy": "hybrid_full",
796
+ "best_final": 0.0014936716062948108,
797
+ "theoretical_bound": 0.02277844078292825,
798
+ "observed_regret": 0.0,
799
+ "bound_valid": true,
800
+ "tightness_ratio": "nan"
801
+ },
802
+ {
803
+ "pde": "reaction_diffusion1d_stiff",
804
+ "k": 100,
805
+ "n_runs": 30,
806
+ "P": 3,
807
+ "rho_k": 0.9167964404894325,
808
+ "rho_p": 1.1157173815784795e-12,
809
+ "sigma": 0.11892722554702172,
810
+ "delta_gap": 0.04085545371053741,
811
+ "best_policy": "hybrid_full",
812
+ "best_final": 0.00922477392014116,
813
+ "theoretical_bound": 0.8028000324155845,
814
+ "observed_regret": 0.012390583753585815,
815
+ "bound_valid": true,
816
+ "tightness_ratio": 64.79113885035929
817
+ },
818
+ {
819
+ "pde": "wave2d",
820
+ "k": 100,
821
+ "n_runs": 30,
822
+ "P": 3,
823
+ "rho_k": 0.8380422691879867,
824
+ "rho_p": 7.548697157347654e-09,
825
+ "sigma": 0.011933024209947561,
826
+ "delta_gap": 0.004747881554067135,
827
+ "best_policy": "hybrid_full",
828
+ "best_final": 0.05684403423219919,
829
+ "theoretical_bound": 0.08812185082213857,
830
+ "observed_regret": 0.03761967290192842,
831
+ "bound_valid": true,
832
+ "tightness_ratio": 2.342440644071133
833
+ }
834
+ ]
results/paper_a/routing_evaluation_full/results.json ADDED
@@ -0,0 +1,753 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "experiment": "routing_evaluation_full",
3
+ "description": "Leave-one-PDE-out routing CV across 13 PDEs (450 decisions)",
4
+ "window_size": 50,
5
+ "n_samples": 450,
6
+ "n_pdes": 13,
7
+ "target_metrics": [
8
+ "pde_residual_norm",
9
+ "relative_l2_error"
10
+ ],
11
+ "results": {
12
+ "pde_residual_norm": {
13
+ "RandomForest": {
14
+ "routing_accuracy": 0.5385,
15
+ "correct_folds": 7,
16
+ "total_folds": 13,
17
+ "mean_r2": -9.9685,
18
+ "fold_details": [
19
+ {
20
+ "held_out_pde": "advdiff1d",
21
+ "n_test": 40,
22
+ "r2": 0.4961,
23
+ "actual_best": "hybrid_no_gate",
24
+ "predicted_best": "hybrid_no_gate",
25
+ "correct": true
26
+ },
27
+ {
28
+ "held_out_pde": "advdiff1d_highpe",
29
+ "n_test": 30,
30
+ "r2": -88.0069,
31
+ "actual_best": "pinn_only",
32
+ "predicted_best": "hybrid_full",
33
+ "correct": false
34
+ },
35
+ {
36
+ "held_out_pde": "allencahn1d",
37
+ "n_test": 40,
38
+ "r2": 0.9714,
39
+ "actual_best": "hybrid_full",
40
+ "predicted_best": "hybrid_full",
41
+ "correct": true
42
+ },
43
+ {
44
+ "held_out_pde": "allencahn1d_sharp",
45
+ "n_test": 30,
46
+ "r2": 0.9175,
47
+ "actual_best": "hybrid_full",
48
+ "predicted_best": "hybrid_full",
49
+ "correct": true
50
+ },
51
+ {
52
+ "held_out_pde": "burgers1d",
53
+ "n_test": 40,
54
+ "r2": 0.7832,
55
+ "actual_best": "hybrid_full",
56
+ "predicted_best": "hybrid_no_gate",
57
+ "correct": false
58
+ },
59
+ {
60
+ "held_out_pde": "burgers1d_lownu",
61
+ "n_test": 40,
62
+ "r2": -0.3254,
63
+ "actual_best": "hybrid_no_gate",
64
+ "predicted_best": "hybrid_no_gate",
65
+ "correct": true
66
+ },
67
+ {
68
+ "held_out_pde": "burgers1d_verylow",
69
+ "n_test": 30,
70
+ "r2": 0.5703,
71
+ "actual_best": "hybrid_no_gate",
72
+ "predicted_best": "hybrid_full",
73
+ "correct": false
74
+ },
75
+ {
76
+ "held_out_pde": "heat1d",
77
+ "n_test": 50,
78
+ "r2": 0.1067,
79
+ "actual_best": "hybrid_full",
80
+ "predicted_best": "hybrid_full",
81
+ "correct": true
82
+ },
83
+ {
84
+ "held_out_pde": "kdv1d",
85
+ "n_test": 30,
86
+ "r2": -35.4865,
87
+ "actual_best": "hybrid_no_gate",
88
+ "predicted_best": "hybrid_full",
89
+ "correct": false
90
+ },
91
+ {
92
+ "held_out_pde": "navier_stokes2d",
93
+ "n_test": 30,
94
+ "r2": -7.5116,
95
+ "actual_best": "hybrid_full",
96
+ "predicted_best": "hybrid_full",
97
+ "correct": true
98
+ },
99
+ {
100
+ "held_out_pde": "reaction_diffusion1d",
101
+ "n_test": 30,
102
+ "r2": -2.5052,
103
+ "actual_best": "hybrid_full",
104
+ "predicted_best": "hybrid_full",
105
+ "correct": true
106
+ },
107
+ {
108
+ "held_out_pde": "reaction_diffusion1d_stiff",
109
+ "n_test": 30,
110
+ "r2": 0.4672,
111
+ "actual_best": "hybrid_full",
112
+ "predicted_best": "hybrid_no_gate",
113
+ "correct": false
114
+ },
115
+ {
116
+ "held_out_pde": "wave2d",
117
+ "n_test": 30,
118
+ "r2": -0.0675,
119
+ "actual_best": "pinn_only",
120
+ "predicted_best": "hybrid_no_gate",
121
+ "correct": false
122
+ }
123
+ ]
124
+ },
125
+ "GradientBoosting": {
126
+ "routing_accuracy": 0.6154,
127
+ "correct_folds": 8,
128
+ "total_folds": 13,
129
+ "mean_r2": -8.0206,
130
+ "fold_details": [
131
+ {
132
+ "held_out_pde": "advdiff1d",
133
+ "n_test": 40,
134
+ "r2": 0.5311,
135
+ "actual_best": "hybrid_no_gate",
136
+ "predicted_best": "hybrid_no_gate",
137
+ "correct": true
138
+ },
139
+ {
140
+ "held_out_pde": "advdiff1d_highpe",
141
+ "n_test": 30,
142
+ "r2": -79.6487,
143
+ "actual_best": "pinn_only",
144
+ "predicted_best": "pinn_only",
145
+ "correct": true
146
+ },
147
+ {
148
+ "held_out_pde": "allencahn1d",
149
+ "n_test": 40,
150
+ "r2": 0.9577,
151
+ "actual_best": "hybrid_full",
152
+ "predicted_best": "hybrid_full",
153
+ "correct": true
154
+ },
155
+ {
156
+ "held_out_pde": "allencahn1d_sharp",
157
+ "n_test": 30,
158
+ "r2": 0.9311,
159
+ "actual_best": "hybrid_full",
160
+ "predicted_best": "hybrid_full",
161
+ "correct": true
162
+ },
163
+ {
164
+ "held_out_pde": "burgers1d",
165
+ "n_test": 40,
166
+ "r2": 0.7384,
167
+ "actual_best": "hybrid_full",
168
+ "predicted_best": "hybrid_no_gate",
169
+ "correct": false
170
+ },
171
+ {
172
+ "held_out_pde": "burgers1d_lownu",
173
+ "n_test": 40,
174
+ "r2": -0.3081,
175
+ "actual_best": "hybrid_no_gate",
176
+ "predicted_best": "hybrid_full",
177
+ "correct": false
178
+ },
179
+ {
180
+ "held_out_pde": "burgers1d_verylow",
181
+ "n_test": 30,
182
+ "r2": 0.6047,
183
+ "actual_best": "hybrid_no_gate",
184
+ "predicted_best": "hybrid_full",
185
+ "correct": false
186
+ },
187
+ {
188
+ "held_out_pde": "heat1d",
189
+ "n_test": 50,
190
+ "r2": -0.0106,
191
+ "actual_best": "hybrid_full",
192
+ "predicted_best": "hybrid_full",
193
+ "correct": true
194
+ },
195
+ {
196
+ "held_out_pde": "kdv1d",
197
+ "n_test": 30,
198
+ "r2": -16.9988,
199
+ "actual_best": "hybrid_no_gate",
200
+ "predicted_best": "hybrid_full",
201
+ "correct": false
202
+ },
203
+ {
204
+ "held_out_pde": "navier_stokes2d",
205
+ "n_test": 30,
206
+ "r2": -10.4736,
207
+ "actual_best": "hybrid_full",
208
+ "predicted_best": "hybrid_full",
209
+ "correct": true
210
+ },
211
+ {
212
+ "held_out_pde": "reaction_diffusion1d",
213
+ "n_test": 30,
214
+ "r2": -0.5074,
215
+ "actual_best": "hybrid_full",
216
+ "predicted_best": "hybrid_full",
217
+ "correct": true
218
+ },
219
+ {
220
+ "held_out_pde": "reaction_diffusion1d_stiff",
221
+ "n_test": 30,
222
+ "r2": 0.4164,
223
+ "actual_best": "hybrid_full",
224
+ "predicted_best": "hybrid_no_gate",
225
+ "correct": false
226
+ },
227
+ {
228
+ "held_out_pde": "wave2d",
229
+ "n_test": 30,
230
+ "r2": -0.5002,
231
+ "actual_best": "pinn_only",
232
+ "predicted_best": "pinn_only",
233
+ "correct": true
234
+ }
235
+ ]
236
+ },
237
+ "Ridge": {
238
+ "routing_accuracy": 0.4615,
239
+ "correct_folds": 6,
240
+ "total_folds": 13,
241
+ "mean_r2": -35.8126,
242
+ "fold_details": [
243
+ {
244
+ "held_out_pde": "advdiff1d",
245
+ "n_test": 40,
246
+ "r2": 0.0002,
247
+ "actual_best": "hybrid_no_gate",
248
+ "predicted_best": "hybrid_full_lambda0.1",
249
+ "correct": false
250
+ },
251
+ {
252
+ "held_out_pde": "advdiff1d_highpe",
253
+ "n_test": 30,
254
+ "r2": -316.75,
255
+ "actual_best": "pinn_only",
256
+ "predicted_best": "hybrid_full",
257
+ "correct": false
258
+ },
259
+ {
260
+ "held_out_pde": "allencahn1d",
261
+ "n_test": 40,
262
+ "r2": 0.4175,
263
+ "actual_best": "hybrid_full",
264
+ "predicted_best": "hybrid_full_lambda0.1",
265
+ "correct": false
266
+ },
267
+ {
268
+ "held_out_pde": "allencahn1d_sharp",
269
+ "n_test": 30,
270
+ "r2": 0.0592,
271
+ "actual_best": "hybrid_full",
272
+ "predicted_best": "hybrid_full",
273
+ "correct": true
274
+ },
275
+ {
276
+ "held_out_pde": "burgers1d",
277
+ "n_test": 40,
278
+ "r2": 0.1255,
279
+ "actual_best": "hybrid_full",
280
+ "predicted_best": "hybrid_no_gate",
281
+ "correct": false
282
+ },
283
+ {
284
+ "held_out_pde": "burgers1d_lownu",
285
+ "n_test": 40,
286
+ "r2": -2.8803,
287
+ "actual_best": "hybrid_no_gate",
288
+ "predicted_best": "hybrid_no_gate",
289
+ "correct": true
290
+ },
291
+ {
292
+ "held_out_pde": "burgers1d_verylow",
293
+ "n_test": 30,
294
+ "r2": 0.2954,
295
+ "actual_best": "hybrid_no_gate",
296
+ "predicted_best": "hybrid_no_gate",
297
+ "correct": true
298
+ },
299
+ {
300
+ "held_out_pde": "heat1d",
301
+ "n_test": 50,
302
+ "r2": -7.1412,
303
+ "actual_best": "hybrid_full",
304
+ "predicted_best": "hybrid_full_lambda0.5",
305
+ "correct": false
306
+ },
307
+ {
308
+ "held_out_pde": "kdv1d",
309
+ "n_test": 30,
310
+ "r2": -117.6034,
311
+ "actual_best": "hybrid_no_gate",
312
+ "predicted_best": "hybrid_no_gate",
313
+ "correct": true
314
+ },
315
+ {
316
+ "held_out_pde": "navier_stokes2d",
317
+ "n_test": 30,
318
+ "r2": -0.3631,
319
+ "actual_best": "hybrid_full",
320
+ "predicted_best": "hybrid_full",
321
+ "correct": true
322
+ },
323
+ {
324
+ "held_out_pde": "reaction_diffusion1d",
325
+ "n_test": 30,
326
+ "r2": -5.9736,
327
+ "actual_best": "hybrid_full",
328
+ "predicted_best": "hybrid_full",
329
+ "correct": true
330
+ },
331
+ {
332
+ "held_out_pde": "reaction_diffusion1d_stiff",
333
+ "n_test": 30,
334
+ "r2": 0.3954,
335
+ "actual_best": "hybrid_full",
336
+ "predicted_best": "hybrid_no_gate",
337
+ "correct": false
338
+ },
339
+ {
340
+ "held_out_pde": "wave2d",
341
+ "n_test": 30,
342
+ "r2": -16.1455,
343
+ "actual_best": "pinn_only",
344
+ "predicted_best": "hybrid_full",
345
+ "correct": false
346
+ }
347
+ ]
348
+ },
349
+ "physics_final": {
350
+ "routing_accuracy": 0.6923,
351
+ "correct_folds": 9,
352
+ "total_folds": 13,
353
+ "mean_r2": -3.2678,
354
+ "fold_details": [
355
+ {
356
+ "held_out_pde": "advdiff1d",
357
+ "n_test": 40,
358
+ "r2": -0.1168,
359
+ "actual_best": "hybrid_no_gate",
360
+ "predicted_best": "hybrid_no_gate",
361
+ "correct": true
362
+ },
363
+ {
364
+ "held_out_pde": "advdiff1d_highpe",
365
+ "n_test": 30,
366
+ "r2": -10.1141,
367
+ "actual_best": "pinn_only",
368
+ "predicted_best": "pinn_only",
369
+ "correct": true
370
+ },
371
+ {
372
+ "held_out_pde": "allencahn1d",
373
+ "n_test": 40,
374
+ "r2": -0.1055,
375
+ "actual_best": "hybrid_full",
376
+ "predicted_best": "hybrid_full",
377
+ "correct": true
378
+ },
379
+ {
380
+ "held_out_pde": "allencahn1d_sharp",
381
+ "n_test": 30,
382
+ "r2": -0.7096,
383
+ "actual_best": "hybrid_full",
384
+ "predicted_best": "hybrid_full",
385
+ "correct": true
386
+ },
387
+ {
388
+ "held_out_pde": "burgers1d",
389
+ "n_test": 40,
390
+ "r2": 0.1058,
391
+ "actual_best": "hybrid_full",
392
+ "predicted_best": "hybrid_no_gate",
393
+ "correct": false
394
+ },
395
+ {
396
+ "held_out_pde": "burgers1d_lownu",
397
+ "n_test": 40,
398
+ "r2": -1.7731,
399
+ "actual_best": "hybrid_no_gate",
400
+ "predicted_best": "pinn_only",
401
+ "correct": false
402
+ },
403
+ {
404
+ "held_out_pde": "burgers1d_verylow",
405
+ "n_test": 30,
406
+ "r2": 0.0792,
407
+ "actual_best": "hybrid_no_gate",
408
+ "predicted_best": "hybrid_full",
409
+ "correct": false
410
+ },
411
+ {
412
+ "held_out_pde": "heat1d",
413
+ "n_test": 50,
414
+ "r2": -1.8716,
415
+ "actual_best": "hybrid_full",
416
+ "predicted_best": "hybrid_full",
417
+ "correct": true
418
+ },
419
+ {
420
+ "held_out_pde": "kdv1d",
421
+ "n_test": 30,
422
+ "r2": -7.3348,
423
+ "actual_best": "hybrid_no_gate",
424
+ "predicted_best": "hybrid_no_gate",
425
+ "correct": true
426
+ },
427
+ {
428
+ "held_out_pde": "navier_stokes2d",
429
+ "n_test": 30,
430
+ "r2": -14.239,
431
+ "actual_best": "hybrid_full",
432
+ "predicted_best": "hybrid_full",
433
+ "correct": true
434
+ },
435
+ {
436
+ "held_out_pde": "reaction_diffusion1d",
437
+ "n_test": 30,
438
+ "r2": -2.5604,
439
+ "actual_best": "hybrid_full",
440
+ "predicted_best": "hybrid_full",
441
+ "correct": true
442
+ },
443
+ {
444
+ "held_out_pde": "reaction_diffusion1d_stiff",
445
+ "n_test": 30,
446
+ "r2": 0.5488,
447
+ "actual_best": "hybrid_full",
448
+ "predicted_best": "hybrid_no_gate",
449
+ "correct": false
450
+ },
451
+ {
452
+ "held_out_pde": "wave2d",
453
+ "n_test": 30,
454
+ "r2": -4.3907,
455
+ "actual_best": "pinn_only",
456
+ "predicted_best": "pinn_only",
457
+ "correct": true
458
+ }
459
+ ]
460
+ }
461
+ },
462
+ "relative_l2_error": {
463
+ "RandomForest": {
464
+ "routing_accuracy": 0.625,
465
+ "correct_folds": 5,
466
+ "total_folds": 8,
467
+ "mean_r2": -11.2523,
468
+ "fold_details": [
469
+ {
470
+ "held_out_pde": "advdiff1d",
471
+ "n_test": 40,
472
+ "r2": 0.8837,
473
+ "actual_best": "hybrid_no_gate",
474
+ "predicted_best": "hybrid_no_gate",
475
+ "correct": true
476
+ },
477
+ {
478
+ "held_out_pde": "advdiff1d_highpe",
479
+ "n_test": 30,
480
+ "r2": -2.7153,
481
+ "actual_best": "hybrid_full",
482
+ "predicted_best": "hybrid_full",
483
+ "correct": true
484
+ },
485
+ {
486
+ "held_out_pde": "allencahn1d",
487
+ "n_test": 40,
488
+ "r2": 0.984,
489
+ "actual_best": "hybrid_full",
490
+ "predicted_best": "hybrid_full_lambda0.1",
491
+ "correct": false
492
+ },
493
+ {
494
+ "held_out_pde": "allencahn1d_sharp",
495
+ "n_test": 30,
496
+ "r2": -0.766,
497
+ "actual_best": "hybrid_full",
498
+ "predicted_best": "hybrid_full",
499
+ "correct": true
500
+ },
501
+ {
502
+ "held_out_pde": "heat1d",
503
+ "n_test": 50,
504
+ "r2": 0.6429,
505
+ "actual_best": "hybrid_no_gate",
506
+ "predicted_best": "hybrid_full",
507
+ "correct": false
508
+ },
509
+ {
510
+ "held_out_pde": "kdv1d",
511
+ "n_test": 30,
512
+ "r2": -29.1038,
513
+ "actual_best": "hybrid_no_gate",
514
+ "predicted_best": "pinn_only",
515
+ "correct": false
516
+ },
517
+ {
518
+ "held_out_pde": "navier_stokes2d",
519
+ "n_test": 30,
520
+ "r2": -59.2537,
521
+ "actual_best": "hybrid_full",
522
+ "predicted_best": "hybrid_full",
523
+ "correct": true
524
+ },
525
+ {
526
+ "held_out_pde": "wave2d",
527
+ "n_test": 30,
528
+ "r2": -0.69,
529
+ "actual_best": "hybrid_full",
530
+ "predicted_best": "hybrid_full",
531
+ "correct": true
532
+ }
533
+ ]
534
+ },
535
+ "GradientBoosting": {
536
+ "routing_accuracy": 0.625,
537
+ "correct_folds": 5,
538
+ "total_folds": 8,
539
+ "mean_r2": -11.68,
540
+ "fold_details": [
541
+ {
542
+ "held_out_pde": "advdiff1d",
543
+ "n_test": 40,
544
+ "r2": 0.6942,
545
+ "actual_best": "hybrid_no_gate",
546
+ "predicted_best": "hybrid_no_gate",
547
+ "correct": true
548
+ },
549
+ {
550
+ "held_out_pde": "advdiff1d_highpe",
551
+ "n_test": 30,
552
+ "r2": -1.866,
553
+ "actual_best": "hybrid_full",
554
+ "predicted_best": "hybrid_full",
555
+ "correct": true
556
+ },
557
+ {
558
+ "held_out_pde": "allencahn1d",
559
+ "n_test": 40,
560
+ "r2": 0.9833,
561
+ "actual_best": "hybrid_full",
562
+ "predicted_best": "hybrid_full_lambda0.1",
563
+ "correct": false
564
+ },
565
+ {
566
+ "held_out_pde": "allencahn1d_sharp",
567
+ "n_test": 30,
568
+ "r2": -1.0721,
569
+ "actual_best": "hybrid_full",
570
+ "predicted_best": "hybrid_full",
571
+ "correct": true
572
+ },
573
+ {
574
+ "held_out_pde": "heat1d",
575
+ "n_test": 50,
576
+ "r2": 0.6744,
577
+ "actual_best": "hybrid_no_gate",
578
+ "predicted_best": "hybrid_full",
579
+ "correct": false
580
+ },
581
+ {
582
+ "held_out_pde": "kdv1d",
583
+ "n_test": 30,
584
+ "r2": -28.1846,
585
+ "actual_best": "hybrid_no_gate",
586
+ "predicted_best": "pinn_only",
587
+ "correct": false
588
+ },
589
+ {
590
+ "held_out_pde": "navier_stokes2d",
591
+ "n_test": 30,
592
+ "r2": -63.6497,
593
+ "actual_best": "hybrid_full",
594
+ "predicted_best": "hybrid_full",
595
+ "correct": true
596
+ },
597
+ {
598
+ "held_out_pde": "wave2d",
599
+ "n_test": 30,
600
+ "r2": -1.0196,
601
+ "actual_best": "hybrid_full",
602
+ "predicted_best": "hybrid_full",
603
+ "correct": true
604
+ }
605
+ ]
606
+ },
607
+ "Ridge": {
608
+ "routing_accuracy": 0.75,
609
+ "correct_folds": 6,
610
+ "total_folds": 8,
611
+ "mean_r2": -85.4629,
612
+ "fold_details": [
613
+ {
614
+ "held_out_pde": "advdiff1d",
615
+ "n_test": 40,
616
+ "r2": -1.5566,
617
+ "actual_best": "hybrid_no_gate",
618
+ "predicted_best": "hybrid_no_gate",
619
+ "correct": true
620
+ },
621
+ {
622
+ "held_out_pde": "advdiff1d_highpe",
623
+ "n_test": 30,
624
+ "r2": 0.0695,
625
+ "actual_best": "hybrid_full",
626
+ "predicted_best": "hybrid_full",
627
+ "correct": true
628
+ },
629
+ {
630
+ "held_out_pde": "allencahn1d",
631
+ "n_test": 40,
632
+ "r2": 0.7642,
633
+ "actual_best": "hybrid_full",
634
+ "predicted_best": "hybrid_full",
635
+ "correct": true
636
+ },
637
+ {
638
+ "held_out_pde": "allencahn1d_sharp",
639
+ "n_test": 30,
640
+ "r2": 0.7137,
641
+ "actual_best": "hybrid_full",
642
+ "predicted_best": "hybrid_full",
643
+ "correct": true
644
+ },
645
+ {
646
+ "held_out_pde": "heat1d",
647
+ "n_test": 50,
648
+ "r2": -1.2455,
649
+ "actual_best": "hybrid_no_gate",
650
+ "predicted_best": "hybrid_full_lambda0.1",
651
+ "correct": false
652
+ },
653
+ {
654
+ "held_out_pde": "kdv1d",
655
+ "n_test": 30,
656
+ "r2": -657.2961,
657
+ "actual_best": "hybrid_no_gate",
658
+ "predicted_best": "hybrid_full",
659
+ "correct": false
660
+ },
661
+ {
662
+ "held_out_pde": "navier_stokes2d",
663
+ "n_test": 30,
664
+ "r2": -21.7633,
665
+ "actual_best": "hybrid_full",
666
+ "predicted_best": "hybrid_full",
667
+ "correct": true
668
+ },
669
+ {
670
+ "held_out_pde": "wave2d",
671
+ "n_test": 30,
672
+ "r2": -3.3891,
673
+ "actual_best": "hybrid_full",
674
+ "predicted_best": "hybrid_full",
675
+ "correct": true
676
+ }
677
+ ]
678
+ },
679
+ "physics_final": {
680
+ "routing_accuracy": 0.625,
681
+ "correct_folds": 5,
682
+ "total_folds": 8,
683
+ "mean_r2": -4.2033,
684
+ "fold_details": [
685
+ {
686
+ "held_out_pde": "advdiff1d",
687
+ "n_test": 40,
688
+ "r2": -0.1232,
689
+ "actual_best": "hybrid_no_gate",
690
+ "predicted_best": "hybrid_no_gate",
691
+ "correct": true
692
+ },
693
+ {
694
+ "held_out_pde": "advdiff1d_highpe",
695
+ "n_test": 30,
696
+ "r2": -16.7223,
697
+ "actual_best": "hybrid_full",
698
+ "predicted_best": "pinn_only",
699
+ "correct": false
700
+ },
701
+ {
702
+ "held_out_pde": "allencahn1d",
703
+ "n_test": 40,
704
+ "r2": -0.0461,
705
+ "actual_best": "hybrid_full",
706
+ "predicted_best": "hybrid_full",
707
+ "correct": true
708
+ },
709
+ {
710
+ "held_out_pde": "allencahn1d_sharp",
711
+ "n_test": 30,
712
+ "r2": -1.1796,
713
+ "actual_best": "hybrid_full",
714
+ "predicted_best": "hybrid_full",
715
+ "correct": true
716
+ },
717
+ {
718
+ "held_out_pde": "heat1d",
719
+ "n_test": 50,
720
+ "r2": -0.5166,
721
+ "actual_best": "hybrid_no_gate",
722
+ "predicted_best": "hybrid_full",
723
+ "correct": false
724
+ },
725
+ {
726
+ "held_out_pde": "kdv1d",
727
+ "n_test": 30,
728
+ "r2": -2.2666,
729
+ "actual_best": "hybrid_no_gate",
730
+ "predicted_best": "hybrid_no_gate",
731
+ "correct": true
732
+ },
733
+ {
734
+ "held_out_pde": "navier_stokes2d",
735
+ "n_test": 30,
736
+ "r2": -3.6428,
737
+ "actual_best": "hybrid_full",
738
+ "predicted_best": "hybrid_full",
739
+ "correct": true
740
+ },
741
+ {
742
+ "held_out_pde": "wave2d",
743
+ "n_test": 30,
744
+ "r2": -9.1289,
745
+ "actual_best": "hybrid_full",
746
+ "predicted_best": "pinn_only",
747
+ "correct": false
748
+ }
749
+ ]
750
+ }
751
+ }
752
+ }
753
+ }
results/paper_a/scaling_ablation/results.json ADDED
@@ -0,0 +1,247 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "experiment": "scaling_and_ablation",
3
+ "target_metric": "pde_residual_norm",
4
+ "window_size": 50,
5
+ "scaling": {
6
+ "5 PDEs": {
7
+ "n_pdes": 5,
8
+ "n_samples": 190,
9
+ "rf_accuracy": 0.8,
10
+ "physics_final_accuracy": 0.8,
11
+ "random_accuracy": 0.2733333333333333,
12
+ "pdes": [
13
+ "advdiff1d",
14
+ "burgers1d",
15
+ "heat1d",
16
+ "kdv1d",
17
+ "wave2d"
18
+ ]
19
+ },
20
+ "9 PDEs": {
21
+ "n_pdes": 9,
22
+ "n_samples": 330,
23
+ "rf_accuracy": 0.7777777777777778,
24
+ "physics_final_accuracy": 0.7777777777777778,
25
+ "random_accuracy": 0.28148148148148144,
26
+ "pdes": [
27
+ "advdiff1d",
28
+ "advdiff1d_highpe",
29
+ "allencahn1d",
30
+ "burgers1d",
31
+ "burgers1d_lownu",
32
+ "heat1d",
33
+ "kdv1d",
34
+ "reaction_diffusion1d",
35
+ "wave2d"
36
+ ]
37
+ },
38
+ "13 PDEs": {
39
+ "n_pdes": 13,
40
+ "n_samples": 450,
41
+ "rf_accuracy": 0.5384615384615384,
42
+ "physics_final_accuracy": 0.6923076923076923,
43
+ "random_accuracy": 0.2974358974358975,
44
+ "pdes": [
45
+ "advdiff1d",
46
+ "advdiff1d_highpe",
47
+ "allencahn1d",
48
+ "allencahn1d_sharp",
49
+ "burgers1d",
50
+ "burgers1d_lownu",
51
+ "burgers1d_verylow",
52
+ "heat1d",
53
+ "kdv1d",
54
+ "navier_stokes2d",
55
+ "reaction_diffusion1d",
56
+ "reaction_diffusion1d_stiff",
57
+ "wave2d"
58
+ ]
59
+ }
60
+ },
61
+ "feature_ablation": {
62
+ "top-3": {
63
+ "k": 3,
64
+ "rf_accuracy": 0.5384615384615384,
65
+ "physics_final_accuracy": 0.0,
66
+ "random_accuracy": 0.0
67
+ },
68
+ "top-5": {
69
+ "k": 5,
70
+ "rf_accuracy": 0.6153846153846154,
71
+ "physics_final_accuracy": 0.0,
72
+ "random_accuracy": 0.0
73
+ },
74
+ "top-10": {
75
+ "k": 10,
76
+ "rf_accuracy": 0.6153846153846154,
77
+ "physics_final_accuracy": 0.0,
78
+ "random_accuracy": 0.0
79
+ },
80
+ "top-20": {
81
+ "k": 20,
82
+ "rf_accuracy": 0.5384615384615384,
83
+ "physics_final_accuracy": 0.0,
84
+ "random_accuracy": 0.0
85
+ },
86
+ "all (38)": {
87
+ "k": 38,
88
+ "rf_accuracy": 0.5384615384615384,
89
+ "physics_final_accuracy": 0.0,
90
+ "random_accuracy": 0.0
91
+ }
92
+ },
93
+ "feature_ranking": [
94
+ {
95
+ "feature": "physics_loss_min",
96
+ "importance": 0.3483558469300632
97
+ },
98
+ {
99
+ "feature": "physics_loss_final",
100
+ "importance": 0.33053396507395816
101
+ },
102
+ {
103
+ "feature": "bc_loss_std",
104
+ "importance": 0.05061896130355744
105
+ },
106
+ {
107
+ "feature": "physics_loss_initial",
108
+ "importance": 0.03409308195107868
109
+ },
110
+ {
111
+ "feature": "physics_loss_std",
112
+ "importance": 0.027531807347155282
113
+ },
114
+ {
115
+ "feature": "physics_loss_slope",
116
+ "importance": 0.02710811784813267
117
+ },
118
+ {
119
+ "feature": "total_initial",
120
+ "importance": 0.020126882651335387
121
+ },
122
+ {
123
+ "feature": "bc_loss_slope",
124
+ "importance": 0.018980168122078474
125
+ },
126
+ {
127
+ "feature": "bc_loss_final",
128
+ "importance": 0.018089290958883356
129
+ },
130
+ {
131
+ "feature": "total_final",
132
+ "importance": 0.016293560707510465
133
+ },
134
+ {
135
+ "feature": "physics_loss_mean",
136
+ "importance": 0.015456433985098779
137
+ },
138
+ {
139
+ "feature": "bc_loss_initial",
140
+ "importance": 0.014164117082104343
141
+ },
142
+ {
143
+ "feature": "total_mean",
144
+ "importance": 0.013887249307004997
145
+ },
146
+ {
147
+ "feature": "bc_loss_total_ratio_final",
148
+ "importance": 0.013350109174540036
149
+ },
150
+ {
151
+ "feature": "physics_loss_data_loss_ratio_final",
152
+ "importance": 0.009494170140382837
153
+ },
154
+ {
155
+ "feature": "total_slope",
156
+ "importance": 0.006311847351155205
157
+ },
158
+ {
159
+ "feature": "total_std",
160
+ "importance": 0.006022093569921297
161
+ },
162
+ {
163
+ "feature": "total_ratio",
164
+ "importance": 0.00477636475553249
165
+ },
166
+ {
167
+ "feature": "physics_loss_ratio",
168
+ "importance": 0.004435545069215676
169
+ },
170
+ {
171
+ "feature": "bc_loss_min",
172
+ "importance": 0.003985693061562903
173
+ },
174
+ {
175
+ "feature": "total_min",
176
+ "importance": 0.003673784738809113
177
+ },
178
+ {
179
+ "feature": "bc_loss_mean",
180
+ "importance": 0.0033868495426139095
181
+ },
182
+ {
183
+ "feature": "bc_loss_ratio",
184
+ "importance": 0.0019763690389400877
185
+ },
186
+ {
187
+ "feature": "physics_loss_total_ratio_final",
188
+ "importance": 0.001953300730766482
189
+ },
190
+ {
191
+ "feature": "data_loss_min",
192
+ "importance": 0.001244007081189644
193
+ },
194
+ {
195
+ "feature": "data_loss_slope",
196
+ "importance": 0.0006097711026164307
197
+ },
198
+ {
199
+ "feature": "data_loss_mean",
200
+ "importance": 0.0005987079713801972
201
+ },
202
+ {
203
+ "feature": "data_loss_std",
204
+ "importance": 0.000558956420596431
205
+ },
206
+ {
207
+ "feature": "data_loss_final",
208
+ "importance": 0.0005109980955471159
209
+ },
210
+ {
211
+ "feature": "data_loss_initial",
212
+ "importance": 0.0004823197744087357
213
+ },
214
+ {
215
+ "feature": "data_loss_ratio",
216
+ "importance": 0.00034410759314898746
217
+ },
218
+ {
219
+ "feature": "lambda_physics_min",
220
+ "importance": 0.0002384595870390791
221
+ },
222
+ {
223
+ "feature": "lambda_physics_mean",
224
+ "importance": 0.00018786603430126896
225
+ },
226
+ {
227
+ "feature": "lambda_physics_initial",
228
+ "importance": 0.00018348230032801623
229
+ },
230
+ {
231
+ "feature": "lambda_physics_slope",
232
+ "importance": 0.00016076495882829512
233
+ },
234
+ {
235
+ "feature": "lambda_physics_final",
236
+ "importance": 0.00014787534285176792
237
+ },
238
+ {
239
+ "feature": "lambda_physics_std",
240
+ "importance": 0.00012707329636285402
241
+ },
242
+ {
243
+ "feature": "lambda_physics_ratio",
244
+ "importance": 0.0
245
+ }
246
+ ]
247
+ }
results/paper_a/wave2d/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_c/ablation_statistics/results.json ADDED
@@ -0,0 +1,554 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ [
2
+ {
3
+ "pde": "advdiff1d",
4
+ "comparison": "Causal WITH pretrain",
5
+ "group_a": "full_pipeline_no_causal",
6
+ "group_b": "full_pipeline_with_causal",
7
+ "metric": "pde_residual_norm",
8
+ "n_pairs": 10,
9
+ "mean_a": 0.01762539455667138,
10
+ "mean_b": 0.016057312302291394,
11
+ "mean_diff": 0.0015680822543799877,
12
+ "bootstrap_95ci": [
13
+ 0.0005543198878876865,
14
+ 0.0025394598348066205
15
+ ],
16
+ "wilcoxon_w": 6.0,
17
+ "wilcoxon_w_plus": 49.0,
18
+ "wilcoxon_p": 0.02734375,
19
+ "cohens_d": 0.9143632870287136,
20
+ "interpretation": "Effect of adding causal loss when operator pretraining is present.",
21
+ "bh_fdr_threshold": 0.03541666666666667,
22
+ "bh_fdr_p_adjusted": 0.03860294117647059,
23
+ "bh_fdr_significant": true
24
+ },
25
+ {
26
+ "pde": "advdiff1d",
27
+ "comparison": "Causal WITHOUT pretrain",
28
+ "group_a": "no_pretrain_no_causal",
29
+ "group_b": "no_pretrain_with_causal",
30
+ "metric": "pde_residual_norm",
31
+ "n_pairs": 10,
32
+ "mean_a": 0.1821247458457947,
33
+ "mean_b": 0.20636147111654282,
34
+ "mean_diff": -0.02423672527074814,
35
+ "bootstrap_95ci": [
36
+ -0.030558788552880287,
37
+ -0.01705584198236466
38
+ ],
39
+ "wilcoxon_w": 0.0,
40
+ "wilcoxon_w_plus": 0.0,
41
+ "wilcoxon_p": 0.001953125,
42
+ "cohens_d": -2.1055616986457526,
43
+ "interpretation": "Effect of adding causal loss when operator pretraining is skipped.",
44
+ "bh_fdr_threshold": 0.0020833333333333333,
45
+ "bh_fdr_p_adjusted": 0.046875,
46
+ "bh_fdr_significant": true
47
+ },
48
+ {
49
+ "pde": "advdiff1d",
50
+ "comparison": "Pretrain effect",
51
+ "group_a": "full_pipeline_no_causal",
52
+ "group_b": "no_pretrain_no_causal",
53
+ "metric": "pde_residual_norm",
54
+ "n_pairs": 10,
55
+ "mean_a": 0.01762539455667138,
56
+ "mean_b": 0.1821247458457947,
57
+ "mean_diff": -0.1644993512891233,
58
+ "bootstrap_95ci": [
59
+ -0.16860973108559846,
60
+ -0.16027858398389072
61
+ ],
62
+ "wilcoxon_w": 0.0,
63
+ "wilcoxon_w_plus": 0.0,
64
+ "wilcoxon_p": 0.001953125,
65
+ "cohens_d": -23.132033999563973,
66
+ "interpretation": "Effect of operator pretraining (stage 1) without causal loss.",
67
+ "bh_fdr_threshold": 0.004166666666666667,
68
+ "bh_fdr_p_adjusted": 0.0234375,
69
+ "bh_fdr_significant": true
70
+ },
71
+ {
72
+ "pde": "allencahn1d",
73
+ "comparison": "Causal WITH pretrain",
74
+ "group_a": "full_pipeline_no_causal",
75
+ "group_b": "full_pipeline_with_causal",
76
+ "metric": "pde_residual_norm",
77
+ "n_pairs": 10,
78
+ "mean_a": 0.030599439330399037,
79
+ "mean_b": 0.028846064768731593,
80
+ "mean_diff": 0.0017533745616674424,
81
+ "bootstrap_95ci": [
82
+ 0.00041445910930633546,
83
+ 0.003101756596006453
84
+ ],
85
+ "wilcoxon_w": 9.0,
86
+ "wilcoxon_w_plus": 46.0,
87
+ "wilcoxon_p": 0.064453125,
88
+ "cohens_d": 0.7725815820422364,
89
+ "interpretation": "Effect of adding causal loss when operator pretraining is present.",
90
+ "bh_fdr_threshold": 0.03958333333333334,
91
+ "bh_fdr_p_adjusted": 0.08141447368421052,
92
+ "bh_fdr_significant": false
93
+ },
94
+ {
95
+ "pde": "allencahn1d",
96
+ "comparison": "Causal WITHOUT pretrain",
97
+ "group_a": "no_pretrain_no_causal",
98
+ "group_b": "no_pretrain_with_causal",
99
+ "metric": "pde_residual_norm",
100
+ "n_pairs": 10,
101
+ "mean_a": 0.21832961440086365,
102
+ "mean_b": 0.20653070658445358,
103
+ "mean_diff": 0.011798907816410065,
104
+ "bootstrap_95ci": [
105
+ 0.007019134983420372,
106
+ 0.01675495583564043
107
+ ],
108
+ "wilcoxon_w": 1.0,
109
+ "wilcoxon_w_plus": 54.0,
110
+ "wilcoxon_p": 0.00390625,
111
+ "cohens_d": 1.4198176815408456,
112
+ "interpretation": "Effect of adding causal loss when operator pretraining is skipped.",
113
+ "bh_fdr_threshold": 0.02916666666666667,
114
+ "bh_fdr_p_adjusted": 0.006696428571428571,
115
+ "bh_fdr_significant": true
116
+ },
117
+ {
118
+ "pde": "allencahn1d",
119
+ "comparison": "Pretrain effect",
120
+ "group_a": "full_pipeline_no_causal",
121
+ "group_b": "no_pretrain_no_causal",
122
+ "metric": "pde_residual_norm",
123
+ "n_pairs": 10,
124
+ "mean_a": 0.030599439330399037,
125
+ "mean_b": 0.21832961440086365,
126
+ "mean_diff": -0.1877301750704646,
127
+ "bootstrap_95ci": [
128
+ -0.212612586915493,
129
+ -0.16854976783972234
130
+ ],
131
+ "wilcoxon_w": 0.0,
132
+ "wilcoxon_w_plus": 0.0,
133
+ "wilcoxon_p": 0.001953125,
134
+ "cohens_d": -4.940132204992188,
135
+ "interpretation": "Effect of operator pretraining (stage 1) without causal loss.",
136
+ "bh_fdr_threshold": 0.006250000000000001,
137
+ "bh_fdr_p_adjusted": 0.015625,
138
+ "bh_fdr_significant": true
139
+ },
140
+ {
141
+ "pde": "allencahn1d_sharp",
142
+ "comparison": "Causal WITH pretrain",
143
+ "group_a": "full_pipeline_no_causal",
144
+ "group_b": "full_pipeline_with_causal",
145
+ "metric": "pde_residual_norm",
146
+ "n_pairs": 10,
147
+ "mean_a": 0.04827256985008717,
148
+ "mean_b": 0.04590620547533035,
149
+ "mean_diff": 0.002366364374756813,
150
+ "bootstrap_95ci": [
151
+ 0.000651429332792759,
152
+ 0.004178189458325505
153
+ ],
154
+ "wilcoxon_w": 7.0,
155
+ "wilcoxon_w_plus": 48.0,
156
+ "wilcoxon_p": 0.037109375,
157
+ "cohens_d": 0.7806599248045102,
158
+ "interpretation": "Effect of adding causal loss when operator pretraining is present.",
159
+ "bh_fdr_threshold": 0.0375,
160
+ "bh_fdr_p_adjusted": 0.049479166666666664,
161
+ "bh_fdr_significant": true
162
+ },
163
+ {
164
+ "pde": "allencahn1d_sharp",
165
+ "comparison": "Causal WITHOUT pretrain",
166
+ "group_a": "no_pretrain_no_causal",
167
+ "group_b": "no_pretrain_with_causal",
168
+ "metric": "pde_residual_norm",
169
+ "n_pairs": 10,
170
+ "mean_a": 0.19317871183156968,
171
+ "mean_b": 0.18315862119197845,
172
+ "mean_diff": 0.010020090639591217,
173
+ "bootstrap_95ci": [
174
+ 0.006050471179187299,
175
+ 0.014340778402984141
176
+ ],
177
+ "wilcoxon_w": 0.0,
178
+ "wilcoxon_w_plus": 55.0,
179
+ "wilcoxon_p": 0.001953125,
180
+ "cohens_d": 1.4111086378179183,
181
+ "interpretation": "Effect of adding causal loss when operator pretraining is skipped.",
182
+ "bh_fdr_threshold": 0.008333333333333333,
183
+ "bh_fdr_p_adjusted": 0.01171875,
184
+ "bh_fdr_significant": true
185
+ },
186
+ {
187
+ "pde": "allencahn1d_sharp",
188
+ "comparison": "Pretrain effect",
189
+ "group_a": "full_pipeline_no_causal",
190
+ "group_b": "no_pretrain_no_causal",
191
+ "metric": "pde_residual_norm",
192
+ "n_pairs": 10,
193
+ "mean_a": 0.04827256985008717,
194
+ "mean_b": 0.19317871183156968,
195
+ "mean_diff": -0.1449061419814825,
196
+ "bootstrap_95ci": [
197
+ -0.16476304744370282,
198
+ -0.12863487262278794
199
+ ],
200
+ "wilcoxon_w": 0.0,
201
+ "wilcoxon_w_plus": 0.0,
202
+ "wilcoxon_p": 0.001953125,
203
+ "cohens_d": -4.681868848490021,
204
+ "interpretation": "Effect of operator pretraining (stage 1) without causal loss.",
205
+ "bh_fdr_threshold": 0.010416666666666666,
206
+ "bh_fdr_p_adjusted": 0.009375,
207
+ "bh_fdr_significant": true
208
+ },
209
+ {
210
+ "pde": "burgers1d",
211
+ "comparison": "Causal WITH pretrain",
212
+ "group_a": "full_pipeline_no_causal",
213
+ "group_b": "full_pipeline_with_causal",
214
+ "metric": "pde_residual_norm",
215
+ "n_pairs": 10,
216
+ "mean_a": 0.08208721615374089,
217
+ "mean_b": 0.07969042696058751,
218
+ "mean_diff": 0.002396789193153381,
219
+ "bootstrap_95ci": [
220
+ -0.0005201654322445393,
221
+ 0.0050468135904520725
222
+ ],
223
+ "wilcoxon_w": 13.0,
224
+ "wilcoxon_w_plus": 42.0,
225
+ "wilcoxon_p": 0.16015625,
226
+ "cohens_d": 0.4964139706693682,
227
+ "interpretation": "Effect of adding causal loss when operator pretraining is present.",
228
+ "bh_fdr_threshold": 0.043750000000000004,
229
+ "bh_fdr_p_adjusted": 0.18303571428571427,
230
+ "bh_fdr_significant": false
231
+ },
232
+ {
233
+ "pde": "burgers1d",
234
+ "comparison": "Causal WITHOUT pretrain",
235
+ "group_a": "no_pretrain_no_causal",
236
+ "group_b": "no_pretrain_with_causal",
237
+ "metric": "pde_residual_norm",
238
+ "n_pairs": 10,
239
+ "mean_a": 0.18207424879074097,
240
+ "mean_b": 0.1989459991455078,
241
+ "mean_diff": -0.016871750354766846,
242
+ "bootstrap_95ci": [
243
+ -0.02079994533210993,
244
+ -0.012488777041435245
245
+ ],
246
+ "wilcoxon_w": 0.0,
247
+ "wilcoxon_w_plus": 0.0,
248
+ "wilcoxon_p": 0.001953125,
249
+ "cohens_d": -2.391120339225372,
250
+ "interpretation": "Effect of adding causal loss when operator pretraining is skipped.",
251
+ "bh_fdr_threshold": 0.012500000000000002,
252
+ "bh_fdr_p_adjusted": 0.0078125,
253
+ "bh_fdr_significant": true
254
+ },
255
+ {
256
+ "pde": "burgers1d",
257
+ "comparison": "Pretrain effect",
258
+ "group_a": "full_pipeline_no_causal",
259
+ "group_b": "no_pretrain_no_causal",
260
+ "metric": "pde_residual_norm",
261
+ "n_pairs": 10,
262
+ "mean_a": 0.08208721615374089,
263
+ "mean_b": 0.18207424879074097,
264
+ "mean_diff": -0.09998703263700008,
265
+ "bootstrap_95ci": [
266
+ -0.11976564859971403,
267
+ -0.07653249855153264
268
+ ],
269
+ "wilcoxon_w": 0.0,
270
+ "wilcoxon_w_plus": 0.0,
271
+ "wilcoxon_p": 0.001953125,
272
+ "cohens_d": -2.7233353753020104,
273
+ "interpretation": "Effect of operator pretraining (stage 1) without causal loss.",
274
+ "bh_fdr_threshold": 0.014583333333333335,
275
+ "bh_fdr_p_adjusted": 0.006696428571428571,
276
+ "bh_fdr_significant": true
277
+ },
278
+ {
279
+ "pde": "burgers1d_verylow",
280
+ "comparison": "Causal WITH pretrain",
281
+ "group_a": "full_pipeline_no_causal",
282
+ "group_b": "full_pipeline_with_causal",
283
+ "metric": "pde_residual_norm",
284
+ "n_pairs": 10,
285
+ "mean_a": 0.02990581523627043,
286
+ "mean_b": 0.02931824270635843,
287
+ "mean_diff": 0.0005875725299119949,
288
+ "bootstrap_95ci": [
289
+ -0.0007758385082706809,
290
+ 0.0018868887564167378
291
+ ],
292
+ "wilcoxon_w": 20.0,
293
+ "wilcoxon_w_plus": 35.0,
294
+ "wilcoxon_p": 0.4921875,
295
+ "cohens_d": 0.2585043012361478,
296
+ "interpretation": "Effect of adding causal loss when operator pretraining is present.",
297
+ "bh_fdr_threshold": 0.05000000000000001,
298
+ "bh_fdr_p_adjusted": 0.4921875,
299
+ "bh_fdr_significant": false
300
+ },
301
+ {
302
+ "pde": "burgers1d_verylow",
303
+ "comparison": "Causal WITHOUT pretrain",
304
+ "group_a": "no_pretrain_no_causal",
305
+ "group_b": "no_pretrain_with_causal",
306
+ "metric": "pde_residual_norm",
307
+ "n_pairs": 10,
308
+ "mean_a": 0.14576154798269272,
309
+ "mean_b": 0.14348772168159485,
310
+ "mean_diff": 0.00227382630109787,
311
+ "bootstrap_95ci": [
312
+ 0.0003224260360002518,
313
+ 0.004439008012413977
314
+ ],
315
+ "wilcoxon_w": 13.0,
316
+ "wilcoxon_w_plus": 42.0,
317
+ "wilcoxon_p": 0.16015625,
318
+ "cohens_d": 0.6413838759603556,
319
+ "interpretation": "Effect of adding causal loss when operator pretraining is skipped.",
320
+ "bh_fdr_threshold": 0.04583333333333334,
321
+ "bh_fdr_p_adjusted": 0.1747159090909091,
322
+ "bh_fdr_significant": false
323
+ },
324
+ {
325
+ "pde": "burgers1d_verylow",
326
+ "comparison": "Pretrain effect",
327
+ "group_a": "full_pipeline_no_causal",
328
+ "group_b": "no_pretrain_no_causal",
329
+ "metric": "pde_residual_norm",
330
+ "n_pairs": 10,
331
+ "mean_a": 0.02990581523627043,
332
+ "mean_b": 0.14576154798269272,
333
+ "mean_diff": -0.11585573274642229,
334
+ "bootstrap_95ci": [
335
+ -0.12284901482518762,
336
+ -0.109043073002249
337
+ ],
338
+ "wilcoxon_w": 0.0,
339
+ "wilcoxon_w_plus": 0.0,
340
+ "wilcoxon_p": 0.001953125,
341
+ "cohens_d": -9.723749957644019,
342
+ "interpretation": "Effect of operator pretraining (stage 1) without causal loss.",
343
+ "bh_fdr_threshold": 0.016666666666666666,
344
+ "bh_fdr_p_adjusted": 0.005859375,
345
+ "bh_fdr_significant": true
346
+ },
347
+ {
348
+ "pde": "heat1d",
349
+ "comparison": "Causal WITH pretrain",
350
+ "group_a": "full_pipeline_no_causal",
351
+ "group_b": "full_pipeline_with_causal",
352
+ "metric": "pde_residual_norm",
353
+ "n_pairs": 10,
354
+ "mean_a": 0.011447346210479737,
355
+ "mean_b": 0.010440928861498833,
356
+ "mean_diff": 0.0010064173489809035,
357
+ "bootstrap_95ci": [
358
+ 0.000630154290702194,
359
+ 0.0014830469409935175
360
+ ],
361
+ "wilcoxon_w": 0.0,
362
+ "wilcoxon_w_plus": 55.0,
363
+ "wilcoxon_p": 0.001953125,
364
+ "cohens_d": 1.3771003367468224,
365
+ "interpretation": "Effect of adding causal loss when operator pretraining is present.",
366
+ "bh_fdr_threshold": 0.01875,
367
+ "bh_fdr_p_adjusted": 0.005208333333333333,
368
+ "bh_fdr_significant": true
369
+ },
370
+ {
371
+ "pde": "heat1d",
372
+ "comparison": "Causal WITHOUT pretrain",
373
+ "group_a": "no_pretrain_no_causal",
374
+ "group_b": "no_pretrain_with_causal",
375
+ "metric": "pde_residual_norm",
376
+ "n_pairs": 10,
377
+ "mean_a": 0.10089385136961937,
378
+ "mean_b": 0.10498911887407303,
379
+ "mean_diff": -0.004095267504453659,
380
+ "bootstrap_95ci": [
381
+ -0.00772341838106513,
382
+ -0.00014242513105273396
383
+ ],
384
+ "wilcoxon_w": 10.0,
385
+ "wilcoxon_w_plus": 10.0,
386
+ "wilcoxon_p": 0.083984375,
387
+ "cohens_d": -0.6328842551929618,
388
+ "interpretation": "Effect of adding causal loss when operator pretraining is skipped.",
389
+ "bh_fdr_threshold": 0.041666666666666664,
390
+ "bh_fdr_p_adjusted": 0.10078125,
391
+ "bh_fdr_significant": false
392
+ },
393
+ {
394
+ "pde": "heat1d",
395
+ "comparison": "Pretrain effect",
396
+ "group_a": "full_pipeline_no_causal",
397
+ "group_b": "no_pretrain_no_causal",
398
+ "metric": "pde_residual_norm",
399
+ "n_pairs": 10,
400
+ "mean_a": 0.011447346210479737,
401
+ "mean_b": 0.10089385136961937,
402
+ "mean_diff": -0.08944650515913963,
403
+ "bootstrap_95ci": [
404
+ -0.09826748856343329,
405
+ -0.08206600181758403
406
+ ],
407
+ "wilcoxon_w": 0.0,
408
+ "wilcoxon_w_plus": 0.0,
409
+ "wilcoxon_p": 0.001953125,
410
+ "cohens_d": -6.425487689783985,
411
+ "interpretation": "Effect of operator pretraining (stage 1) without causal loss.",
412
+ "bh_fdr_threshold": 0.020833333333333332,
413
+ "bh_fdr_p_adjusted": 0.0046875,
414
+ "bh_fdr_significant": true
415
+ },
416
+ {
417
+ "pde": "kdv1d",
418
+ "comparison": "Causal WITH pretrain",
419
+ "group_a": "full_pipeline_no_causal",
420
+ "group_b": "full_pipeline_with_causal",
421
+ "metric": "pde_residual_norm",
422
+ "n_pairs": 10,
423
+ "mean_a": 0.014544954057782888,
424
+ "mean_b": 0.013440604414790868,
425
+ "mean_diff": 0.0011043496429920196,
426
+ "bootstrap_95ci": [
427
+ 0.0007740404340438545,
428
+ 0.0014605597942136228
429
+ ],
430
+ "wilcoxon_w": 0.0,
431
+ "wilcoxon_w_plus": 55.0,
432
+ "wilcoxon_p": 0.001953125,
433
+ "cohens_d": 1.8714990967532308,
434
+ "interpretation": "Effect of adding causal loss when operator pretraining is present.",
435
+ "bh_fdr_threshold": 0.02291666666666667,
436
+ "bh_fdr_p_adjusted": 0.004261363636363636,
437
+ "bh_fdr_significant": true
438
+ },
439
+ {
440
+ "pde": "kdv1d",
441
+ "comparison": "Causal WITHOUT pretrain",
442
+ "group_a": "no_pretrain_no_causal",
443
+ "group_b": "no_pretrain_with_causal",
444
+ "metric": "pde_residual_norm",
445
+ "n_pairs": 10,
446
+ "mean_a": 0.14176027551293374,
447
+ "mean_b": 0.14455095827579498,
448
+ "mean_diff": -0.0027906827628612517,
449
+ "bootstrap_95ci": [
450
+ -0.006660649627447128,
451
+ 0.001315351147204637
452
+ ],
453
+ "wilcoxon_w": 15.0,
454
+ "wilcoxon_w_plus": 15.0,
455
+ "wilcoxon_p": 0.232421875,
456
+ "cohens_d": -0.4090918744528993,
457
+ "interpretation": "Effect of adding causal loss when operator pretraining is skipped.",
458
+ "bh_fdr_threshold": 0.04791666666666667,
459
+ "bh_fdr_p_adjusted": 0.2425271739130435,
460
+ "bh_fdr_significant": false
461
+ },
462
+ {
463
+ "pde": "kdv1d",
464
+ "comparison": "Pretrain effect",
465
+ "group_a": "full_pipeline_no_causal",
466
+ "group_b": "no_pretrain_no_causal",
467
+ "metric": "pde_residual_norm",
468
+ "n_pairs": 10,
469
+ "mean_a": 0.014544954057782888,
470
+ "mean_b": 0.14176027551293374,
471
+ "mean_diff": -0.12721532145515085,
472
+ "bootstrap_95ci": [
473
+ -0.13861644329736011,
474
+ -0.11660776630509645
475
+ ],
476
+ "wilcoxon_w": 0.0,
477
+ "wilcoxon_w_plus": 0.0,
478
+ "wilcoxon_p": 0.001953125,
479
+ "cohens_d": -6.756701147577776,
480
+ "interpretation": "Effect of operator pretraining (stage 1) without causal loss.",
481
+ "bh_fdr_threshold": 0.025000000000000005,
482
+ "bh_fdr_p_adjusted": 0.00390625,
483
+ "bh_fdr_significant": true
484
+ },
485
+ {
486
+ "pde": "reaction_diffusion1d_stiff",
487
+ "comparison": "Causal WITH pretrain",
488
+ "group_a": "full_pipeline_no_causal",
489
+ "group_b": "full_pipeline_with_causal",
490
+ "metric": "pde_residual_norm",
491
+ "n_pairs": 10,
492
+ "mean_a": 0.04647967703640461,
493
+ "mean_b": 0.04315285235643387,
494
+ "mean_diff": 0.003326824679970741,
495
+ "bootstrap_95ci": [
496
+ 0.001539106578566134,
497
+ 0.0052979352278634895
498
+ ],
499
+ "wilcoxon_w": 3.0,
500
+ "wilcoxon_w_plus": 52.0,
501
+ "wilcoxon_p": 0.009765625,
502
+ "cohens_d": 1.0280537440005328,
503
+ "interpretation": "Effect of adding causal loss when operator pretraining is present.",
504
+ "bh_fdr_threshold": 0.03333333333333333,
505
+ "bh_fdr_p_adjusted": 0.0146484375,
506
+ "bh_fdr_significant": true
507
+ },
508
+ {
509
+ "pde": "reaction_diffusion1d_stiff",
510
+ "comparison": "Causal WITHOUT pretrain",
511
+ "group_a": "no_pretrain_no_causal",
512
+ "group_b": "no_pretrain_with_causal",
513
+ "metric": "pde_residual_norm",
514
+ "n_pairs": 10,
515
+ "mean_a": 0.2540644884109497,
516
+ "mean_b": 0.27207669615745544,
517
+ "mean_diff": -0.018012207746505738,
518
+ "bootstrap_95ci": [
519
+ -0.029249142780900003,
520
+ -0.008687216751277448
521
+ ],
522
+ "wilcoxon_w": 2.0,
523
+ "wilcoxon_w_plus": 2.0,
524
+ "wilcoxon_p": 0.005859375,
525
+ "cohens_d": -1.0165913027303293,
526
+ "interpretation": "Effect of adding causal loss when operator pretraining is skipped.",
527
+ "bh_fdr_threshold": 0.03125,
528
+ "bh_fdr_p_adjusted": 0.009375,
529
+ "bh_fdr_significant": true
530
+ },
531
+ {
532
+ "pde": "reaction_diffusion1d_stiff",
533
+ "comparison": "Pretrain effect",
534
+ "group_a": "full_pipeline_no_causal",
535
+ "group_b": "no_pretrain_no_causal",
536
+ "metric": "pde_residual_norm",
537
+ "n_pairs": 10,
538
+ "mean_a": 0.04647967703640461,
539
+ "mean_b": 0.2540644884109497,
540
+ "mean_diff": -0.2075848113745451,
541
+ "bootstrap_95ci": [
542
+ -0.24594585119746626,
543
+ -0.17396876748651266
544
+ ],
545
+ "wilcoxon_w": 0.0,
546
+ "wilcoxon_w_plus": 0.0,
547
+ "wilcoxon_p": 0.001953125,
548
+ "cohens_d": -3.3855038335316414,
549
+ "interpretation": "Effect of operator pretraining (stage 1) without causal loss.",
550
+ "bh_fdr_threshold": 0.027083333333333334,
551
+ "bh_fdr_p_adjusted": 0.003605769230769231,
552
+ "bh_fdr_significant": true
553
+ }
554
+ ]
results/paper_c/advdiff1d_ablation/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_c/allencahn1d_standard_ablation/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_c/allencahn_sharp_ablation/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_c/burgers1d_ablation/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_c/burgers1d_verylow_ablation/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_c/causal_weight_evolution/causal_weight_evolution.json ADDED
@@ -0,0 +1,2082 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "config": {
3
+ "seed": 42,
4
+ "device": "cuda",
5
+ "stage1_epochs": 200,
6
+ "stage2_epochs": 300,
7
+ "stage3_epochs": 200,
8
+ "eval_epsilon": 100.0,
9
+ "snapshot_epochs": [
10
+ 0,
11
+ 50,
12
+ 100,
13
+ 150,
14
+ 200
15
+ ],
16
+ "pde": "Heat1D"
17
+ },
18
+ "with_pretrain": {
19
+ "0": {
20
+ "t_fraction": [
21
+ 0.0,
22
+ 0.010101010101010102,
23
+ 0.020202020202020204,
24
+ 0.030303030303030304,
25
+ 0.04040404040404041,
26
+ 0.05050505050505051,
27
+ 0.06060606060606061,
28
+ 0.07070707070707072,
29
+ 0.08080808080808081,
30
+ 0.09090909090909091,
31
+ 0.10101010101010102,
32
+ 0.11111111111111112,
33
+ 0.12121212121212122,
34
+ 0.13131313131313133,
35
+ 0.14141414141414144,
36
+ 0.15151515151515152,
37
+ 0.16161616161616163,
38
+ 0.17171717171717174,
39
+ 0.18181818181818182,
40
+ 0.19191919191919193,
41
+ 0.20202020202020204,
42
+ 0.21212121212121213,
43
+ 0.22222222222222224,
44
+ 0.23232323232323235,
45
+ 0.24242424242424243,
46
+ 0.25252525252525254,
47
+ 0.26262626262626265,
48
+ 0.27272727272727276,
49
+ 0.2828282828282829,
50
+ 0.29292929292929293,
51
+ 0.30303030303030304,
52
+ 0.31313131313131315,
53
+ 0.32323232323232326,
54
+ 0.33333333333333337,
55
+ 0.3434343434343435,
56
+ 0.3535353535353536,
57
+ 0.36363636363636365,
58
+ 0.37373737373737376,
59
+ 0.38383838383838387,
60
+ 0.393939393939394,
61
+ 0.4040404040404041,
62
+ 0.4141414141414142,
63
+ 0.42424242424242425,
64
+ 0.43434343434343436,
65
+ 0.4444444444444445,
66
+ 0.4545454545454546,
67
+ 0.4646464646464647,
68
+ 0.4747474747474748,
69
+ 0.48484848484848486,
70
+ 0.494949494949495,
71
+ 0.5050505050505051,
72
+ 0.5151515151515152,
73
+ 0.5252525252525253,
74
+ 0.5353535353535354,
75
+ 0.5454545454545455,
76
+ 0.5555555555555556,
77
+ 0.5656565656565657,
78
+ 0.5757575757575758,
79
+ 0.5858585858585859,
80
+ 0.595959595959596,
81
+ 0.6060606060606061,
82
+ 0.6161616161616162,
83
+ 0.6262626262626263,
84
+ 0.6363636363636365,
85
+ 0.6464646464646465,
86
+ 0.6565656565656566,
87
+ 0.6666666666666667,
88
+ 0.6767676767676768,
89
+ 0.686868686868687,
90
+ 0.696969696969697,
91
+ 0.7070707070707072,
92
+ 0.7171717171717172,
93
+ 0.7272727272727273,
94
+ 0.7373737373737375,
95
+ 0.7474747474747475,
96
+ 0.7575757575757577,
97
+ 0.7676767676767677,
98
+ 0.7777777777777778,
99
+ 0.787878787878788,
100
+ 0.797979797979798,
101
+ 0.8080808080808082,
102
+ 0.8181818181818182,
103
+ 0.8282828282828284,
104
+ 0.8383838383838385,
105
+ 0.8484848484848485,
106
+ 0.8585858585858587,
107
+ 0.8686868686868687,
108
+ 0.8787878787878789,
109
+ 0.888888888888889,
110
+ 0.8989898989898991,
111
+ 0.9090909090909092,
112
+ 0.9191919191919192,
113
+ 0.9292929292929294,
114
+ 0.9393939393939394,
115
+ 0.9494949494949496,
116
+ 0.9595959595959597,
117
+ 0.9696969696969697,
118
+ 0.9797979797979799,
119
+ 0.98989898989899,
120
+ 1.0
121
+ ],
122
+ "weights": [
123
+ 1.0,
124
+ 0.32936532481062714,
125
+ 0.4682143239600672,
126
+ 0.5625570198016796,
127
+ 0.6228177740978944,
128
+ 0.6637606874611971,
129
+ 0.69485810434919,
130
+ 0.7205639257477118,
131
+ 0.7425296160704321,
132
+ 0.7612535453860629,
133
+ 0.7769320347127406,
134
+ 0.7897902021764567,
135
+ 0.800153510465519,
136
+ 0.808423998240885,
137
+ 0.8150359667056399,
138
+ 0.8204165343344803,
139
+ 0.8249558570014627,
140
+ 0.8289867103946118,
141
+ 0.8327724345908575,
142
+ 0.836502871306961,
143
+ 0.8402977422686277,
144
+ 0.8442156586495431,
145
+ 0.8482666574254134,
146
+ 0.8524261195046157,
147
+ 0.8566480787369607,
148
+ 0.8608767516160472,
149
+ 0.8650554621259708,
150
+ 0.8691329163823808,
151
+ 0.8730669454636882,
152
+ 0.876826205408195,
153
+ 0.8803903096964959,
154
+ 0.8837489102323256,
155
+ 0.8869001727321751,
156
+ 0.8898489852583025,
157
+ 0.8926051629871171,
158
+ 0.8951817910202564,
159
+ 0.897593820555618,
160
+ 0.8998569356026342,
161
+ 0.9019866954689494,
162
+ 0.9039979232336655,
163
+ 0.9059043129316381,
164
+ 0.9077182015888586,
165
+ 0.9094504782295372,
166
+ 0.9111105852386066,
167
+ 0.9127065892010174,
168
+ 0.914245291535861,
169
+ 0.9157323620120433,
170
+ 0.9171724823511478,
171
+ 0.9185694899392493,
172
+ 0.9199265131516715,
173
+ 0.9212460946130612,
174
+ 0.9225303036022817,
175
+ 0.9237808322674889,
176
+ 0.9249990784813648,
177
+ 0.9261862150373587,
178
+ 0.9273432460146414,
179
+ 0.9284710529773808,
180
+ 0.9295704311831243,
181
+ 0.9306421170804255,
182
+ 0.9316868092206575,
183
+ 0.9327051832305134,
184
+ 0.9336979021395482,
185
+ 0.9346656225572837,
186
+ 0.9356089987713923,
187
+ 0.9365286839169832,
188
+ 0.937425329909753,
189
+ 0.9382995861168868,
190
+ 0.9391520976934291,
191
+ 0.9399835030487522,
192
+ 0.940794431756823,
193
+ 0.9415855020223207,
194
+ 0.9423573186907361,
195
+ 0.9431104713956006,
196
+ 0.9438455329084828,
197
+ 0.9445630580873466,
198
+ 0.9452635830109613,
199
+ 0.9459476242971404,
200
+ 0.9466156790466747,
201
+ 0.9472682247471185,
202
+ 0.9479057195493684,
203
+ 0.9485286026534868,
204
+ 0.9491372949656134,
205
+ 0.9497321996629613,
206
+ 0.9503137030254283,
207
+ 0.9508821752210456,
208
+ 0.951437971182951,
209
+ 0.9519814313973058,
210
+ 0.9525128827789175,
211
+ 0.9530326394335338,
212
+ 0.9535410034791388,
213
+ 0.9540382657016981,
214
+ 0.9545247063252008,
215
+ 0.9550005956064571,
216
+ 0.9554661944425337,
217
+ 0.9559217548586706,
218
+ 0.9563675205678336,
219
+ 0.9568037273884791,
220
+ 0.9572306036614261,
221
+ 0.9576483706552811,
222
+ 0.9580572428419833
223
+ ]
224
+ },
225
+ "50": {
226
+ "t_fraction": [
227
+ 0.0,
228
+ 0.010101010101010102,
229
+ 0.020202020202020204,
230
+ 0.030303030303030304,
231
+ 0.04040404040404041,
232
+ 0.05050505050505051,
233
+ 0.06060606060606061,
234
+ 0.07070707070707072,
235
+ 0.08080808080808081,
236
+ 0.09090909090909091,
237
+ 0.10101010101010102,
238
+ 0.11111111111111112,
239
+ 0.12121212121212122,
240
+ 0.13131313131313133,
241
+ 0.14141414141414144,
242
+ 0.15151515151515152,
243
+ 0.16161616161616163,
244
+ 0.17171717171717174,
245
+ 0.18181818181818182,
246
+ 0.19191919191919193,
247
+ 0.20202020202020204,
248
+ 0.21212121212121213,
249
+ 0.22222222222222224,
250
+ 0.23232323232323235,
251
+ 0.24242424242424243,
252
+ 0.25252525252525254,
253
+ 0.26262626262626265,
254
+ 0.27272727272727276,
255
+ 0.2828282828282829,
256
+ 0.29292929292929293,
257
+ 0.30303030303030304,
258
+ 0.31313131313131315,
259
+ 0.32323232323232326,
260
+ 0.33333333333333337,
261
+ 0.3434343434343435,
262
+ 0.3535353535353536,
263
+ 0.36363636363636365,
264
+ 0.37373737373737376,
265
+ 0.38383838383838387,
266
+ 0.393939393939394,
267
+ 0.4040404040404041,
268
+ 0.4141414141414142,
269
+ 0.42424242424242425,
270
+ 0.43434343434343436,
271
+ 0.4444444444444445,
272
+ 0.4545454545454546,
273
+ 0.4646464646464647,
274
+ 0.4747474747474748,
275
+ 0.48484848484848486,
276
+ 0.494949494949495,
277
+ 0.5050505050505051,
278
+ 0.5151515151515152,
279
+ 0.5252525252525253,
280
+ 0.5353535353535354,
281
+ 0.5454545454545455,
282
+ 0.5555555555555556,
283
+ 0.5656565656565657,
284
+ 0.5757575757575758,
285
+ 0.5858585858585859,
286
+ 0.595959595959596,
287
+ 0.6060606060606061,
288
+ 0.6161616161616162,
289
+ 0.6262626262626263,
290
+ 0.6363636363636365,
291
+ 0.6464646464646465,
292
+ 0.6565656565656566,
293
+ 0.6666666666666667,
294
+ 0.6767676767676768,
295
+ 0.686868686868687,
296
+ 0.696969696969697,
297
+ 0.7070707070707072,
298
+ 0.7171717171717172,
299
+ 0.7272727272727273,
300
+ 0.7373737373737375,
301
+ 0.7474747474747475,
302
+ 0.7575757575757577,
303
+ 0.7676767676767677,
304
+ 0.7777777777777778,
305
+ 0.787878787878788,
306
+ 0.797979797979798,
307
+ 0.8080808080808082,
308
+ 0.8181818181818182,
309
+ 0.8282828282828284,
310
+ 0.8383838383838385,
311
+ 0.8484848484848485,
312
+ 0.8585858585858587,
313
+ 0.8686868686868687,
314
+ 0.8787878787878789,
315
+ 0.888888888888889,
316
+ 0.8989898989898991,
317
+ 0.9090909090909092,
318
+ 0.9191919191919192,
319
+ 0.9292929292929294,
320
+ 0.9393939393939394,
321
+ 0.9494949494949496,
322
+ 0.9595959595959597,
323
+ 0.9696969696969697,
324
+ 0.9797979797979799,
325
+ 0.98989898989899,
326
+ 1.0
327
+ ],
328
+ "weights": [
329
+ 1.0,
330
+ 0.32069429560443835,
331
+ 0.46560929087037334,
332
+ 0.5659248114639587,
333
+ 0.6298604153002797,
334
+ 0.6722357690116001,
335
+ 0.703266171830607,
336
+ 0.7281066764191922,
337
+ 0.7489034866431727,
338
+ 0.7664557722937501,
339
+ 0.7811157717378366,
340
+ 0.7931659492113785,
341
+ 0.8029303841295712,
342
+ 0.8107805476437874,
343
+ 0.8171100557766595,
344
+ 0.8223067464481131,
345
+ 0.8267280287424238,
346
+ 0.8306817197581645,
347
+ 0.834413453409917,
348
+ 0.8381012778265245,
349
+ 0.8418576061705914,
350
+ 0.8457369034936449,
351
+ 0.8497472694391736,
352
+ 0.8538635898036124,
353
+ 0.8580402786807348,
354
+ 0.8622223958086213,
355
+ 0.8663543202098681,
356
+ 0.8703858090426526,
357
+ 0.8742756420399946,
358
+ 0.8779932412150754,
359
+ 0.881518779777495,
360
+ 0.8848422671095947,
361
+ 0.8879620415428975,
362
+ 0.8908830032394315,
363
+ 0.8936148499728449,
364
+ 0.89617046150464,
365
+ 0.8985645161109059,
366
+ 0.9008123874497662,
367
+ 0.9029293057144014,
368
+ 0.9049297651677772,
369
+ 0.9068271390211712,
370
+ 0.9086334648278244,
371
+ 0.9103593534123673,
372
+ 0.9120139977164727,
373
+ 0.9136052410310439,
374
+ 0.9151396899254143,
375
+ 0.9166228444039112,
376
+ 0.9180592432793022,
377
+ 0.9194526018212758,
378
+ 0.9208059471550128,
379
+ 0.9221217398045392,
380
+ 0.9234019830446306,
381
+ 0.9246483173983387,
382
+ 0.925862101891396,
383
+ 0.9270444809487773,
384
+ 0.9281964401637378,
385
+ 0.9293188505328883,
386
+ 0.9304125034949944,
387
+ 0.9314781379870308,
388
+ 0.932516459555691,
389
+ 0.9335281549114235,
390
+ 0.9345139012208314,
391
+ 0.9354743723164894,
392
+ 0.9364102415092985,
393
+ 0.9373221825683153,
394
+ 0.9382108691646045,
395
+ 0.9390769733159893,
396
+ 0.9399211631738844,
397
+ 0.9407441004656135,
398
+ 0.9415464379011386,
399
+ 0.9423288167659704,
400
+ 0.9430918644804634,
401
+ 0.9438361926965624,
402
+ 0.9445623956625344,
403
+ 0.9452710489158256,
404
+ 0.9459627083512153,
405
+ 0.9466379096716107,
406
+ 0.9472971680277988,
407
+ 0.9479409780646709,
408
+ 0.9485698140900175,
409
+ 0.9491841305578236,
410
+ 0.9497843625760626,
411
+ 0.9503709265922158,
412
+ 0.9509442212560552,
413
+ 0.9515046281038216,
414
+ 0.9520525125302903,
415
+ 0.9525882246357158,
416
+ 0.9531121000256585,
417
+ 0.9536244607270765,
418
+ 0.9541256159678487,
419
+ 0.9546158628782175,
420
+ 0.955095487322837,
421
+ 0.9555647645167886,
422
+ 0.9560239596445437,
423
+ 0.9564733284151076,
424
+ 0.9569131176531958,
425
+ 0.9573435657716143,
426
+ 0.9577649031627515,
427
+ 0.9581773526668306,
428
+ 0.9585811299462079
429
+ ]
430
+ },
431
+ "100": {
432
+ "t_fraction": [
433
+ 0.0,
434
+ 0.010101010101010102,
435
+ 0.020202020202020204,
436
+ 0.030303030303030304,
437
+ 0.04040404040404041,
438
+ 0.05050505050505051,
439
+ 0.06060606060606061,
440
+ 0.07070707070707072,
441
+ 0.08080808080808081,
442
+ 0.09090909090909091,
443
+ 0.10101010101010102,
444
+ 0.11111111111111112,
445
+ 0.12121212121212122,
446
+ 0.13131313131313133,
447
+ 0.14141414141414144,
448
+ 0.15151515151515152,
449
+ 0.16161616161616163,
450
+ 0.17171717171717174,
451
+ 0.18181818181818182,
452
+ 0.19191919191919193,
453
+ 0.20202020202020204,
454
+ 0.21212121212121213,
455
+ 0.22222222222222224,
456
+ 0.23232323232323235,
457
+ 0.24242424242424243,
458
+ 0.25252525252525254,
459
+ 0.26262626262626265,
460
+ 0.27272727272727276,
461
+ 0.2828282828282829,
462
+ 0.29292929292929293,
463
+ 0.30303030303030304,
464
+ 0.31313131313131315,
465
+ 0.32323232323232326,
466
+ 0.33333333333333337,
467
+ 0.3434343434343435,
468
+ 0.3535353535353536,
469
+ 0.36363636363636365,
470
+ 0.37373737373737376,
471
+ 0.38383838383838387,
472
+ 0.393939393939394,
473
+ 0.4040404040404041,
474
+ 0.4141414141414142,
475
+ 0.42424242424242425,
476
+ 0.43434343434343436,
477
+ 0.4444444444444445,
478
+ 0.4545454545454546,
479
+ 0.4646464646464647,
480
+ 0.4747474747474748,
481
+ 0.48484848484848486,
482
+ 0.494949494949495,
483
+ 0.5050505050505051,
484
+ 0.5151515151515152,
485
+ 0.5252525252525253,
486
+ 0.5353535353535354,
487
+ 0.5454545454545455,
488
+ 0.5555555555555556,
489
+ 0.5656565656565657,
490
+ 0.5757575757575758,
491
+ 0.5858585858585859,
492
+ 0.595959595959596,
493
+ 0.6060606060606061,
494
+ 0.6161616161616162,
495
+ 0.6262626262626263,
496
+ 0.6363636363636365,
497
+ 0.6464646464646465,
498
+ 0.6565656565656566,
499
+ 0.6666666666666667,
500
+ 0.6767676767676768,
501
+ 0.686868686868687,
502
+ 0.696969696969697,
503
+ 0.7070707070707072,
504
+ 0.7171717171717172,
505
+ 0.7272727272727273,
506
+ 0.7373737373737375,
507
+ 0.7474747474747475,
508
+ 0.7575757575757577,
509
+ 0.7676767676767677,
510
+ 0.7777777777777778,
511
+ 0.787878787878788,
512
+ 0.797979797979798,
513
+ 0.8080808080808082,
514
+ 0.8181818181818182,
515
+ 0.8282828282828284,
516
+ 0.8383838383838385,
517
+ 0.8484848484848485,
518
+ 0.8585858585858587,
519
+ 0.8686868686868687,
520
+ 0.8787878787878789,
521
+ 0.888888888888889,
522
+ 0.8989898989898991,
523
+ 0.9090909090909092,
524
+ 0.9191919191919192,
525
+ 0.9292929292929294,
526
+ 0.9393939393939394,
527
+ 0.9494949494949496,
528
+ 0.9595959595959597,
529
+ 0.9696969696969697,
530
+ 0.9797979797979799,
531
+ 0.98989898989899,
532
+ 1.0
533
+ ],
534
+ "weights": [
535
+ 1.0,
536
+ 0.31068142527001336,
537
+ 0.45867227469754307,
538
+ 0.5631090852145064,
539
+ 0.6302097793807879,
540
+ 0.6744142778220243,
541
+ 0.7062322941419592,
542
+ 0.7312128386443705,
543
+ 0.7518109925865496,
544
+ 0.7690271269879652,
545
+ 0.7833282797994419,
546
+ 0.7950526000078084,
547
+ 0.8045453019335437,
548
+ 0.8121808675837222,
549
+ 0.8183480942753083,
550
+ 0.8234273879942968,
551
+ 0.8277681601601249,
552
+ 0.8316706321607253,
553
+ 0.835373316403405,
554
+ 0.8390479401522222,
555
+ 0.8428013988488675,
556
+ 0.8466836230536874,
557
+ 0.8506991747740017,
558
+ 0.8548203793644961,
559
+ 0.8590000136333417,
560
+ 0.8631822615978741,
561
+ 0.8673112084615942,
562
+ 0.8713367520810876,
563
+ 0.875218081079715,
564
+ 0.8789251688352839,
565
+ 0.8824387917507085,
566
+ 0.8857495374443051,
567
+ 0.888856254885688,
568
+ 0.8917642658545177,
569
+ 0.8944835953038383,
570
+ 0.8970273514755851,
571
+ 0.8994103562102055,
572
+ 0.9016480558465192,
573
+ 0.9037556946746982,
574
+ 0.9057477358890372,
575
+ 0.9076374926464539,
576
+ 0.9094369210834159,
577
+ 0.9111565409805649,
578
+ 0.9128054493768203,
579
+ 0.9143913972156544,
580
+ 0.9159209024569027,
581
+ 0.917399385605195,
582
+ 0.9188313136061552,
583
+ 0.9202203408919919,
584
+ 0.921569442365009,
585
+ 0.9228810350775986,
586
+ 0.9241570870989353,
587
+ 0.9253992110842939,
588
+ 0.9266087436278234,
589
+ 0.9277868123373331,
590
+ 0.9289343903096859,
591
+ 0.930052339063938,
592
+ 0.9311414433828498,
593
+ 0.9322024371402284,
594
+ 0.9332360228326597,
595
+ 0.9342428850392289,
596
+ 0.935223699899728,
597
+ 0.9361791406290974,
598
+ 0.937109880489767,
599
+ 0.938016593862798,
600
+ 0.9388999552012363,
601
+ 0.9397606377999613,
602
+ 0.9405993114915242,
603
+ 0.9414166400399734,
604
+ 0.9422132786172368,
605
+ 0.9429898714993362,
606
+ 0.9437470495345136,
607
+ 0.9444854283018843,
608
+ 0.9452056064156834,
609
+ 0.9459081642613215,
610
+ 0.9465936630934054,
611
+ 0.947262644342143,
612
+ 0.9479156293210619,
613
+ 0.9485531191606844,
614
+ 0.9491755950106936,
615
+ 0.9497835183579423,
616
+ 0.9503773315684619,
617
+ 0.9509574585047665,
618
+ 0.9515243053169138,
619
+ 0.952078261080381,
620
+ 0.9526196987332977,
621
+ 0.9531489757809559,
622
+ 0.9536664352382228,
623
+ 0.9541724063097224,
624
+ 0.9546672052100242,
625
+ 0.9551511359340253,
626
+ 0.9556244908771862,
627
+ 0.9560875515519818,
628
+ 0.9565405891243193,
629
+ 0.9569838650356056,
630
+ 0.9574176315147591,
631
+ 0.9578421320369169,
632
+ 0.9582576017721168,
633
+ 0.9586642680166864,
634
+ 0.9590623505592196
635
+ ]
636
+ },
637
+ "150": {
638
+ "t_fraction": [
639
+ 0.0,
640
+ 0.010101010101010102,
641
+ 0.020202020202020204,
642
+ 0.030303030303030304,
643
+ 0.04040404040404041,
644
+ 0.05050505050505051,
645
+ 0.06060606060606061,
646
+ 0.07070707070707072,
647
+ 0.08080808080808081,
648
+ 0.09090909090909091,
649
+ 0.10101010101010102,
650
+ 0.11111111111111112,
651
+ 0.12121212121212122,
652
+ 0.13131313131313133,
653
+ 0.14141414141414144,
654
+ 0.15151515151515152,
655
+ 0.16161616161616163,
656
+ 0.17171717171717174,
657
+ 0.18181818181818182,
658
+ 0.19191919191919193,
659
+ 0.20202020202020204,
660
+ 0.21212121212121213,
661
+ 0.22222222222222224,
662
+ 0.23232323232323235,
663
+ 0.24242424242424243,
664
+ 0.25252525252525254,
665
+ 0.26262626262626265,
666
+ 0.27272727272727276,
667
+ 0.2828282828282829,
668
+ 0.29292929292929293,
669
+ 0.30303030303030304,
670
+ 0.31313131313131315,
671
+ 0.32323232323232326,
672
+ 0.33333333333333337,
673
+ 0.3434343434343435,
674
+ 0.3535353535353536,
675
+ 0.36363636363636365,
676
+ 0.37373737373737376,
677
+ 0.38383838383838387,
678
+ 0.393939393939394,
679
+ 0.4040404040404041,
680
+ 0.4141414141414142,
681
+ 0.42424242424242425,
682
+ 0.43434343434343436,
683
+ 0.4444444444444445,
684
+ 0.4545454545454546,
685
+ 0.4646464646464647,
686
+ 0.4747474747474748,
687
+ 0.48484848484848486,
688
+ 0.494949494949495,
689
+ 0.5050505050505051,
690
+ 0.5151515151515152,
691
+ 0.5252525252525253,
692
+ 0.5353535353535354,
693
+ 0.5454545454545455,
694
+ 0.5555555555555556,
695
+ 0.5656565656565657,
696
+ 0.5757575757575758,
697
+ 0.5858585858585859,
698
+ 0.595959595959596,
699
+ 0.6060606060606061,
700
+ 0.6161616161616162,
701
+ 0.6262626262626263,
702
+ 0.6363636363636365,
703
+ 0.6464646464646465,
704
+ 0.6565656565656566,
705
+ 0.6666666666666667,
706
+ 0.6767676767676768,
707
+ 0.686868686868687,
708
+ 0.696969696969697,
709
+ 0.7070707070707072,
710
+ 0.7171717171717172,
711
+ 0.7272727272727273,
712
+ 0.7373737373737375,
713
+ 0.7474747474747475,
714
+ 0.7575757575757577,
715
+ 0.7676767676767677,
716
+ 0.7777777777777778,
717
+ 0.787878787878788,
718
+ 0.797979797979798,
719
+ 0.8080808080808082,
720
+ 0.8181818181818182,
721
+ 0.8282828282828284,
722
+ 0.8383838383838385,
723
+ 0.8484848484848485,
724
+ 0.8585858585858587,
725
+ 0.8686868686868687,
726
+ 0.8787878787878789,
727
+ 0.888888888888889,
728
+ 0.8989898989898991,
729
+ 0.9090909090909092,
730
+ 0.9191919191919192,
731
+ 0.9292929292929294,
732
+ 0.9393939393939394,
733
+ 0.9494949494949496,
734
+ 0.9595959595959597,
735
+ 0.9696969696969697,
736
+ 0.9797979797979799,
737
+ 0.98989898989899,
738
+ 1.0
739
+ ],
740
+ "weights": [
741
+ 1.0,
742
+ 0.31654047199916563,
743
+ 0.46619270199639595,
744
+ 0.5708945312621326,
745
+ 0.6374152494150166,
746
+ 0.6807262091102325,
747
+ 0.7116469433657451,
748
+ 0.7358678936759666,
749
+ 0.7558896109428429,
750
+ 0.7727058298427286,
751
+ 0.7867516687642945,
752
+ 0.7983260801523536,
753
+ 0.807737374305047,
754
+ 0.8153314969629547,
755
+ 0.821477832399913,
756
+ 0.8265449029326991,
757
+ 0.8308756410205382,
758
+ 0.8347668366174069,
759
+ 0.8384552019698165,
760
+ 0.8421112183085488,
761
+ 0.8458408994087867,
762
+ 0.8496935089887075,
763
+ 0.8536732476185778,
764
+ 0.8577524302893997,
765
+ 0.8618841844340661,
766
+ 0.8660133613691802,
767
+ 0.870084952600101,
768
+ 0.8740499190297938,
769
+ 0.8778685675274659,
770
+ 0.8815119613760424,
771
+ 0.8849618780161408,
772
+ 0.8882097743253451,
773
+ 0.8912552112886198,
774
+ 0.8941040623008423,
775
+ 0.8967667436130138,
776
+ 0.8992566151935975,
777
+ 0.9015886288725176,
778
+ 0.903778255889262,
779
+ 0.9058406879872767,
780
+ 0.9077902764555185,
781
+ 0.9096401802686681,
782
+ 0.9114021741348578,
783
+ 0.9130865844191378,
784
+ 0.9147023095837954,
785
+ 0.9162569041049186,
786
+ 0.9177566987964307,
787
+ 0.9192069391437921,
788
+ 0.9206119305233271,
789
+ 0.9219751802221856,
790
+ 0.9232995318403364,
791
+ 0.9245872859317307,
792
+ 0.9258403071403302,
793
+ 0.9270601179973327,
794
+ 0.9282479761038327,
795
+ 0.9294049408250432,
796
+ 0.9305319260794072,
797
+ 0.9316297423396186,
798
+ 0.9326991303390403,
799
+ 0.9337407861437799,
800
+ 0.93475537945189,
801
+ 0.9357435669441612,
802
+ 0.9367060006308804,
803
+ 0.937643333119497,
804
+ 0.9385562202563213,
805
+ 0.9394453214240901,
806
+ 0.9403112986968064,
807
+ 0.9411548149509891,
808
+ 0.9419765314253062,
809
+ 0.9427771051735069,
810
+ 0.9435571861775635,
811
+ 0.9443174148063188,
812
+ 0.945058419348214,
813
+ 0.9457808138865427,
814
+ 0.9464851965880251,
815
+ 0.9471721483657972,
816
+ 0.9478422316829888,
817
+ 0.948495989900453,
818
+ 0.9491339468945146,
819
+ 0.9497566068091249,
820
+ 0.9503644541984048,
821
+ 0.9509579542863139,
822
+ 0.9515375534142282,
823
+ 0.9521036794924445,
824
+ 0.9526567428188054,
825
+ 0.9531971366461925,
826
+ 0.953725237966787,
827
+ 0.9542414082885455,
828
+ 0.9547459943946655,
829
+ 0.9552393290825294,
830
+ 0.955721731932632,
831
+ 0.9561935100077756,
832
+ 0.9566549584887241,
833
+ 0.9571063613210508,
834
+ 0.9575479918443637,
835
+ 0.9579801132745492,
836
+ 0.958402979300888,
837
+ 0.9588168344803182,
838
+ 0.959221914782017,
839
+ 0.9596184478953295,
840
+ 0.9600066537246186
841
+ ]
842
+ },
843
+ "200": {
844
+ "t_fraction": [
845
+ 0.0,
846
+ 0.010101010101010102,
847
+ 0.020202020202020204,
848
+ 0.030303030303030304,
849
+ 0.04040404040404041,
850
+ 0.05050505050505051,
851
+ 0.06060606060606061,
852
+ 0.07070707070707072,
853
+ 0.08080808080808081,
854
+ 0.09090909090909091,
855
+ 0.10101010101010102,
856
+ 0.11111111111111112,
857
+ 0.12121212121212122,
858
+ 0.13131313131313133,
859
+ 0.14141414141414144,
860
+ 0.15151515151515152,
861
+ 0.16161616161616163,
862
+ 0.17171717171717174,
863
+ 0.18181818181818182,
864
+ 0.19191919191919193,
865
+ 0.20202020202020204,
866
+ 0.21212121212121213,
867
+ 0.22222222222222224,
868
+ 0.23232323232323235,
869
+ 0.24242424242424243,
870
+ 0.25252525252525254,
871
+ 0.26262626262626265,
872
+ 0.27272727272727276,
873
+ 0.2828282828282829,
874
+ 0.29292929292929293,
875
+ 0.30303030303030304,
876
+ 0.31313131313131315,
877
+ 0.32323232323232326,
878
+ 0.33333333333333337,
879
+ 0.3434343434343435,
880
+ 0.3535353535353536,
881
+ 0.36363636363636365,
882
+ 0.37373737373737376,
883
+ 0.38383838383838387,
884
+ 0.393939393939394,
885
+ 0.4040404040404041,
886
+ 0.4141414141414142,
887
+ 0.42424242424242425,
888
+ 0.43434343434343436,
889
+ 0.4444444444444445,
890
+ 0.4545454545454546,
891
+ 0.4646464646464647,
892
+ 0.4747474747474748,
893
+ 0.48484848484848486,
894
+ 0.494949494949495,
895
+ 0.5050505050505051,
896
+ 0.5151515151515152,
897
+ 0.5252525252525253,
898
+ 0.5353535353535354,
899
+ 0.5454545454545455,
900
+ 0.5555555555555556,
901
+ 0.5656565656565657,
902
+ 0.5757575757575758,
903
+ 0.5858585858585859,
904
+ 0.595959595959596,
905
+ 0.6060606060606061,
906
+ 0.6161616161616162,
907
+ 0.6262626262626263,
908
+ 0.6363636363636365,
909
+ 0.6464646464646465,
910
+ 0.6565656565656566,
911
+ 0.6666666666666667,
912
+ 0.6767676767676768,
913
+ 0.686868686868687,
914
+ 0.696969696969697,
915
+ 0.7070707070707072,
916
+ 0.7171717171717172,
917
+ 0.7272727272727273,
918
+ 0.7373737373737375,
919
+ 0.7474747474747475,
920
+ 0.7575757575757577,
921
+ 0.7676767676767677,
922
+ 0.7777777777777778,
923
+ 0.787878787878788,
924
+ 0.797979797979798,
925
+ 0.8080808080808082,
926
+ 0.8181818181818182,
927
+ 0.8282828282828284,
928
+ 0.8383838383838385,
929
+ 0.8484848484848485,
930
+ 0.8585858585858587,
931
+ 0.8686868686868687,
932
+ 0.8787878787878789,
933
+ 0.888888888888889,
934
+ 0.8989898989898991,
935
+ 0.9090909090909092,
936
+ 0.9191919191919192,
937
+ 0.9292929292929294,
938
+ 0.9393939393939394,
939
+ 0.9494949494949496,
940
+ 0.9595959595959597,
941
+ 0.9696969696969697,
942
+ 0.9797979797979799,
943
+ 0.98989898989899,
944
+ 1.0
945
+ ],
946
+ "weights": [
947
+ 1.0,
948
+ 0.3220390606886065,
949
+ 0.4723028197706335,
950
+ 0.5768804161146588,
951
+ 0.6430379848644835,
952
+ 0.6859626080329346,
953
+ 0.7165372189619739,
954
+ 0.740465664109255,
955
+ 0.7602484385595681,
956
+ 0.7768744253574829,
957
+ 0.7907707577801671,
958
+ 0.8022269793137158,
959
+ 0.8115437070877175,
960
+ 0.8190611140595933,
961
+ 0.8251450539646829,
962
+ 0.8301619255711424,
963
+ 0.834452784640735,
964
+ 0.8383121872865791,
965
+ 0.8419740728986222,
966
+ 0.845605784859866,
967
+ 0.8493102822165338,
968
+ 0.8531341637187188,
969
+ 0.8570796423479411,
970
+ 0.8611178397616738,
971
+ 0.8652014590155104,
972
+ 0.8692756153435306,
973
+ 0.8732861028992422,
974
+ 0.8771850159177665,
975
+ 0.8809339779036633,
976
+ 0.8845054189559638,
977
+ 0.8878824153312838,
978
+ 0.8910575828028949,
979
+ 0.8940314617435583,
980
+ 0.8968107036320682,
981
+ 0.8994063114088545,
982
+ 0.9018320414655455,
983
+ 0.9041030891720152,
984
+ 0.9062350328144977,
985
+ 0.9082430629732957,
986
+ 0.9101414495589656,
987
+ 0.9119432100349005,
988
+ 0.9136599390717544,
989
+ 0.9153017566375364,
990
+ 0.916877346062195,
991
+ 0.9183940426784538,
992
+ 0.919857964730041,
993
+ 0.9212741540777193,
994
+ 0.9226467264397348,
995
+ 0.923979014554231,
996
+ 0.9252737033510294,
997
+ 0.9265329499622761,
998
+ 0.9277584917350828,
999
+ 0.928951738011777,
1000
+ 0.930113846966307,
1001
+ 0.9312457907459972,
1002
+ 0.9323484068099306,
1003
+ 0.9334224395136895,
1004
+ 0.9344685721713782,
1005
+ 0.9354874513642929,
1006
+ 0.93647970425157,
1007
+ 0.9374459508425848,
1008
+ 0.9383868120071636,
1009
+ 0.9393029140199938,
1010
+ 0.9401948903260106,
1011
+ 0.9410633817687307,
1012
+ 0.9419090349504791,
1013
+ 0.9427325002473257,
1014
+ 0.9435344289573144,
1015
+ 0.9443154703486948,
1016
+ 0.9450762686480638,
1017
+ 0.9458174601613311,
1018
+ 0.9465396707289656,
1019
+ 0.9472435133619562,
1020
+ 0.9479295862822606,
1021
+ 0.9485984714683025,
1022
+ 0.9492507333124145,
1023
+ 0.9498869178389409,
1024
+ 0.9505075521183354,
1025
+ 0.9511131439640166,
1026
+ 0.9517041820243245,
1027
+ 0.9522811357790084,
1028
+ 0.9528444559715495,
1029
+ 0.9533945750265197,
1030
+ 0.9539319076624599,
1031
+ 0.9544568514865123,
1032
+ 0.9549697876521229,
1033
+ 0.9554710816670255,
1034
+ 0.955961084049281,
1035
+ 0.9564401309992479,
1036
+ 0.9569085451548537,
1037
+ 0.9573666363021751,
1038
+ 0.9578147019403681,
1039
+ 0.9582530279617516,
1040
+ 0.9586818892588028,
1041
+ 0.9591015501798399,
1042
+ 0.9595122651215758,
1043
+ 0.9599142790071177,
1044
+ 0.9603078277150296,
1045
+ 0.9606931385136919,
1046
+ 0.9610704304308859
1047
+ ]
1048
+ }
1049
+ },
1050
+ "without_pretrain": {
1051
+ "0": {
1052
+ "t_fraction": [
1053
+ 0.0,
1054
+ 0.010101010101010102,
1055
+ 0.020202020202020204,
1056
+ 0.030303030303030304,
1057
+ 0.04040404040404041,
1058
+ 0.05050505050505051,
1059
+ 0.06060606060606061,
1060
+ 0.07070707070707072,
1061
+ 0.08080808080808081,
1062
+ 0.09090909090909091,
1063
+ 0.10101010101010102,
1064
+ 0.11111111111111112,
1065
+ 0.12121212121212122,
1066
+ 0.13131313131313133,
1067
+ 0.14141414141414144,
1068
+ 0.15151515151515152,
1069
+ 0.16161616161616163,
1070
+ 0.17171717171717174,
1071
+ 0.18181818181818182,
1072
+ 0.19191919191919193,
1073
+ 0.20202020202020204,
1074
+ 0.21212121212121213,
1075
+ 0.22222222222222224,
1076
+ 0.23232323232323235,
1077
+ 0.24242424242424243,
1078
+ 0.25252525252525254,
1079
+ 0.26262626262626265,
1080
+ 0.27272727272727276,
1081
+ 0.2828282828282829,
1082
+ 0.29292929292929293,
1083
+ 0.30303030303030304,
1084
+ 0.31313131313131315,
1085
+ 0.32323232323232326,
1086
+ 0.33333333333333337,
1087
+ 0.3434343434343435,
1088
+ 0.3535353535353536,
1089
+ 0.36363636363636365,
1090
+ 0.37373737373737376,
1091
+ 0.38383838383838387,
1092
+ 0.393939393939394,
1093
+ 0.4040404040404041,
1094
+ 0.4141414141414142,
1095
+ 0.42424242424242425,
1096
+ 0.43434343434343436,
1097
+ 0.4444444444444445,
1098
+ 0.4545454545454546,
1099
+ 0.4646464646464647,
1100
+ 0.4747474747474748,
1101
+ 0.48484848484848486,
1102
+ 0.494949494949495,
1103
+ 0.5050505050505051,
1104
+ 0.5151515151515152,
1105
+ 0.5252525252525253,
1106
+ 0.5353535353535354,
1107
+ 0.5454545454545455,
1108
+ 0.5555555555555556,
1109
+ 0.5656565656565657,
1110
+ 0.5757575757575758,
1111
+ 0.5858585858585859,
1112
+ 0.595959595959596,
1113
+ 0.6060606060606061,
1114
+ 0.6161616161616162,
1115
+ 0.6262626262626263,
1116
+ 0.6363636363636365,
1117
+ 0.6464646464646465,
1118
+ 0.6565656565656566,
1119
+ 0.6666666666666667,
1120
+ 0.6767676767676768,
1121
+ 0.686868686868687,
1122
+ 0.696969696969697,
1123
+ 0.7070707070707072,
1124
+ 0.7171717171717172,
1125
+ 0.7272727272727273,
1126
+ 0.7373737373737375,
1127
+ 0.7474747474747475,
1128
+ 0.7575757575757577,
1129
+ 0.7676767676767677,
1130
+ 0.7777777777777778,
1131
+ 0.787878787878788,
1132
+ 0.797979797979798,
1133
+ 0.8080808080808082,
1134
+ 0.8181818181818182,
1135
+ 0.8282828282828284,
1136
+ 0.8383838383838385,
1137
+ 0.8484848484848485,
1138
+ 0.8585858585858587,
1139
+ 0.8686868686868687,
1140
+ 0.8787878787878789,
1141
+ 0.888888888888889,
1142
+ 0.8989898989898991,
1143
+ 0.9090909090909092,
1144
+ 0.9191919191919192,
1145
+ 0.9292929292929294,
1146
+ 0.9393939393939394,
1147
+ 0.9494949494949496,
1148
+ 0.9595959595959597,
1149
+ 0.9696969696969697,
1150
+ 0.9797979797979799,
1151
+ 0.98989898989899,
1152
+ 1.0
1153
+ ],
1154
+ "weights": [
1155
+ 1.0,
1156
+ 0.1519775952854079,
1157
+ 0.15424593520953053,
1158
+ 0.1565368664079195,
1159
+ 0.15885030348921259,
1160
+ 0.16118613897939113,
1161
+ 0.16354426254528484,
1162
+ 0.16592454665535009,
1163
+ 0.16832683825969474,
1164
+ 0.17075094790513695,
1165
+ 0.1731966987140588,
1166
+ 0.17566387416211454,
1167
+ 0.17815227713140563,
1168
+ 0.18066164767748796,
1169
+ 0.18319175179916172,
1170
+ 0.18574230541788384,
1171
+ 0.18831302484455623,
1172
+ 0.1909035924815838,
1173
+ 0.1935136836230132,
1174
+ 0.19614294994967843,
1175
+ 0.19879101329805757,
1176
+ 0.20145749453080083,
1177
+ 0.20414197774918647,
1178
+ 0.20684403827453396,
1179
+ 0.20956322155896365,
1180
+ 0.21229905808930954,
1181
+ 0.2150510627179222,
1182
+ 0.21781871984238257,
1183
+ 0.22060149783408628,
1184
+ 0.22339885209492497,
1185
+ 0.22621021370620312,
1186
+ 0.22903499601806848,
1187
+ 0.23187259571353758,
1188
+ 0.23472239244754495,
1189
+ 0.23758374529691947,
1190
+ 0.24045600303047626,
1191
+ 0.24333849324409074,
1192
+ 0.24623053364596767,
1193
+ 0.24913142096889465,
1194
+ 0.2520404503914606,
1195
+ 0.2549568930012475,
1196
+ 0.25788001498253244,
1197
+ 0.2608090716199709,
1198
+ 0.2637433058243509,
1199
+ 0.2666819569749377,
1200
+ 0.26962425469008766,
1201
+ 0.2725694219163012,
1202
+ 0.2755166778673533,
1203
+ 0.2784652359749644,
1204
+ 0.2814143111188986,
1205
+ 0.28436310927370007,
1206
+ 0.28731084089848946,
1207
+ 0.2902567138727733,
1208
+ 0.2931999400191381,
1209
+ 0.2961397329071298,
1210
+ 0.29907530912053526,
1211
+ 0.3020058922753988,
1212
+ 0.3049307066807578,
1213
+ 0.30784898741698596,
1214
+ 0.31075997478269446,
1215
+ 0.3136629226761637,
1216
+ 0.31655708876573796,
1217
+ 0.3194417438456356,
1218
+ 0.32231616843979194,
1219
+ 0.3251796566845176,
1220
+ 0.3280315151513777,
1221
+ 0.33087106431888286,
1222
+ 0.33369763676915903,
1223
+ 0.33651058354729174,
1224
+ 0.33930926839625675,
1225
+ 0.34209307179072934,
1226
+ 0.34486139031809165,
1227
+ 0.34761363834952386,
1228
+ 0.35034924788030086,
1229
+ 0.35306766683593804,
1230
+ 0.3557683638560829,
1231
+ 0.35845082304125414,
1232
+ 0.3611145491526851,
1233
+ 0.36375906526055635,
1234
+ 0.366383913068997,
1235
+ 0.36898865323493935,
1236
+ 0.37157286546621543,
1237
+ 0.3741361481935761,
1238
+ 0.37667811994466743,
1239
+ 0.3791984181514304,
1240
+ 0.38169669945768114,
1241
+ 0.3841726375184939,
1242
+ 0.38662592665909146,
1243
+ 0.3890562796520456,
1244
+ 0.39146342719672755,
1245
+ 0.39384711761301266,
1246
+ 0.3962071183629998,
1247
+ 0.3985432138892128,
1248
+ 0.4008552062204965,
1249
+ 0.40314291455388723,
1250
+ 0.4054061750399871,
1251
+ 0.40764483997354806,
1252
+ 0.4098587788690099,
1253
+ 0.412047874992773,
1254
+ 0.4142120289052947
1255
+ ]
1256
+ },
1257
+ "50": {
1258
+ "t_fraction": [
1259
+ 0.0,
1260
+ 0.010101010101010102,
1261
+ 0.020202020202020204,
1262
+ 0.030303030303030304,
1263
+ 0.04040404040404041,
1264
+ 0.05050505050505051,
1265
+ 0.06060606060606061,
1266
+ 0.07070707070707072,
1267
+ 0.08080808080808081,
1268
+ 0.09090909090909091,
1269
+ 0.10101010101010102,
1270
+ 0.11111111111111112,
1271
+ 0.12121212121212122,
1272
+ 0.13131313131313133,
1273
+ 0.14141414141414144,
1274
+ 0.15151515151515152,
1275
+ 0.16161616161616163,
1276
+ 0.17171717171717174,
1277
+ 0.18181818181818182,
1278
+ 0.19191919191919193,
1279
+ 0.20202020202020204,
1280
+ 0.21212121212121213,
1281
+ 0.22222222222222224,
1282
+ 0.23232323232323235,
1283
+ 0.24242424242424243,
1284
+ 0.25252525252525254,
1285
+ 0.26262626262626265,
1286
+ 0.27272727272727276,
1287
+ 0.2828282828282829,
1288
+ 0.29292929292929293,
1289
+ 0.30303030303030304,
1290
+ 0.31313131313131315,
1291
+ 0.32323232323232326,
1292
+ 0.33333333333333337,
1293
+ 0.3434343434343435,
1294
+ 0.3535353535353536,
1295
+ 0.36363636363636365,
1296
+ 0.37373737373737376,
1297
+ 0.38383838383838387,
1298
+ 0.393939393939394,
1299
+ 0.4040404040404041,
1300
+ 0.4141414141414142,
1301
+ 0.42424242424242425,
1302
+ 0.43434343434343436,
1303
+ 0.4444444444444445,
1304
+ 0.4545454545454546,
1305
+ 0.4646464646464647,
1306
+ 0.4747474747474748,
1307
+ 0.48484848484848486,
1308
+ 0.494949494949495,
1309
+ 0.5050505050505051,
1310
+ 0.5151515151515152,
1311
+ 0.5252525252525253,
1312
+ 0.5353535353535354,
1313
+ 0.5454545454545455,
1314
+ 0.5555555555555556,
1315
+ 0.5656565656565657,
1316
+ 0.5757575757575758,
1317
+ 0.5858585858585859,
1318
+ 0.595959595959596,
1319
+ 0.6060606060606061,
1320
+ 0.6161616161616162,
1321
+ 0.6262626262626263,
1322
+ 0.6363636363636365,
1323
+ 0.6464646464646465,
1324
+ 0.6565656565656566,
1325
+ 0.6666666666666667,
1326
+ 0.6767676767676768,
1327
+ 0.686868686868687,
1328
+ 0.696969696969697,
1329
+ 0.7070707070707072,
1330
+ 0.7171717171717172,
1331
+ 0.7272727272727273,
1332
+ 0.7373737373737375,
1333
+ 0.7474747474747475,
1334
+ 0.7575757575757577,
1335
+ 0.7676767676767677,
1336
+ 0.7777777777777778,
1337
+ 0.787878787878788,
1338
+ 0.797979797979798,
1339
+ 0.8080808080808082,
1340
+ 0.8181818181818182,
1341
+ 0.8282828282828284,
1342
+ 0.8383838383838385,
1343
+ 0.8484848484848485,
1344
+ 0.8585858585858587,
1345
+ 0.8686868686868687,
1346
+ 0.8787878787878789,
1347
+ 0.888888888888889,
1348
+ 0.8989898989898991,
1349
+ 0.9090909090909092,
1350
+ 0.9191919191919192,
1351
+ 0.9292929292929294,
1352
+ 0.9393939393939394,
1353
+ 0.9494949494949496,
1354
+ 0.9595959595959597,
1355
+ 0.9696969696969697,
1356
+ 0.9797979797979799,
1357
+ 0.98989898989899,
1358
+ 1.0
1359
+ ],
1360
+ "weights": [
1361
+ 1.0,
1362
+ 0.14109661401935203,
1363
+ 0.14334418986260597,
1364
+ 0.14561735130484213,
1365
+ 0.14791618258396583,
1366
+ 0.15024072465819688,
1367
+ 0.15259101941534745,
1368
+ 0.15496712935002174,
1369
+ 0.15736904546547667,
1370
+ 0.1597967593374663,
1371
+ 0.1622502345977953,
1372
+ 0.1647294699666027,
1373
+ 0.1672344003183972,
1374
+ 0.16976496048842007,
1375
+ 0.17232104060704692,
1376
+ 0.17490252526650993,
1377
+ 0.1775092832061699,
1378
+ 0.18014116677584874,
1379
+ 0.18279798208696996,
1380
+ 0.18547952780430746,
1381
+ 0.18818556792785765,
1382
+ 0.1909158423513249,
1383
+ 0.19367007752316942,
1384
+ 0.19644795845816876,
1385
+ 0.19924915417472663,
1386
+ 0.20207330939542414,
1387
+ 0.2049200250113321,
1388
+ 0.20778889353798927,
1389
+ 0.21067946997124418,
1390
+ 0.21359128417391698,
1391
+ 0.21652384352115606,
1392
+ 0.2194766292617633,
1393
+ 0.2224490913179342,
1394
+ 0.2254406512186596,
1395
+ 0.22845071468315314,
1396
+ 0.23147865526229944,
1397
+ 0.234523829238346,
1398
+ 0.23758556706371228,
1399
+ 0.24066317499230686,
1400
+ 0.24375593483483984,
1401
+ 0.24686311409101686,
1402
+ 0.2499839605991125,
1403
+ 0.25311769874918233,
1404
+ 0.2562635382000597,
1405
+ 0.25942067382382017,
1406
+ 0.26258828354318864,
1407
+ 0.26576553496727834,
1408
+ 0.268951578906699,
1409
+ 0.2721455583693323,
1410
+ 0.27534660377793074,
1411
+ 0.27855383862745725,
1412
+ 0.2817663815723264,
1413
+ 0.28498334363505895,
1414
+ 0.2882038337208314,
1415
+ 0.29142695514717964,
1416
+ 0.294651812375952,
1417
+ 0.2978775098376307,
1418
+ 0.30110315210402605,
1419
+ 0.30432784900279064,
1420
+ 0.3075507133072205,
1421
+ 0.31077086219577416,
1422
+ 0.31398742158784043,
1423
+ 0.31719952251253747,
1424
+ 0.3204063092663291,
1425
+ 0.32360693296952664,
1426
+ 0.32680055897354365,
1427
+ 0.32998636335106857,
1428
+ 0.33316353602918547,
1429
+ 0.3363312804038497,
1430
+ 0.3394888168975932,
1431
+ 0.3426353809690499,
1432
+ 0.34577022484328396,
1433
+ 0.3488926187656832,
1434
+ 0.3520018504474608,
1435
+ 0.3550972272313696,
1436
+ 0.3581780754349312,
1437
+ 0.3612437409475741,
1438
+ 0.36429359004635475,
1439
+ 0.3673270093248336,
1440
+ 0.37034340683548617,
1441
+ 0.373342210384954,
1442
+ 0.3763228707499103,
1443
+ 0.37928485888928914,
1444
+ 0.3822276672011649,
1445
+ 0.3851508096810503,
1446
+ 0.38805382271455424,
1447
+ 0.3909362637322736,
1448
+ 0.393797710635096,
1449
+ 0.3966377641695234,
1450
+ 0.39945604543199037,
1451
+ 0.4022521954084449,
1452
+ 0.4050258772141813,
1453
+ 0.40777677362764636,
1454
+ 0.4105045882755698,
1455
+ 0.4132090435062123,
1456
+ 0.41588988197650334,
1457
+ 0.4185468652481373,
1458
+ 0.421179773218156,
1459
+ 0.42378840486347724,
1460
+ 0.4263725764513295
1461
+ ]
1462
+ },
1463
+ "100": {
1464
+ "t_fraction": [
1465
+ 0.0,
1466
+ 0.010101010101010102,
1467
+ 0.020202020202020204,
1468
+ 0.030303030303030304,
1469
+ 0.04040404040404041,
1470
+ 0.05050505050505051,
1471
+ 0.06060606060606061,
1472
+ 0.07070707070707072,
1473
+ 0.08080808080808081,
1474
+ 0.09090909090909091,
1475
+ 0.10101010101010102,
1476
+ 0.11111111111111112,
1477
+ 0.12121212121212122,
1478
+ 0.13131313131313133,
1479
+ 0.14141414141414144,
1480
+ 0.15151515151515152,
1481
+ 0.16161616161616163,
1482
+ 0.17171717171717174,
1483
+ 0.18181818181818182,
1484
+ 0.19191919191919193,
1485
+ 0.20202020202020204,
1486
+ 0.21212121212121213,
1487
+ 0.22222222222222224,
1488
+ 0.23232323232323235,
1489
+ 0.24242424242424243,
1490
+ 0.25252525252525254,
1491
+ 0.26262626262626265,
1492
+ 0.27272727272727276,
1493
+ 0.2828282828282829,
1494
+ 0.29292929292929293,
1495
+ 0.30303030303030304,
1496
+ 0.31313131313131315,
1497
+ 0.32323232323232326,
1498
+ 0.33333333333333337,
1499
+ 0.3434343434343435,
1500
+ 0.3535353535353536,
1501
+ 0.36363636363636365,
1502
+ 0.37373737373737376,
1503
+ 0.38383838383838387,
1504
+ 0.393939393939394,
1505
+ 0.4040404040404041,
1506
+ 0.4141414141414142,
1507
+ 0.42424242424242425,
1508
+ 0.43434343434343436,
1509
+ 0.4444444444444445,
1510
+ 0.4545454545454546,
1511
+ 0.4646464646464647,
1512
+ 0.4747474747474748,
1513
+ 0.48484848484848486,
1514
+ 0.494949494949495,
1515
+ 0.5050505050505051,
1516
+ 0.5151515151515152,
1517
+ 0.5252525252525253,
1518
+ 0.5353535353535354,
1519
+ 0.5454545454545455,
1520
+ 0.5555555555555556,
1521
+ 0.5656565656565657,
1522
+ 0.5757575757575758,
1523
+ 0.5858585858585859,
1524
+ 0.595959595959596,
1525
+ 0.6060606060606061,
1526
+ 0.6161616161616162,
1527
+ 0.6262626262626263,
1528
+ 0.6363636363636365,
1529
+ 0.6464646464646465,
1530
+ 0.6565656565656566,
1531
+ 0.6666666666666667,
1532
+ 0.6767676767676768,
1533
+ 0.686868686868687,
1534
+ 0.696969696969697,
1535
+ 0.7070707070707072,
1536
+ 0.7171717171717172,
1537
+ 0.7272727272727273,
1538
+ 0.7373737373737375,
1539
+ 0.7474747474747475,
1540
+ 0.7575757575757577,
1541
+ 0.7676767676767677,
1542
+ 0.7777777777777778,
1543
+ 0.787878787878788,
1544
+ 0.797979797979798,
1545
+ 0.8080808080808082,
1546
+ 0.8181818181818182,
1547
+ 0.8282828282828284,
1548
+ 0.8383838383838385,
1549
+ 0.8484848484848485,
1550
+ 0.8585858585858587,
1551
+ 0.8686868686868687,
1552
+ 0.8787878787878789,
1553
+ 0.888888888888889,
1554
+ 0.8989898989898991,
1555
+ 0.9090909090909092,
1556
+ 0.9191919191919192,
1557
+ 0.9292929292929294,
1558
+ 0.9393939393939394,
1559
+ 0.9494949494949496,
1560
+ 0.9595959595959597,
1561
+ 0.9696969696969697,
1562
+ 0.9797979797979799,
1563
+ 0.98989898989899,
1564
+ 1.0
1565
+ ],
1566
+ "weights": [
1567
+ 1.0,
1568
+ 0.13884620491953997,
1569
+ 0.1410742635229736,
1570
+ 0.14332922976989948,
1571
+ 0.14561132778181593,
1572
+ 0.14792075620682213,
1573
+ 0.1502577793880847,
1574
+ 0.15262261609281377,
1575
+ 0.15501548195203407,
1576
+ 0.15743654940214702,
1577
+ 0.15988602044145328,
1578
+ 0.16236404043499086,
1579
+ 0.16487074600865273,
1580
+ 0.16740627152635373,
1581
+ 0.16997070339900736,
1582
+ 0.17256410769629124,
1583
+ 0.17518654252291133,
1584
+ 0.17783802190173575,
1585
+ 0.1805185343149441,
1586
+ 0.1832280427304383,
1587
+ 0.18596647735047794,
1588
+ 0.18873374624947356,
1589
+ 0.1915297079469825,
1590
+ 0.19435420843884418,
1591
+ 0.19720703806997603,
1592
+ 0.2000879726500671,
1593
+ 0.2029967352663196,
1594
+ 0.20593302590663382,
1595
+ 0.20889650438847043,
1596
+ 0.21188679847839792,
1597
+ 0.214903497488207,
1598
+ 0.21794615497447814,
1599
+ 0.2210142897018719,
1600
+ 0.22410738638952402,
1601
+ 0.22722488695444276,
1602
+ 0.2303662131244609,
1603
+ 0.2335307398424837,
1604
+ 0.2367178203701354,
1605
+ 0.23992676342092178,
1606
+ 0.2431568590960218,
1607
+ 0.24640736098875934,
1608
+ 0.2496774962505051,
1609
+ 0.2529664609481025,
1610
+ 0.2562734285168165,
1611
+ 0.2595975467301597,
1612
+ 0.26293794225153727,
1613
+ 0.26629371500519455,
1614
+ 0.26966395321903885,
1615
+ 0.2730477159515991,
1616
+ 0.2764440538871212,
1617
+ 0.27985200285133394,
1618
+ 0.28327057850547,
1619
+ 0.28669879471615245,
1620
+ 0.2901356483166301,
1621
+ 0.2935801324539655,
1622
+ 0.29703123286760236,
1623
+ 0.3004879333997654,
1624
+ 0.3039492124386896,
1625
+ 0.3074140521638612,
1626
+ 0.31088143379789945,
1627
+ 0.3143503418897096,
1628
+ 0.31781976585711513,
1629
+ 0.3212887032419091,
1630
+ 0.32475615645122574,
1631
+ 0.32822114041504985,
1632
+ 0.33168268009283747,
1633
+ 0.33513981048217056,
1634
+ 0.33859158538952283,
1635
+ 0.3420370705461413,
1636
+ 0.34547534722715173,
1637
+ 0.3489055158153955,
1638
+ 0.3523266942287154,
1639
+ 0.3557380213750217,
1640
+ 0.3591386544822791,
1641
+ 0.36252777234599476,
1642
+ 0.36590457602392634,
1643
+ 0.3692682877291927,
1644
+ 0.3726181549553443,
1645
+ 0.37595344655344104,
1646
+ 0.37927345663200845,
1647
+ 0.3825775028112138,
1648
+ 0.38586492763467356,
1649
+ 0.38913509863143514,
1650
+ 0.3923874078328193,
1651
+ 0.39562127240127076,
1652
+ 0.3988361344828781,
1653
+ 0.40203146095521597,
1654
+ 0.40520674383068767,
1655
+ 0.4083614993522698,
1656
+ 0.411495269258617,
1657
+ 0.4146076183701266,
1658
+ 0.4176981363897399,
1659
+ 0.42076643625064447,
1660
+ 0.42381215429596863,
1661
+ 0.4268349495478982,
1662
+ 0.4298345037212183,
1663
+ 0.4328105207025758,
1664
+ 0.43576272587438825,
1665
+ 0.43869086513058997,
1666
+ 0.4415947056168169
1667
+ ]
1668
+ },
1669
+ "150": {
1670
+ "t_fraction": [
1671
+ 0.0,
1672
+ 0.010101010101010102,
1673
+ 0.020202020202020204,
1674
+ 0.030303030303030304,
1675
+ 0.04040404040404041,
1676
+ 0.05050505050505051,
1677
+ 0.06060606060606061,
1678
+ 0.07070707070707072,
1679
+ 0.08080808080808081,
1680
+ 0.09090909090909091,
1681
+ 0.10101010101010102,
1682
+ 0.11111111111111112,
1683
+ 0.12121212121212122,
1684
+ 0.13131313131313133,
1685
+ 0.14141414141414144,
1686
+ 0.15151515151515152,
1687
+ 0.16161616161616163,
1688
+ 0.17171717171717174,
1689
+ 0.18181818181818182,
1690
+ 0.19191919191919193,
1691
+ 0.20202020202020204,
1692
+ 0.21212121212121213,
1693
+ 0.22222222222222224,
1694
+ 0.23232323232323235,
1695
+ 0.24242424242424243,
1696
+ 0.25252525252525254,
1697
+ 0.26262626262626265,
1698
+ 0.27272727272727276,
1699
+ 0.2828282828282829,
1700
+ 0.29292929292929293,
1701
+ 0.30303030303030304,
1702
+ 0.31313131313131315,
1703
+ 0.32323232323232326,
1704
+ 0.33333333333333337,
1705
+ 0.3434343434343435,
1706
+ 0.3535353535353536,
1707
+ 0.36363636363636365,
1708
+ 0.37373737373737376,
1709
+ 0.38383838383838387,
1710
+ 0.393939393939394,
1711
+ 0.4040404040404041,
1712
+ 0.4141414141414142,
1713
+ 0.42424242424242425,
1714
+ 0.43434343434343436,
1715
+ 0.4444444444444445,
1716
+ 0.4545454545454546,
1717
+ 0.4646464646464647,
1718
+ 0.4747474747474748,
1719
+ 0.48484848484848486,
1720
+ 0.494949494949495,
1721
+ 0.5050505050505051,
1722
+ 0.5151515151515152,
1723
+ 0.5252525252525253,
1724
+ 0.5353535353535354,
1725
+ 0.5454545454545455,
1726
+ 0.5555555555555556,
1727
+ 0.5656565656565657,
1728
+ 0.5757575757575758,
1729
+ 0.5858585858585859,
1730
+ 0.595959595959596,
1731
+ 0.6060606060606061,
1732
+ 0.6161616161616162,
1733
+ 0.6262626262626263,
1734
+ 0.6363636363636365,
1735
+ 0.6464646464646465,
1736
+ 0.6565656565656566,
1737
+ 0.6666666666666667,
1738
+ 0.6767676767676768,
1739
+ 0.686868686868687,
1740
+ 0.696969696969697,
1741
+ 0.7070707070707072,
1742
+ 0.7171717171717172,
1743
+ 0.7272727272727273,
1744
+ 0.7373737373737375,
1745
+ 0.7474747474747475,
1746
+ 0.7575757575757577,
1747
+ 0.7676767676767677,
1748
+ 0.7777777777777778,
1749
+ 0.787878787878788,
1750
+ 0.797979797979798,
1751
+ 0.8080808080808082,
1752
+ 0.8181818181818182,
1753
+ 0.8282828282828284,
1754
+ 0.8383838383838385,
1755
+ 0.8484848484848485,
1756
+ 0.8585858585858587,
1757
+ 0.8686868686868687,
1758
+ 0.8787878787878789,
1759
+ 0.888888888888889,
1760
+ 0.8989898989898991,
1761
+ 0.9090909090909092,
1762
+ 0.9191919191919192,
1763
+ 0.9292929292929294,
1764
+ 0.9393939393939394,
1765
+ 0.9494949494949496,
1766
+ 0.9595959595959597,
1767
+ 0.9696969696969697,
1768
+ 0.9797979797979799,
1769
+ 0.98989898989899,
1770
+ 1.0
1771
+ ],
1772
+ "weights": [
1773
+ 1.0,
1774
+ 0.13900858460583534,
1775
+ 0.14116037366807452,
1776
+ 0.1433393839454123,
1777
+ 0.14554619477294514,
1778
+ 0.14778125815999943,
1779
+ 0.15004506969515732,
1780
+ 0.15233816112169024,
1781
+ 0.15466099177478937,
1782
+ 0.15701399259203494,
1783
+ 0.15939761646945566,
1784
+ 0.16181227899592507,
1785
+ 0.16425838051763797,
1786
+ 0.16673627784852765,
1787
+ 0.1692463056591957,
1788
+ 0.17178877808208107,
1789
+ 0.17436396384745764,
1790
+ 0.1769721024693994,
1791
+ 0.17961339681018038,
1792
+ 0.18228802375593262,
1793
+ 0.18499611608275787,
1794
+ 0.18773774838706075,
1795
+ 0.19051297498891834,
1796
+ 0.19332179221856224,
1797
+ 0.1961641623210112,
1798
+ 0.1990399980929249,
1799
+ 0.20194916681541422,
1800
+ 0.20489148680713823,
1801
+ 0.20786672957568852,
1802
+ 0.21087462132247745,
1803
+ 0.2139148412972845,
1804
+ 0.2169870115905135,
1805
+ 0.22009071656080734,
1806
+ 0.22322548663190037,
1807
+ 0.22639081202391598,
1808
+ 0.22958612753885937,
1809
+ 0.23281082745205273,
1810
+ 0.23606425880964205,
1811
+ 0.23934572691347725,
1812
+ 0.24265449278175535,
1813
+ 0.24598977189364754,
1814
+ 0.249350747135574,
1815
+ 0.25273656071579936,
1816
+ 0.25614631604685567,
1817
+ 0.25957908254995143,
1818
+ 0.2630338961372013,
1819
+ 0.26650976350037636,
1820
+ 0.2700056592873042,
1821
+ 0.2735205354367603,
1822
+ 0.27705331909007164,
1823
+ 0.28060291096337553,
1824
+ 0.28416819711759583,
1825
+ 0.28774804435423534,
1826
+ 0.29134130462072616,
1827
+ 0.29494681655305877,
1828
+ 0.29856341061237957,
1829
+ 0.3021899091237375,
1830
+ 0.3058251286797561,
1831
+ 0.30946788182967844,
1832
+ 0.3131169825302818,
1833
+ 0.3167712461241242,
1834
+ 0.3204294923630817,
1835
+ 0.3240905467404975,
1836
+ 0.32775324382223175,
1837
+ 0.3314164272025777,
1838
+ 0.33507895459305104,
1839
+ 0.3387396964069811,
1840
+ 0.34239754088795205,
1841
+ 0.34605139219137604,
1842
+ 0.34970017401302234,
1843
+ 0.35334283189980803,
1844
+ 0.3569783326389627,
1845
+ 0.36060566663182037,
1846
+ 0.3642238488678807,
1847
+ 0.3678319194585594,
1848
+ 0.3714289453518074,
1849
+ 0.375014021584546,
1850
+ 0.3785862700205314,
1851
+ 0.3821448416780604,
1852
+ 0.38568891698468033,
1853
+ 0.3892177051394272,
1854
+ 0.39273044700316584,
1855
+ 0.39622641197906855,
1856
+ 0.39970490045992363,
1857
+ 0.4031652429914829,
1858
+ 0.4066068007929769,
1859
+ 0.41002896465911587,
1860
+ 0.4134311554875193,
1861
+ 0.4168128250137748,
1862
+ 0.4201734533402321,
1863
+ 0.42351254968468516,
1864
+ 0.42682965272525625,
1865
+ 0.4301243285900922,
1866
+ 0.4333961714809263,
1867
+ 0.43664480238200576,
1868
+ 0.4398698694003773,
1869
+ 0.4430710457780954,
1870
+ 0.44624803093023757,
1871
+ 0.4494005478742759,
1872
+ 0.45252834426194855
1873
+ ]
1874
+ },
1875
+ "200": {
1876
+ "t_fraction": [
1877
+ 0.0,
1878
+ 0.010101010101010102,
1879
+ 0.020202020202020204,
1880
+ 0.030303030303030304,
1881
+ 0.04040404040404041,
1882
+ 0.05050505050505051,
1883
+ 0.06060606060606061,
1884
+ 0.07070707070707072,
1885
+ 0.08080808080808081,
1886
+ 0.09090909090909091,
1887
+ 0.10101010101010102,
1888
+ 0.11111111111111112,
1889
+ 0.12121212121212122,
1890
+ 0.13131313131313133,
1891
+ 0.14141414141414144,
1892
+ 0.15151515151515152,
1893
+ 0.16161616161616163,
1894
+ 0.17171717171717174,
1895
+ 0.18181818181818182,
1896
+ 0.19191919191919193,
1897
+ 0.20202020202020204,
1898
+ 0.21212121212121213,
1899
+ 0.22222222222222224,
1900
+ 0.23232323232323235,
1901
+ 0.24242424242424243,
1902
+ 0.25252525252525254,
1903
+ 0.26262626262626265,
1904
+ 0.27272727272727276,
1905
+ 0.2828282828282829,
1906
+ 0.29292929292929293,
1907
+ 0.30303030303030304,
1908
+ 0.31313131313131315,
1909
+ 0.32323232323232326,
1910
+ 0.33333333333333337,
1911
+ 0.3434343434343435,
1912
+ 0.3535353535353536,
1913
+ 0.36363636363636365,
1914
+ 0.37373737373737376,
1915
+ 0.38383838383838387,
1916
+ 0.393939393939394,
1917
+ 0.4040404040404041,
1918
+ 0.4141414141414142,
1919
+ 0.42424242424242425,
1920
+ 0.43434343434343436,
1921
+ 0.4444444444444445,
1922
+ 0.4545454545454546,
1923
+ 0.4646464646464647,
1924
+ 0.4747474747474748,
1925
+ 0.48484848484848486,
1926
+ 0.494949494949495,
1927
+ 0.5050505050505051,
1928
+ 0.5151515151515152,
1929
+ 0.5252525252525253,
1930
+ 0.5353535353535354,
1931
+ 0.5454545454545455,
1932
+ 0.5555555555555556,
1933
+ 0.5656565656565657,
1934
+ 0.5757575757575758,
1935
+ 0.5858585858585859,
1936
+ 0.595959595959596,
1937
+ 0.6060606060606061,
1938
+ 0.6161616161616162,
1939
+ 0.6262626262626263,
1940
+ 0.6363636363636365,
1941
+ 0.6464646464646465,
1942
+ 0.6565656565656566,
1943
+ 0.6666666666666667,
1944
+ 0.6767676767676768,
1945
+ 0.686868686868687,
1946
+ 0.696969696969697,
1947
+ 0.7070707070707072,
1948
+ 0.7171717171717172,
1949
+ 0.7272727272727273,
1950
+ 0.7373737373737375,
1951
+ 0.7474747474747475,
1952
+ 0.7575757575757577,
1953
+ 0.7676767676767677,
1954
+ 0.7777777777777778,
1955
+ 0.787878787878788,
1956
+ 0.797979797979798,
1957
+ 0.8080808080808082,
1958
+ 0.8181818181818182,
1959
+ 0.8282828282828284,
1960
+ 0.8383838383838385,
1961
+ 0.8484848484848485,
1962
+ 0.8585858585858587,
1963
+ 0.8686868686868687,
1964
+ 0.8787878787878789,
1965
+ 0.888888888888889,
1966
+ 0.8989898989898991,
1967
+ 0.9090909090909092,
1968
+ 0.9191919191919192,
1969
+ 0.9292929292929294,
1970
+ 0.9393939393939394,
1971
+ 0.9494949494949496,
1972
+ 0.9595959595959597,
1973
+ 0.9696969696969697,
1974
+ 0.9797979797979799,
1975
+ 0.98989898989899,
1976
+ 1.0
1977
+ ],
1978
+ "weights": [
1979
+ 1.0,
1980
+ 0.14037580478880685,
1981
+ 0.14240468106380735,
1982
+ 0.14446181370568079,
1983
+ 0.14654796924255145,
1984
+ 0.148664096554772,
1985
+ 0.1508109550107285,
1986
+ 0.1529893937815348,
1987
+ 0.15520018625106038,
1988
+ 0.15744413168567137,
1989
+ 0.15972195130061487,
1990
+ 0.16203435122140786,
1991
+ 0.16438203543866356,
1992
+ 0.1667656412928576,
1993
+ 0.16918576902688773,
1994
+ 0.17164300624722006,
1995
+ 0.17413786500337083,
1996
+ 0.17667081963015316,
1997
+ 0.17924230733286384,
1998
+ 0.1818526983469155,
1999
+ 0.18450232333326255,
2000
+ 0.18719144914128807,
2001
+ 0.18992029947710903,
2002
+ 0.19268901861716645,
2003
+ 0.19549771033301305,
2004
+ 0.1983464038945293,
2005
+ 0.2012350822736977,
2006
+ 0.20416365277892112,
2007
+ 0.20713196793281669,
2008
+ 0.21013980661202272,
2009
+ 0.21318689003596927,
2010
+ 0.21627287917616494,
2011
+ 0.219397361216214,
2012
+ 0.2225598633721938,
2013
+ 0.22575985757973518,
2014
+ 0.22899674013599078,
2015
+ 0.23226985731724775,
2016
+ 0.2355784865527715,
2017
+ 0.23892185230504454,
2018
+ 0.24229912673493306,
2019
+ 0.24570941195867574,
2020
+ 0.24915176585965942,
2021
+ 0.252625198185479,
2022
+ 0.2561286669249464,
2023
+ 0.25966108042178815,
2024
+ 0.2632213051270777,
2025
+ 0.26680816977172456,
2026
+ 0.2704204589868648,
2027
+ 0.27405692860755254,
2028
+ 0.27771629717263513,
2029
+ 0.2813972570724398,
2030
+ 0.285098471053011,
2031
+ 0.2888185829836867,
2032
+ 0.2925562180890034,
2033
+ 0.29630998334688186,
2034
+ 0.30007847185093434,
2035
+ 0.3038602689578016,
2036
+ 0.30765395463292045,
2037
+ 0.311458104893395,
2038
+ 0.31527129511366037,
2039
+ 0.31909210487852513,
2040
+ 0.3229191196492977,
2041
+ 0.326750934007337,
2042
+ 0.3305861537324231,
2043
+ 0.33442340088319505,
2044
+ 0.33826131294221073,
2045
+ 0.34209854874109447,
2046
+ 0.3459337870242481,
2047
+ 0.34976573209738104,
2048
+ 0.3535931144330134,
2049
+ 0.3574146925412652,
2050
+ 0.36122925405176337,
2051
+ 0.36503561861611195,
2052
+ 0.3688326381094815,
2053
+ 0.372619198996805,
2054
+ 0.3763942228326832,
2055
+ 0.3801566671454652,
2056
+ 0.38390552622602697,
2057
+ 0.38763983204913505,
2058
+ 0.39135865422336463,
2059
+ 0.3950611022055404,
2060
+ 0.39874632324928866,
2061
+ 0.4024135041179501,
2062
+ 0.40606186918572973,
2063
+ 0.40969068385903756,
2064
+ 0.41329925023796277,
2065
+ 0.4168869092325345,
2066
+ 0.4204530400481373,
2067
+ 0.4239970594494581,
2068
+ 0.42751842024640313,
2069
+ 0.43101661141404296,
2070
+ 0.43449115836553526,
2071
+ 0.43794161977142715,
2072
+ 0.441367589118682,
2073
+ 0.44476869267418334,
2074
+ 0.44814458854054834,
2075
+ 0.4514949660966035,
2076
+ 0.45481954474970937,
2077
+ 0.45811807209590594,
2078
+ 0.46139032472870534
2079
+ ]
2080
+ }
2081
+ }
2082
+ }
results/paper_c/gradient_flow_advdiff1d/fig_gradient_alignment.pdf ADDED
Binary file (19.9 kB). View file
 
results/paper_c/gradient_flow_advdiff1d/gradient_flow_results.json ADDED
@@ -0,0 +1,1039 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "experiment": "gradient_flow_analysis",
3
+ "pde": "advdiff1d",
4
+ "seed": 42,
5
+ "device": "cuda",
6
+ "hyperparameters": {
7
+ "stage1_epochs": 200,
8
+ "stage2_epochs": 300,
9
+ "stage3_epochs": 200,
10
+ "stage1_lr": 0.001,
11
+ "stage2_lr": 0.0001,
12
+ "stage3_lr": 1e-05,
13
+ "causal_epsilon": 1.0,
14
+ "num_collocation": 2000,
15
+ "num_boundary": 200,
16
+ "batch_size": 256,
17
+ "hidden_dims": [
18
+ 64,
19
+ 64,
20
+ 64,
21
+ 64
22
+ ],
23
+ "probe_every": 10
24
+ },
25
+ "conditions": {
26
+ "with_pretrain": {
27
+ "condition": "with_pretrain",
28
+ "probes": [
29
+ {
30
+ "stage": "stage2",
31
+ "epoch": 0,
32
+ "cosine_similarity": 1.0,
33
+ "grad_magnitude_ratio": 0.9998404589353741,
34
+ "physics_grad_norm": 0.055993396788835526,
35
+ "causal_grad_norm": 0.055984463542699814,
36
+ "physics_loss": 0.0034163743257522583,
37
+ "causal_loss": 0.003415988991037011
38
+ },
39
+ {
40
+ "stage": "stage2",
41
+ "epoch": 10,
42
+ "cosine_similarity": 1.0,
43
+ "grad_magnitude_ratio": 0.9994223074504749,
44
+ "physics_grad_norm": 0.08344448357820511,
45
+ "causal_grad_norm": 0.08339627832174301,
46
+ "physics_loss": 0.0045177023857831955,
47
+ "causal_loss": 0.004515939857810736
48
+ },
49
+ {
50
+ "stage": "stage2",
51
+ "epoch": 20,
52
+ "cosine_similarity": 0.9999998807907104,
53
+ "grad_magnitude_ratio": 0.9986903669585943,
54
+ "physics_grad_norm": 0.10462749749422073,
55
+ "causal_grad_norm": 0.10449047386646271,
56
+ "physics_loss": 0.005294404458254576,
57
+ "causal_loss": 0.005290493369102478
58
+ },
59
+ {
60
+ "stage": "stage2",
61
+ "epoch": 30,
62
+ "cosine_similarity": 0.9999998807907104,
63
+ "grad_magnitude_ratio": 0.9980896013835184,
64
+ "physics_grad_norm": 0.12200802564620972,
65
+ "causal_grad_norm": 0.12177494168281555,
66
+ "physics_loss": 0.0060091204941272736,
67
+ "causal_loss": 0.006002471782267094
68
+ },
69
+ {
70
+ "stage": "stage2",
71
+ "epoch": 40,
72
+ "cosine_similarity": 0.9999997615814209,
73
+ "grad_magnitude_ratio": 0.9973816998367308,
74
+ "physics_grad_norm": 0.11488741636276245,
75
+ "causal_grad_norm": 0.11458660662174225,
76
+ "physics_loss": 0.006303117144852877,
77
+ "causal_loss": 0.006293265614658594
78
+ },
79
+ {
80
+ "stage": "stage2",
81
+ "epoch": 50,
82
+ "cosine_similarity": 0.999999463558197,
83
+ "grad_magnitude_ratio": 0.9965748566774266,
84
+ "physics_grad_norm": 0.10993333905935287,
85
+ "causal_grad_norm": 0.10955680161714554,
86
+ "physics_loss": 0.006795892957597971,
87
+ "causal_loss": 0.006782693788409233
88
+ },
89
+ {
90
+ "stage": "stage2",
91
+ "epoch": 60,
92
+ "cosine_similarity": 0.9999993443489075,
93
+ "grad_magnitude_ratio": 0.9964962420571906,
94
+ "physics_grad_norm": 0.10952302068471909,
95
+ "causal_grad_norm": 0.10913927853107452,
96
+ "physics_loss": 0.006419304758310318,
97
+ "causal_loss": 0.00640634773299098
98
+ },
99
+ {
100
+ "stage": "stage2",
101
+ "epoch": 70,
102
+ "cosine_similarity": 0.9999980926513672,
103
+ "grad_magnitude_ratio": 0.9962138807268617,
104
+ "physics_grad_norm": 0.09437695145606995,
105
+ "causal_grad_norm": 0.09401962906122208,
106
+ "physics_loss": 0.006669539958238602,
107
+ "causal_loss": 0.006652982905507088
108
+ },
109
+ {
110
+ "stage": "stage2",
111
+ "epoch": 80,
112
+ "cosine_similarity": 0.9999989867210388,
113
+ "grad_magnitude_ratio": 0.9958360441534138,
114
+ "physics_grad_norm": 0.09846358001232147,
115
+ "causal_grad_norm": 0.09805358201265335,
116
+ "physics_loss": 0.006579127162694931,
117
+ "causal_loss": 0.006561832036823034
118
+ },
119
+ {
120
+ "stage": "stage2",
121
+ "epoch": 90,
122
+ "cosine_similarity": 0.9999971985816956,
123
+ "grad_magnitude_ratio": 0.9952122669660262,
124
+ "physics_grad_norm": 0.09150968492031097,
125
+ "causal_grad_norm": 0.09107156097888947,
126
+ "physics_loss": 0.006722255609929562,
127
+ "causal_loss": 0.006700052879750729
128
+ },
129
+ {
130
+ "stage": "stage2",
131
+ "epoch": 100,
132
+ "cosine_similarity": 0.9999917149543762,
133
+ "grad_magnitude_ratio": 0.9947683389640084,
134
+ "physics_grad_norm": 0.08297425508499146,
135
+ "causal_grad_norm": 0.08254016190767288,
136
+ "physics_loss": 0.006235565058887005,
137
+ "causal_loss": 0.006213376298546791
138
+ },
139
+ {
140
+ "stage": "stage2",
141
+ "epoch": 110,
142
+ "cosine_similarity": 0.9999793767929077,
143
+ "grad_magnitude_ratio": 0.9951363787653194,
144
+ "physics_grad_norm": 0.07413935661315918,
145
+ "causal_grad_norm": 0.07377877086400986,
146
+ "physics_loss": 0.006782819051295519,
147
+ "causal_loss": 0.006754019297659397
148
+ },
149
+ {
150
+ "stage": "stage2",
151
+ "epoch": 120,
152
+ "cosine_similarity": 0.9999700784683228,
153
+ "grad_magnitude_ratio": 0.9937431472246299,
154
+ "physics_grad_norm": 0.07239629328250885,
155
+ "causal_grad_norm": 0.07194332033395767,
156
+ "physics_loss": 0.006860552821308374,
157
+ "causal_loss": 0.006824939977377653
158
+ },
159
+ {
160
+ "stage": "stage2",
161
+ "epoch": 130,
162
+ "cosine_similarity": 0.9999411702156067,
163
+ "grad_magnitude_ratio": 0.9916506395595069,
164
+ "physics_grad_norm": 0.07337643951177597,
165
+ "causal_grad_norm": 0.07276379317045212,
166
+ "physics_loss": 0.007018768694251776,
167
+ "causal_loss": 0.0069791278801858425
168
+ },
169
+ {
170
+ "stage": "stage2",
171
+ "epoch": 140,
172
+ "cosine_similarity": 0.9998835325241089,
173
+ "grad_magnitude_ratio": 0.9941594907831282,
174
+ "physics_grad_norm": 0.056699205189943314,
175
+ "causal_grad_norm": 0.05636805295944214,
176
+ "physics_loss": 0.0069340672343969345,
177
+ "causal_loss": 0.006885282229632139
178
+ },
179
+ {
180
+ "stage": "stage2",
181
+ "epoch": 150,
182
+ "cosine_similarity": 0.9997420310974121,
183
+ "grad_magnitude_ratio": 0.9829683839223398,
184
+ "physics_grad_norm": 0.06688962876796722,
185
+ "causal_grad_norm": 0.06575039029121399,
186
+ "physics_loss": 0.007728659547865391,
187
+ "causal_loss": 0.007658537942916155
188
+ },
189
+ {
190
+ "stage": "stage2",
191
+ "epoch": 160,
192
+ "cosine_similarity": 0.999845027923584,
193
+ "grad_magnitude_ratio": 0.9894927377701583,
194
+ "physics_grad_norm": 0.05993926525115967,
195
+ "causal_grad_norm": 0.0593094676733017,
196
+ "physics_loss": 0.006888104137033224,
197
+ "causal_loss": 0.006833693012595177
198
+ },
199
+ {
200
+ "stage": "stage2",
201
+ "epoch": 170,
202
+ "cosine_similarity": 0.9996508955955505,
203
+ "grad_magnitude_ratio": 0.9876203270464392,
204
+ "physics_grad_norm": 0.05528320372104645,
205
+ "causal_grad_norm": 0.054598815739154816,
206
+ "physics_loss": 0.007355723530054092,
207
+ "causal_loss": 0.0072853416204452515
208
+ },
209
+ {
210
+ "stage": "stage2",
211
+ "epoch": 180,
212
+ "cosine_similarity": 0.9996204972267151,
213
+ "grad_magnitude_ratio": 0.9881565215746457,
214
+ "physics_grad_norm": 0.058688487857580185,
215
+ "causal_grad_norm": 0.057993412017822266,
216
+ "physics_loss": 0.007988538593053818,
217
+ "causal_loss": 0.007903717458248138
218
+ },
219
+ {
220
+ "stage": "stage2",
221
+ "epoch": 190,
222
+ "cosine_similarity": 0.999470055103302,
223
+ "grad_magnitude_ratio": 0.9803539058737719,
224
+ "physics_grad_norm": 0.060941748321056366,
225
+ "causal_grad_norm": 0.05974448099732399,
226
+ "physics_loss": 0.008436641655862331,
227
+ "causal_loss": 0.008335218764841557
228
+ },
229
+ {
230
+ "stage": "stage2",
231
+ "epoch": 200,
232
+ "cosine_similarity": 0.9992625713348389,
233
+ "grad_magnitude_ratio": 0.974982899124777,
234
+ "physics_grad_norm": 0.06407824903726578,
235
+ "causal_grad_norm": 0.06247519701719284,
236
+ "physics_loss": 0.008694429881870747,
237
+ "causal_loss": 0.008579445071518421
238
+ },
239
+ {
240
+ "stage": "stage2",
241
+ "epoch": 210,
242
+ "cosine_similarity": 0.9991307258605957,
243
+ "grad_magnitude_ratio": 0.9696386101835861,
244
+ "physics_grad_norm": 0.06008277088403702,
245
+ "causal_grad_norm": 0.058258574455976486,
246
+ "physics_loss": 0.00829549040645361,
247
+ "causal_loss": 0.008172254078090191
248
+ },
249
+ {
250
+ "stage": "stage2",
251
+ "epoch": 220,
252
+ "cosine_similarity": 0.9990769624710083,
253
+ "grad_magnitude_ratio": 0.9616318039744515,
254
+ "physics_grad_norm": 0.07127299904823303,
255
+ "causal_grad_norm": 0.06853838264942169,
256
+ "physics_loss": 0.009139413014054298,
257
+ "causal_loss": 0.008989324793219566
258
+ },
259
+ {
260
+ "stage": "stage2",
261
+ "epoch": 230,
262
+ "cosine_similarity": 0.9993254542350769,
263
+ "grad_magnitude_ratio": 0.9656225920072916,
264
+ "physics_grad_norm": 0.07736227661371231,
265
+ "causal_grad_norm": 0.07470276206731796,
266
+ "physics_loss": 0.00855631660670042,
267
+ "causal_loss": 0.008425564505159855
268
+ },
269
+ {
270
+ "stage": "stage2",
271
+ "epoch": 240,
272
+ "cosine_similarity": 0.9984538555145264,
273
+ "grad_magnitude_ratio": 0.9494146546061107,
274
+ "physics_grad_norm": 0.07792972773313522,
275
+ "causal_grad_norm": 0.07398762553930283,
276
+ "physics_loss": 0.01005198061466217,
277
+ "causal_loss": 0.009835399687290192
278
+ },
279
+ {
280
+ "stage": "stage2",
281
+ "epoch": 250,
282
+ "cosine_similarity": 0.9976674914360046,
283
+ "grad_magnitude_ratio": 0.9450957109540828,
284
+ "physics_grad_norm": 0.07680147886276245,
285
+ "causal_grad_norm": 0.07258474826812744,
286
+ "physics_loss": 0.010146722197532654,
287
+ "causal_loss": 0.009899907745420933
288
+ },
289
+ {
290
+ "stage": "stage2",
291
+ "epoch": 260,
292
+ "cosine_similarity": 0.9979865550994873,
293
+ "grad_magnitude_ratio": 0.9318051380128963,
294
+ "physics_grad_norm": 0.08613388985395432,
295
+ "causal_grad_norm": 0.08026000112295151,
296
+ "physics_loss": 0.010258553549647331,
297
+ "causal_loss": 0.010008711367845535
298
+ },
299
+ {
300
+ "stage": "stage2",
301
+ "epoch": 270,
302
+ "cosine_similarity": 0.9980309009552002,
303
+ "grad_magnitude_ratio": 0.9453165857912249,
304
+ "physics_grad_norm": 0.07936648279428482,
305
+ "causal_grad_norm": 0.07502645254135132,
306
+ "physics_loss": 0.010200506076216698,
307
+ "causal_loss": 0.009947787038981915
308
+ },
309
+ {
310
+ "stage": "stage2",
311
+ "epoch": 280,
312
+ "cosine_similarity": 0.9974075555801392,
313
+ "grad_magnitude_ratio": 0.934266953762732,
314
+ "physics_grad_norm": 0.08631131052970886,
315
+ "causal_grad_norm": 0.08063780516386032,
316
+ "physics_loss": 0.010349437594413757,
317
+ "causal_loss": 0.010043546557426453
318
+ },
319
+ {
320
+ "stage": "stage2",
321
+ "epoch": 290,
322
+ "cosine_similarity": 0.9973978996276855,
323
+ "grad_magnitude_ratio": 0.941478916226771,
324
+ "physics_grad_norm": 0.08592784404754639,
325
+ "causal_grad_norm": 0.08089925348758698,
326
+ "physics_loss": 0.011045156978070736,
327
+ "causal_loss": 0.010736704804003239
328
+ },
329
+ {
330
+ "stage": "stage3",
331
+ "epoch": 0,
332
+ "cosine_similarity": 0.999999463558197,
333
+ "grad_magnitude_ratio": 0.9986644266290763,
334
+ "physics_grad_norm": 0.09647009521722794,
335
+ "causal_grad_norm": 0.09634125232696533,
336
+ "physics_loss": 0.011543264612555504,
337
+ "causal_loss": 0.011537494137883186
338
+ },
339
+ {
340
+ "stage": "stage3",
341
+ "epoch": 10,
342
+ "cosine_similarity": 0.9999886751174927,
343
+ "grad_magnitude_ratio": 0.9936787868738048,
344
+ "physics_grad_norm": 0.1007356196641922,
345
+ "causal_grad_norm": 0.10009884834289551,
346
+ "physics_loss": 0.011911875568330288,
347
+ "causal_loss": 0.011884705163538456
348
+ },
349
+ {
350
+ "stage": "stage3",
351
+ "epoch": 20,
352
+ "cosine_similarity": 0.9999568462371826,
353
+ "grad_magnitude_ratio": 0.9896699202619473,
354
+ "physics_grad_norm": 0.08882422745227814,
355
+ "causal_grad_norm": 0.08790666610002518,
356
+ "physics_loss": 0.01068958267569542,
357
+ "causal_loss": 0.010649185627698898
358
+ },
359
+ {
360
+ "stage": "stage3",
361
+ "epoch": 30,
362
+ "cosine_similarity": 0.9999328851699829,
363
+ "grad_magnitude_ratio": 0.9872905774468492,
364
+ "physics_grad_norm": 0.08849769085645676,
365
+ "causal_grad_norm": 0.08737293630838394,
366
+ "physics_loss": 0.010518821887671947,
367
+ "causal_loss": 0.010463893413543701
368
+ },
369
+ {
370
+ "stage": "stage3",
371
+ "epoch": 40,
372
+ "cosine_similarity": 0.9998841285705566,
373
+ "grad_magnitude_ratio": 0.9817110104164594,
374
+ "physics_grad_norm": 0.0977037325501442,
375
+ "causal_grad_norm": 0.09591683000326157,
376
+ "physics_loss": 0.011329064145684242,
377
+ "causal_loss": 0.011252670548856258
378
+ },
379
+ {
380
+ "stage": "stage3",
381
+ "epoch": 50,
382
+ "cosine_similarity": 0.9998154640197754,
383
+ "grad_magnitude_ratio": 0.9786734527707964,
384
+ "physics_grad_norm": 0.0910012349486351,
385
+ "causal_grad_norm": 0.08906049281358719,
386
+ "physics_loss": 0.011198875494301319,
387
+ "causal_loss": 0.011100389994680882
388
+ },
389
+ {
390
+ "stage": "stage3",
391
+ "epoch": 60,
392
+ "cosine_similarity": 0.9998053908348083,
393
+ "grad_magnitude_ratio": 0.9748327175716844,
394
+ "physics_grad_norm": 0.09266213327646255,
395
+ "causal_grad_norm": 0.0903300791978836,
396
+ "physics_loss": 0.010296616703271866,
397
+ "causal_loss": 0.010198394767940044
398
+ },
399
+ {
400
+ "stage": "stage3",
401
+ "epoch": 70,
402
+ "cosine_similarity": 0.9996676445007324,
403
+ "grad_magnitude_ratio": 0.9688620184305139,
404
+ "physics_grad_norm": 0.10033141821622849,
405
+ "causal_grad_norm": 0.09720730036497116,
406
+ "physics_loss": 0.011815696023404598,
407
+ "causal_loss": 0.0116725517436862
408
+ },
409
+ {
410
+ "stage": "stage3",
411
+ "epoch": 80,
412
+ "cosine_similarity": 0.9996067881584167,
413
+ "grad_magnitude_ratio": 0.9706451429671374,
414
+ "physics_grad_norm": 0.08906298130750656,
415
+ "causal_grad_norm": 0.0864485502243042,
416
+ "physics_loss": 0.011180342175066471,
417
+ "causal_loss": 0.011038387194275856
418
+ },
419
+ {
420
+ "stage": "stage3",
421
+ "epoch": 90,
422
+ "cosine_similarity": 0.9993175864219666,
423
+ "grad_magnitude_ratio": 0.968755302001572,
424
+ "physics_grad_norm": 0.08514871448278427,
425
+ "causal_grad_norm": 0.08248826861381531,
426
+ "physics_loss": 0.010905045084655285,
427
+ "causal_loss": 0.010751339606940746
428
+ },
429
+ {
430
+ "stage": "stage3",
431
+ "epoch": 100,
432
+ "cosine_similarity": 0.9993963241577148,
433
+ "grad_magnitude_ratio": 0.9643473482548944,
434
+ "physics_grad_norm": 0.09550724923610687,
435
+ "causal_grad_norm": 0.09210216253995895,
436
+ "physics_loss": 0.010999101214110851,
437
+ "causal_loss": 0.010821323841810226
438
+ },
439
+ {
440
+ "stage": "stage3",
441
+ "epoch": 110,
442
+ "cosine_similarity": 0.9994335770606995,
443
+ "grad_magnitude_ratio": 0.9445947370031309,
444
+ "physics_grad_norm": 0.12054432183504105,
445
+ "causal_grad_norm": 0.11386553198099136,
446
+ "physics_loss": 0.01253183651715517,
447
+ "causal_loss": 0.012291199527680874
448
+ },
449
+ {
450
+ "stage": "stage3",
451
+ "epoch": 120,
452
+ "cosine_similarity": 0.9991256594657898,
453
+ "grad_magnitude_ratio": 0.9576903998495547,
454
+ "physics_grad_norm": 0.09076675027608871,
455
+ "causal_grad_norm": 0.08692644536495209,
456
+ "physics_loss": 0.011071969754993916,
457
+ "causal_loss": 0.010874495841562748
458
+ },
459
+ {
460
+ "stage": "stage3",
461
+ "epoch": 130,
462
+ "cosine_similarity": 0.9986855983734131,
463
+ "grad_magnitude_ratio": 0.9509358686267446,
464
+ "physics_grad_norm": 0.09381884336471558,
465
+ "causal_grad_norm": 0.0892157033085823,
466
+ "physics_loss": 0.011346649378538132,
467
+ "causal_loss": 0.011100348085165024
468
+ },
469
+ {
470
+ "stage": "stage3",
471
+ "epoch": 140,
472
+ "cosine_similarity": 0.9990009069442749,
473
+ "grad_magnitude_ratio": 0.9591603889827771,
474
+ "physics_grad_norm": 0.09530193358659744,
475
+ "causal_grad_norm": 0.0914098396897316,
476
+ "physics_loss": 0.01101767923682928,
477
+ "causal_loss": 0.010798675939440727
478
+ },
479
+ {
480
+ "stage": "stage3",
481
+ "epoch": 150,
482
+ "cosine_similarity": 0.998563289642334,
483
+ "grad_magnitude_ratio": 0.9462527812573098,
484
+ "physics_grad_norm": 0.0913187637925148,
485
+ "causal_grad_norm": 0.08641063421964645,
486
+ "physics_loss": 0.010869511403143406,
487
+ "causal_loss": 0.010610752739012241
488
+ },
489
+ {
490
+ "stage": "stage3",
491
+ "epoch": 160,
492
+ "cosine_similarity": 0.9977527856826782,
493
+ "grad_magnitude_ratio": 0.9217187299086727,
494
+ "physics_grad_norm": 0.10134243220090866,
495
+ "causal_grad_norm": 0.0934092178940773,
496
+ "physics_loss": 0.011904627084732056,
497
+ "causal_loss": 0.01152908056974411
498
+ },
499
+ {
500
+ "stage": "stage3",
501
+ "epoch": 170,
502
+ "cosine_similarity": 0.9978342056274414,
503
+ "grad_magnitude_ratio": 0.925259397846285,
504
+ "physics_grad_norm": 0.09661851823329926,
505
+ "causal_grad_norm": 0.08939719200134277,
506
+ "physics_loss": 0.011778481304645538,
507
+ "causal_loss": 0.011416609399020672
508
+ },
509
+ {
510
+ "stage": "stage3",
511
+ "epoch": 180,
512
+ "cosine_similarity": 0.9975749254226685,
513
+ "grad_magnitude_ratio": 0.9255472247918766,
514
+ "physics_grad_norm": 0.10015178471803665,
515
+ "causal_grad_norm": 0.0926952064037323,
516
+ "physics_loss": 0.011684686876833439,
517
+ "causal_loss": 0.011326046660542488
518
+ },
519
+ {
520
+ "stage": "stage3",
521
+ "epoch": 190,
522
+ "cosine_similarity": 0.9978646039962769,
523
+ "grad_magnitude_ratio": 0.9360690313657964,
524
+ "physics_grad_norm": 0.09708811342716217,
525
+ "causal_grad_norm": 0.09088117629289627,
526
+ "physics_loss": 0.011591719463467598,
527
+ "causal_loss": 0.011255831457674503
528
+ }
529
+ ],
530
+ "wall_time_s": 90.95
531
+ },
532
+ "without_pretrain": {
533
+ "condition": "without_pretrain",
534
+ "probes": [
535
+ {
536
+ "stage": "stage2",
537
+ "epoch": 0,
538
+ "cosine_similarity": 0.9999999403953552,
539
+ "grad_magnitude_ratio": 0.9999990097491992,
540
+ "physics_grad_norm": 0.005172703880816698,
541
+ "causal_grad_norm": 0.005172698758542538,
542
+ "physics_loss": 6.007065894664265e-05,
543
+ "causal_loss": 6.0070629842812195e-05
544
+ },
545
+ {
546
+ "stage": "stage2",
547
+ "epoch": 10,
548
+ "cosine_similarity": 1.0000001192092896,
549
+ "grad_magnitude_ratio": 0.9999508562806955,
550
+ "physics_grad_norm": 0.021073510870337486,
551
+ "causal_grad_norm": 0.021072475239634514,
552
+ "physics_loss": 0.0006428785854950547,
553
+ "causal_loss": 0.000642863567918539
554
+ },
555
+ {
556
+ "stage": "stage2",
557
+ "epoch": 20,
558
+ "cosine_similarity": 1.0,
559
+ "grad_magnitude_ratio": 0.9997715635122826,
560
+ "physics_grad_norm": 0.03382232040166855,
561
+ "causal_grad_norm": 0.03381459414958954,
562
+ "physics_loss": 0.0016030319966375828,
563
+ "causal_loss": 0.0016028543468564749
564
+ },
565
+ {
566
+ "stage": "stage2",
567
+ "epoch": 30,
568
+ "cosine_similarity": 0.9999999403953552,
569
+ "grad_magnitude_ratio": 0.9994659411510339,
570
+ "physics_grad_norm": 0.04347088187932968,
571
+ "causal_grad_norm": 0.04344766587018967,
572
+ "physics_loss": 0.0025469406973570585,
573
+ "causal_loss": 0.002546274336054921
574
+ },
575
+ {
576
+ "stage": "stage2",
577
+ "epoch": 40,
578
+ "cosine_similarity": 1.0,
579
+ "grad_magnitude_ratio": 0.9990423076577669,
580
+ "physics_grad_norm": 0.051851850003004074,
581
+ "causal_grad_norm": 0.05180219188332558,
582
+ "physics_loss": 0.0034354785457253456,
583
+ "causal_loss": 0.003433853853493929
584
+ },
585
+ {
586
+ "stage": "stage2",
587
+ "epoch": 50,
588
+ "cosine_similarity": 1.0,
589
+ "grad_magnitude_ratio": 0.9985626011520556,
590
+ "physics_grad_norm": 0.05858512222766876,
591
+ "causal_grad_norm": 0.05850091204047203,
592
+ "physics_loss": 0.004124571569263935,
593
+ "causal_loss": 0.0041216290555894375
594
+ },
595
+ {
596
+ "stage": "stage2",
597
+ "epoch": 60,
598
+ "cosine_similarity": 1.0,
599
+ "grad_magnitude_ratio": 0.9981002974577372,
600
+ "physics_grad_norm": 0.06364576518535614,
601
+ "causal_grad_norm": 0.06352485716342926,
602
+ "physics_loss": 0.004552289377897978,
603
+ "causal_loss": 0.004547975026071072
604
+ },
605
+ {
606
+ "stage": "stage2",
607
+ "epoch": 70,
608
+ "cosine_similarity": 0.9999998807907104,
609
+ "grad_magnitude_ratio": 0.9977784483199161,
610
+ "physics_grad_norm": 0.06575407832860947,
611
+ "causal_grad_norm": 0.06560800224542618,
612
+ "physics_loss": 0.004533091560006142,
613
+ "causal_loss": 0.0045280419290065765
614
+ },
615
+ {
616
+ "stage": "stage2",
617
+ "epoch": 80,
618
+ "cosine_similarity": 1.0,
619
+ "grad_magnitude_ratio": 0.9974663535525198,
620
+ "physics_grad_norm": 0.06831730157136917,
621
+ "causal_grad_norm": 0.06814420968294144,
622
+ "physics_loss": 0.004515456967055798,
623
+ "causal_loss": 0.0045096976682543755
624
+ },
625
+ {
626
+ "stage": "stage2",
627
+ "epoch": 90,
628
+ "cosine_similarity": 1.0,
629
+ "grad_magnitude_ratio": 0.9972923065852383,
630
+ "physics_grad_norm": 0.0687495693564415,
631
+ "causal_grad_norm": 0.06856341660022736,
632
+ "physics_loss": 0.004206297919154167,
633
+ "causal_loss": 0.004200510215014219
634
+ },
635
+ {
636
+ "stage": "stage2",
637
+ "epoch": 100,
638
+ "cosine_similarity": 0.9999998807907104,
639
+ "grad_magnitude_ratio": 0.9972158554810722,
640
+ "physics_grad_norm": 0.06864400953054428,
641
+ "causal_grad_norm": 0.06845289468765259,
642
+ "physics_loss": 0.0038285995833575726,
643
+ "causal_loss": 0.003823139937594533
644
+ },
645
+ {
646
+ "stage": "stage2",
647
+ "epoch": 110,
648
+ "cosine_similarity": 1.0,
649
+ "grad_magnitude_ratio": 0.9971225395696763,
650
+ "physics_grad_norm": 0.06890619546175003,
651
+ "causal_grad_norm": 0.0687079206109047,
652
+ "physics_loss": 0.0035211045760661364,
653
+ "causal_loss": 0.003515873569995165
654
+ },
655
+ {
656
+ "stage": "stage2",
657
+ "epoch": 120,
658
+ "cosine_similarity": 0.9999999403953552,
659
+ "grad_magnitude_ratio": 0.9967808279410386,
660
+ "physics_grad_norm": 0.07218506932258606,
661
+ "causal_grad_norm": 0.0719526931643486,
662
+ "physics_loss": 0.003503829473629594,
663
+ "causal_loss": 0.003497929312288761
664
+ },
665
+ {
666
+ "stage": "stage2",
667
+ "epoch": 130,
668
+ "cosine_similarity": 1.0,
669
+ "grad_magnitude_ratio": 0.9960767460001485,
670
+ "physics_grad_norm": 0.07959052175283432,
671
+ "causal_grad_norm": 0.07927826792001724,
672
+ "physics_loss": 0.0038235255051404238,
673
+ "causal_loss": 0.00381560274399817
674
+ },
675
+ {
676
+ "stage": "stage2",
677
+ "epoch": 140,
678
+ "cosine_similarity": 1.0,
679
+ "grad_magnitude_ratio": 0.9962518216924812,
680
+ "physics_grad_norm": 0.07486602663993835,
681
+ "causal_grad_norm": 0.07458541542291641,
682
+ "physics_loss": 0.0031713340431451797,
683
+ "causal_loss": 0.0031649190932512283
684
+ },
685
+ {
686
+ "stage": "stage2",
687
+ "epoch": 150,
688
+ "cosine_similarity": 1.0,
689
+ "grad_magnitude_ratio": 0.9962828370848974,
690
+ "physics_grad_norm": 0.07291507720947266,
691
+ "causal_grad_norm": 0.07264403998851776,
692
+ "physics_loss": 0.002817156258970499,
693
+ "causal_loss": 0.002811450744047761
694
+ },
695
+ {
696
+ "stage": "stage2",
697
+ "epoch": 160,
698
+ "cosine_similarity": 0.9999998807907104,
699
+ "grad_magnitude_ratio": 0.9952414328209864,
700
+ "physics_grad_norm": 0.08263866603374481,
701
+ "causal_grad_norm": 0.08224542438983917,
702
+ "physics_loss": 0.003290734952315688,
703
+ "causal_loss": 0.0032821600325405598
704
+ },
705
+ {
706
+ "stage": "stage2",
707
+ "epoch": 170,
708
+ "cosine_similarity": 0.9999999403953552,
709
+ "grad_magnitude_ratio": 0.9951736382820371,
710
+ "physics_grad_norm": 0.07710294425487518,
711
+ "causal_grad_norm": 0.07673081755638123,
712
+ "physics_loss": 0.0028405492193996906,
713
+ "causal_loss": 0.0028328944463282824
714
+ },
715
+ {
716
+ "stage": "stage2",
717
+ "epoch": 180,
718
+ "cosine_similarity": 1.0000001192092896,
719
+ "grad_magnitude_ratio": 0.9956626304845126,
720
+ "physics_grad_norm": 0.0658591017127037,
721
+ "causal_grad_norm": 0.06557344645261765,
722
+ "physics_loss": 0.0022462569177150726,
723
+ "causal_loss": 0.0022409490775316954
724
+ },
725
+ {
726
+ "stage": "stage2",
727
+ "epoch": 190,
728
+ "cosine_similarity": 0.9999998807907104,
729
+ "grad_magnitude_ratio": 0.9941898069364343,
730
+ "physics_grad_norm": 0.07692565023899078,
731
+ "causal_grad_norm": 0.07647869735956192,
732
+ "physics_loss": 0.002775580156594515,
733
+ "causal_loss": 0.0027665640227496624
734
+ },
735
+ {
736
+ "stage": "stage2",
737
+ "epoch": 200,
738
+ "cosine_similarity": 0.9999999403953552,
739
+ "grad_magnitude_ratio": 0.9924085960405302,
740
+ "physics_grad_norm": 0.08861017972230911,
741
+ "causal_grad_norm": 0.08793750405311584,
742
+ "physics_loss": 0.003468562616035342,
743
+ "causal_loss": 0.0034538675099611282
744
+ },
745
+ {
746
+ "stage": "stage2",
747
+ "epoch": 210,
748
+ "cosine_similarity": 0.9999998211860657,
749
+ "grad_magnitude_ratio": 0.9902938319473193,
750
+ "physics_grad_norm": 0.10555599629878998,
751
+ "causal_grad_norm": 0.10453145205974579,
752
+ "physics_loss": 0.0044480422511696815,
753
+ "causal_loss": 0.004423984792083502
754
+ },
755
+ {
756
+ "stage": "stage2",
757
+ "epoch": 220,
758
+ "cosine_similarity": 0.9999998211860657,
759
+ "grad_magnitude_ratio": 0.9910120200601743,
760
+ "physics_grad_norm": 0.0860946848988533,
761
+ "causal_grad_norm": 0.0853208675980568,
762
+ "physics_loss": 0.003377170767635107,
763
+ "causal_loss": 0.0033603874035179615
764
+ },
765
+ {
766
+ "stage": "stage2",
767
+ "epoch": 230,
768
+ "cosine_similarity": 0.9999997615814209,
769
+ "grad_magnitude_ratio": 0.9900017557030916,
770
+ "physics_grad_norm": 0.08606112003326416,
771
+ "causal_grad_norm": 0.08520065993070602,
772
+ "physics_loss": 0.003424955764785409,
773
+ "causal_loss": 0.003406098810955882
774
+ },
775
+ {
776
+ "stage": "stage2",
777
+ "epoch": 240,
778
+ "cosine_similarity": 0.9999997615814209,
779
+ "grad_magnitude_ratio": 0.9882494825070736,
780
+ "physics_grad_norm": 0.0941629484295845,
781
+ "causal_grad_norm": 0.09305648505687714,
782
+ "physics_loss": 0.003910308238118887,
783
+ "causal_loss": 0.0038851939607411623
784
+ },
785
+ {
786
+ "stage": "stage2",
787
+ "epoch": 250,
788
+ "cosine_similarity": 0.9999997615814209,
789
+ "grad_magnitude_ratio": 0.9867977194648623,
790
+ "physics_grad_norm": 0.1002364531159401,
791
+ "causal_grad_norm": 0.09891310334205627,
792
+ "physics_loss": 0.004210616461932659,
793
+ "causal_loss": 0.0041801538318395615
794
+ },
795
+ {
796
+ "stage": "stage2",
797
+ "epoch": 260,
798
+ "cosine_similarity": 0.9999997019767761,
799
+ "grad_magnitude_ratio": 0.9859990604257455,
800
+ "physics_grad_norm": 0.09406258910894394,
801
+ "causal_grad_norm": 0.09274562448263168,
802
+ "physics_loss": 0.003969599958509207,
803
+ "causal_loss": 0.003939607180655003
804
+ },
805
+ {
806
+ "stage": "stage2",
807
+ "epoch": 270,
808
+ "cosine_similarity": 0.9999996423721313,
809
+ "grad_magnitude_ratio": 0.9832974048746155,
810
+ "physics_grad_norm": 0.09857460111379623,
811
+ "causal_grad_norm": 0.09692814946174622,
812
+ "physics_loss": 0.004330507479608059,
813
+ "causal_loss": 0.004291379824280739
814
+ },
815
+ {
816
+ "stage": "stage2",
817
+ "epoch": 280,
818
+ "cosine_similarity": 0.9999997615814209,
819
+ "grad_magnitude_ratio": 0.9835506505807979,
820
+ "physics_grad_norm": 0.08260642737150192,
821
+ "causal_grad_norm": 0.08124760538339615,
822
+ "physics_loss": 0.0037687665317207575,
823
+ "causal_loss": 0.0037379618734121323
824
+ },
825
+ {
826
+ "stage": "stage2",
827
+ "epoch": 290,
828
+ "cosine_similarity": 0.9999996423721313,
829
+ "grad_magnitude_ratio": 0.9811455191039222,
830
+ "physics_grad_norm": 0.09622321277856827,
831
+ "causal_grad_norm": 0.09440897405147552,
832
+ "physics_loss": 0.004341182764619589,
833
+ "causal_loss": 0.004299050662666559
834
+ },
835
+ {
836
+ "stage": "stage3",
837
+ "epoch": 0,
838
+ "cosine_similarity": 1.0,
839
+ "grad_magnitude_ratio": 0.9996936164682254,
840
+ "physics_grad_norm": 0.09768469631671906,
841
+ "causal_grad_norm": 0.09765476733446121,
842
+ "physics_loss": 0.004479090683162212,
843
+ "causal_loss": 0.0044783977791666985
844
+ },
845
+ {
846
+ "stage": "stage3",
847
+ "epoch": 10,
848
+ "cosine_similarity": 0.9999999403953552,
849
+ "grad_magnitude_ratio": 0.9985982368527863,
850
+ "physics_grad_norm": 0.10338497161865234,
851
+ "causal_grad_norm": 0.10324005037546158,
852
+ "physics_loss": 0.00483230035752058,
853
+ "causal_loss": 0.004828836768865585
854
+ },
855
+ {
856
+ "stage": "stage3",
857
+ "epoch": 20,
858
+ "cosine_similarity": 1.0,
859
+ "grad_magnitude_ratio": 0.9977624341633582,
860
+ "physics_grad_norm": 0.10054241865873337,
861
+ "causal_grad_norm": 0.10031744837760925,
862
+ "physics_loss": 0.004580569453537464,
863
+ "causal_loss": 0.004575460683554411
864
+ },
865
+ {
866
+ "stage": "stage3",
867
+ "epoch": 30,
868
+ "cosine_similarity": 1.0,
869
+ "grad_magnitude_ratio": 0.9966299933918826,
870
+ "physics_grad_norm": 0.1006622314453125,
871
+ "causal_grad_norm": 0.10032299906015396,
872
+ "physics_loss": 0.004598794970661402,
873
+ "causal_loss": 0.004590906668454409
874
+ },
875
+ {
876
+ "stage": "stage3",
877
+ "epoch": 40,
878
+ "cosine_similarity": 0.9999999403953552,
879
+ "grad_magnitude_ratio": 0.9954545788805828,
880
+ "physics_grad_norm": 0.10030388087034225,
881
+ "causal_grad_norm": 0.0998479574918747,
882
+ "physics_loss": 0.0046126204542815685,
883
+ "causal_loss": 0.004601873457431793
884
+ },
885
+ {
886
+ "stage": "stage3",
887
+ "epoch": 50,
888
+ "cosine_similarity": 0.9999999403953552,
889
+ "grad_magnitude_ratio": 0.9944002010104602,
890
+ "physics_grad_norm": 0.10553327947854996,
891
+ "causal_grad_norm": 0.10494231432676315,
892
+ "physics_loss": 0.004848843906074762,
893
+ "causal_loss": 0.004835017956793308
894
+ },
895
+ {
896
+ "stage": "stage3",
897
+ "epoch": 60,
898
+ "cosine_similarity": 0.9999998807907104,
899
+ "grad_magnitude_ratio": 0.9936716410663317,
900
+ "physics_grad_norm": 0.0957488939166069,
901
+ "causal_grad_norm": 0.09514296054840088,
902
+ "physics_loss": 0.004383309744298458,
903
+ "causal_loss": 0.004369436297565699
904
+ },
905
+ {
906
+ "stage": "stage3",
907
+ "epoch": 70,
908
+ "cosine_similarity": 1.0,
909
+ "grad_magnitude_ratio": 0.9922994900448506,
910
+ "physics_grad_norm": 0.10029655694961548,
911
+ "causal_grad_norm": 0.09952422231435776,
912
+ "physics_loss": 0.00462031364440918,
913
+ "causal_loss": 0.004602192901074886
914
+ },
915
+ {
916
+ "stage": "stage3",
917
+ "epoch": 80,
918
+ "cosine_similarity": 1.0,
919
+ "grad_magnitude_ratio": 0.9915433987771705,
920
+ "physics_grad_norm": 0.10519760847091675,
921
+ "causal_grad_norm": 0.10430799424648285,
922
+ "physics_loss": 0.004788943100720644,
923
+ "causal_loss": 0.004768447019159794
924
+ },
925
+ {
926
+ "stage": "stage3",
927
+ "epoch": 90,
928
+ "cosine_similarity": 0.9999999403953552,
929
+ "grad_magnitude_ratio": 0.9897303268259274,
930
+ "physics_grad_norm": 0.11086555570363998,
931
+ "causal_grad_norm": 0.10972700268030167,
932
+ "physics_loss": 0.005119639914482832,
933
+ "causal_loss": 0.005092385224997997
934
+ },
935
+ {
936
+ "stage": "stage3",
937
+ "epoch": 100,
938
+ "cosine_similarity": 0.9999999403953552,
939
+ "grad_magnitude_ratio": 0.9889659472205042,
940
+ "physics_grad_norm": 0.11163865774869919,
941
+ "causal_grad_norm": 0.11040683090686798,
942
+ "physics_loss": 0.005009226035326719,
943
+ "causal_loss": 0.004980392754077911
944
+ },
945
+ {
946
+ "stage": "stage3",
947
+ "epoch": 110,
948
+ "cosine_similarity": 0.9999997615814209,
949
+ "grad_magnitude_ratio": 0.98757526620597,
950
+ "physics_grad_norm": 0.10692127048969269,
951
+ "causal_grad_norm": 0.10559280216693878,
952
+ "physics_loss": 0.0049437363632023335,
953
+ "causal_loss": 0.004912350792437792
954
+ },
955
+ {
956
+ "stage": "stage3",
957
+ "epoch": 120,
958
+ "cosine_similarity": 0.9999997615814209,
959
+ "grad_magnitude_ratio": 0.9858682102912334,
960
+ "physics_grad_norm": 0.11053352802991867,
961
+ "causal_grad_norm": 0.1089714914560318,
962
+ "physics_loss": 0.005119122564792633,
963
+ "causal_loss": 0.0050815618596971035
964
+ },
965
+ {
966
+ "stage": "stage3",
967
+ "epoch": 130,
968
+ "cosine_similarity": 0.9999997615814209,
969
+ "grad_magnitude_ratio": 0.9856348377625963,
970
+ "physics_grad_norm": 0.10856304317712784,
971
+ "causal_grad_norm": 0.10700351744890213,
972
+ "physics_loss": 0.004947827663272619,
973
+ "causal_loss": 0.0049114772118628025
974
+ },
975
+ {
976
+ "stage": "stage3",
977
+ "epoch": 140,
978
+ "cosine_similarity": 0.9999997615814209,
979
+ "grad_magnitude_ratio": 0.9835248885643483,
980
+ "physics_grad_norm": 0.1110827699303627,
981
+ "causal_grad_norm": 0.10925266891717911,
982
+ "physics_loss": 0.005168053787201643,
983
+ "causal_loss": 0.005124166142195463
984
+ },
985
+ {
986
+ "stage": "stage3",
987
+ "epoch": 150,
988
+ "cosine_similarity": 0.9999997615814209,
989
+ "grad_magnitude_ratio": 0.9826254953941017,
990
+ "physics_grad_norm": 0.10476093739271164,
991
+ "causal_grad_norm": 0.10294076800346375,
992
+ "physics_loss": 0.004929827060550451,
993
+ "causal_loss": 0.004886602517217398
994
+ },
995
+ {
996
+ "stage": "stage3",
997
+ "epoch": 160,
998
+ "cosine_similarity": 0.9999997019767761,
999
+ "grad_magnitude_ratio": 0.9821123845026086,
1000
+ "physics_grad_norm": 0.10451529920101166,
1001
+ "causal_grad_norm": 0.10264576971530914,
1002
+ "physics_loss": 0.004871193785220385,
1003
+ "causal_loss": 0.004827685654163361
1004
+ },
1005
+ {
1006
+ "stage": "stage3",
1007
+ "epoch": 170,
1008
+ "cosine_similarity": 0.9999998211860657,
1009
+ "grad_magnitude_ratio": 0.9808885292878162,
1010
+ "physics_grad_norm": 0.09824497252702713,
1011
+ "causal_grad_norm": 0.09636736661195755,
1012
+ "physics_loss": 0.004650169052183628,
1013
+ "causal_loss": 0.0046059987507760525
1014
+ },
1015
+ {
1016
+ "stage": "stage3",
1017
+ "epoch": 180,
1018
+ "cosine_similarity": 0.9999995827674866,
1019
+ "grad_magnitude_ratio": 0.9803050186799054,
1020
+ "physics_grad_norm": 0.10156253725290298,
1021
+ "causal_grad_norm": 0.09956226497888565,
1022
+ "physics_loss": 0.004708824213594198,
1023
+ "causal_loss": 0.0046625882387161255
1024
+ },
1025
+ {
1026
+ "stage": "stage3",
1027
+ "epoch": 190,
1028
+ "cosine_similarity": 0.9999995827674866,
1029
+ "grad_magnitude_ratio": 0.9795530187398922,
1030
+ "physics_grad_norm": 0.1030893549323082,
1031
+ "causal_grad_norm": 0.10098148882389069,
1032
+ "physics_loss": 0.004759280476719141,
1033
+ "causal_loss": 0.004710627719759941
1034
+ }
1035
+ ],
1036
+ "wall_time_s": 83.41
1037
+ }
1038
+ }
1039
+ }
results/paper_c/gradient_flow_allencahn/fig_gradient_alignment.pdf ADDED
Binary file (19.6 kB). View file
 
results/paper_c/gradient_flow_allencahn/gradient_flow_results.json ADDED
@@ -0,0 +1,1039 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "experiment": "gradient_flow_analysis",
3
+ "pde": "allencahn1d_sharp",
4
+ "seed": 42,
5
+ "device": "cuda",
6
+ "hyperparameters": {
7
+ "stage1_epochs": 200,
8
+ "stage2_epochs": 300,
9
+ "stage3_epochs": 200,
10
+ "stage1_lr": 0.001,
11
+ "stage2_lr": 0.0001,
12
+ "stage3_lr": 1e-05,
13
+ "causal_epsilon": 1.0,
14
+ "num_collocation": 2000,
15
+ "num_boundary": 200,
16
+ "batch_size": 256,
17
+ "hidden_dims": [
18
+ 64,
19
+ 64,
20
+ 64,
21
+ 64
22
+ ],
23
+ "probe_every": 10
24
+ },
25
+ "conditions": {
26
+ "with_pretrain": {
27
+ "condition": "with_pretrain",
28
+ "probes": [
29
+ {
30
+ "stage": "stage2",
31
+ "epoch": 0,
32
+ "cosine_similarity": 0.9999998807907104,
33
+ "grad_magnitude_ratio": 0.9986308129196532,
34
+ "physics_grad_norm": 0.15356220304965973,
35
+ "causal_grad_norm": 0.15335194766521454,
36
+ "physics_loss": 0.04626054689288139,
37
+ "causal_loss": 0.04623350501060486
38
+ },
39
+ {
40
+ "stage": "stage2",
41
+ "epoch": 10,
42
+ "cosine_similarity": 1.0,
43
+ "grad_magnitude_ratio": 0.9946895369316797,
44
+ "physics_grad_norm": 0.6578274965286255,
45
+ "causal_grad_norm": 0.6543341279029846,
46
+ "physics_loss": 0.055286161601543427,
47
+ "causal_loss": 0.055148299783468246
48
+ },
49
+ {
50
+ "stage": "stage2",
51
+ "epoch": 20,
52
+ "cosine_similarity": 0.9999997615814209,
53
+ "grad_magnitude_ratio": 0.9916434520120395,
54
+ "physics_grad_norm": 0.5733753442764282,
55
+ "causal_grad_norm": 0.5685839056968689,
56
+ "physics_loss": 0.05373471602797508,
57
+ "causal_loss": 0.05351337417960167
58
+ },
59
+ {
60
+ "stage": "stage2",
61
+ "epoch": 30,
62
+ "cosine_similarity": 0.9999985098838806,
63
+ "grad_magnitude_ratio": 0.9864146174191079,
64
+ "physics_grad_norm": 0.4517606496810913,
65
+ "causal_grad_norm": 0.4456233084201813,
66
+ "physics_loss": 0.0526578351855278,
67
+ "causal_loss": 0.05234511196613312
68
+ },
69
+ {
70
+ "stage": "stage2",
71
+ "epoch": 40,
72
+ "cosine_similarity": 0.9999950528144836,
73
+ "grad_magnitude_ratio": 0.9841734173640323,
74
+ "physics_grad_norm": 0.4010021686553955,
75
+ "causal_grad_norm": 0.39465567469596863,
76
+ "physics_loss": 0.05236883834004402,
77
+ "causal_loss": 0.05198736861348152
78
+ },
79
+ {
80
+ "stage": "stage2",
81
+ "epoch": 50,
82
+ "cosine_similarity": 0.999998927116394,
83
+ "grad_magnitude_ratio": 0.9820598707669854,
84
+ "physics_grad_norm": 0.36608749628067017,
85
+ "causal_grad_norm": 0.3595198392868042,
86
+ "physics_loss": 0.04799763858318329,
87
+ "causal_loss": 0.04760118946433067
88
+ },
89
+ {
90
+ "stage": "stage2",
91
+ "epoch": 60,
92
+ "cosine_similarity": 0.9999983906745911,
93
+ "grad_magnitude_ratio": 0.9767744706906435,
94
+ "physics_grad_norm": 0.4472042918205261,
95
+ "causal_grad_norm": 0.4368177354335785,
96
+ "physics_loss": 0.04923512414097786,
97
+ "causal_loss": 0.04872800037264824
98
+ },
99
+ {
100
+ "stage": "stage2",
101
+ "epoch": 70,
102
+ "cosine_similarity": 0.9999827146530151,
103
+ "grad_magnitude_ratio": 0.9721881599421448,
104
+ "physics_grad_norm": 0.39165547490119934,
105
+ "causal_grad_norm": 0.38076281547546387,
106
+ "physics_loss": 0.04616240784525871,
107
+ "causal_loss": 0.045640602707862854
108
+ },
109
+ {
110
+ "stage": "stage2",
111
+ "epoch": 80,
112
+ "cosine_similarity": 0.9999732971191406,
113
+ "grad_magnitude_ratio": 0.9685504395906435,
114
+ "physics_grad_norm": 0.3172631859779358,
115
+ "causal_grad_norm": 0.3072853982448578,
116
+ "physics_loss": 0.04640024155378342,
117
+ "causal_loss": 0.04582277685403824
118
+ },
119
+ {
120
+ "stage": "stage2",
121
+ "epoch": 90,
122
+ "cosine_similarity": 0.9999709129333496,
123
+ "grad_magnitude_ratio": 0.9658152680478862,
124
+ "physics_grad_norm": 0.3207307755947113,
125
+ "causal_grad_norm": 0.3097666800022125,
126
+ "physics_loss": 0.04501647129654884,
127
+ "causal_loss": 0.044405076652765274
128
+ },
129
+ {
130
+ "stage": "stage2",
131
+ "epoch": 100,
132
+ "cosine_similarity": 0.9999583959579468,
133
+ "grad_magnitude_ratio": 0.9598944199142009,
134
+ "physics_grad_norm": 0.34673187136650085,
135
+ "causal_grad_norm": 0.33282598853111267,
136
+ "physics_loss": 0.046900372952222824,
137
+ "causal_loss": 0.046147484332323074
138
+ },
139
+ {
140
+ "stage": "stage2",
141
+ "epoch": 110,
142
+ "cosine_similarity": 0.9999510049819946,
143
+ "grad_magnitude_ratio": 0.9645604179137234,
144
+ "physics_grad_norm": 0.36121025681495667,
145
+ "causal_grad_norm": 0.34840911626815796,
146
+ "physics_loss": 0.040983714163303375,
147
+ "causal_loss": 0.04035401716828346
148
+ },
149
+ {
150
+ "stage": "stage2",
151
+ "epoch": 120,
152
+ "cosine_similarity": 0.9999864101409912,
153
+ "grad_magnitude_ratio": 0.9592713742607792,
154
+ "physics_grad_norm": 0.4431922435760498,
155
+ "causal_grad_norm": 0.4251416325569153,
156
+ "physics_loss": 0.04210872948169708,
157
+ "causal_loss": 0.04138747602701187
158
+ },
159
+ {
160
+ "stage": "stage2",
161
+ "epoch": 130,
162
+ "cosine_similarity": 0.9999455213546753,
163
+ "grad_magnitude_ratio": 0.9553393666171731,
164
+ "physics_grad_norm": 0.3593004047870636,
165
+ "causal_grad_norm": 0.34325382113456726,
166
+ "physics_loss": 0.042613305151462555,
167
+ "causal_loss": 0.04183541238307953
168
+ },
169
+ {
170
+ "stage": "stage2",
171
+ "epoch": 140,
172
+ "cosine_similarity": 0.9999660849571228,
173
+ "grad_magnitude_ratio": 0.9486518363437049,
174
+ "physics_grad_norm": 0.46844425797462463,
175
+ "causal_grad_norm": 0.44439050555229187,
176
+ "physics_loss": 0.04113662987947464,
177
+ "causal_loss": 0.0403292216360569
178
+ },
179
+ {
180
+ "stage": "stage2",
181
+ "epoch": 150,
182
+ "cosine_similarity": 0.9999217987060547,
183
+ "grad_magnitude_ratio": 0.9430435386047774,
184
+ "physics_grad_norm": 0.4416956603527069,
185
+ "causal_grad_norm": 0.4165382385253906,
186
+ "physics_loss": 0.04304005950689316,
187
+ "causal_loss": 0.0421101413667202
188
+ },
189
+ {
190
+ "stage": "stage2",
191
+ "epoch": 160,
192
+ "cosine_similarity": 0.999975323677063,
193
+ "grad_magnitude_ratio": 0.9482623587265413,
194
+ "physics_grad_norm": 0.4516807198524475,
195
+ "causal_grad_norm": 0.428311824798584,
196
+ "physics_loss": 0.039881058037281036,
197
+ "causal_loss": 0.03904062882065773
198
+ },
199
+ {
200
+ "stage": "stage2",
201
+ "epoch": 170,
202
+ "cosine_similarity": 0.999968409538269,
203
+ "grad_magnitude_ratio": 0.9358178783305582,
204
+ "physics_grad_norm": 0.5870185494422913,
205
+ "causal_grad_norm": 0.5493424534797668,
206
+ "physics_loss": 0.04126196354627609,
207
+ "causal_loss": 0.04023442044854164
208
+ },
209
+ {
210
+ "stage": "stage2",
211
+ "epoch": 180,
212
+ "cosine_similarity": 0.9999568462371826,
213
+ "grad_magnitude_ratio": 0.9390971761333297,
214
+ "physics_grad_norm": 0.5606794953346252,
215
+ "causal_grad_norm": 0.5265325307846069,
216
+ "physics_loss": 0.04073183238506317,
217
+ "causal_loss": 0.039743341505527496
218
+ },
219
+ {
220
+ "stage": "stage2",
221
+ "epoch": 190,
222
+ "cosine_similarity": 0.9999952912330627,
223
+ "grad_magnitude_ratio": 0.9339056668843159,
224
+ "physics_grad_norm": 0.797105073928833,
225
+ "causal_grad_norm": 0.7444209456443787,
226
+ "physics_loss": 0.04433261230587959,
227
+ "causal_loss": 0.043070804327726364
228
+ },
229
+ {
230
+ "stage": "stage2",
231
+ "epoch": 200,
232
+ "cosine_similarity": 0.9998545050621033,
233
+ "grad_magnitude_ratio": 0.9320911463901345,
234
+ "physics_grad_norm": 0.4729363024234772,
235
+ "causal_grad_norm": 0.44081974029541016,
236
+ "physics_loss": 0.04273498058319092,
237
+ "causal_loss": 0.04155761003494263
238
+ },
239
+ {
240
+ "stage": "stage2",
241
+ "epoch": 210,
242
+ "cosine_similarity": 0.9999892711639404,
243
+ "grad_magnitude_ratio": 0.9245105627153487,
244
+ "physics_grad_norm": 0.8137046098709106,
245
+ "causal_grad_norm": 0.7522785067558289,
246
+ "physics_loss": 0.0449252612888813,
247
+ "causal_loss": 0.04346334934234619
248
+ },
249
+ {
250
+ "stage": "stage2",
251
+ "epoch": 220,
252
+ "cosine_similarity": 0.9999704360961914,
253
+ "grad_magnitude_ratio": 0.9205110427157861,
254
+ "physics_grad_norm": 0.6666764616966248,
255
+ "causal_grad_norm": 0.6136830449104309,
256
+ "physics_loss": 0.044204678386449814,
257
+ "causal_loss": 0.042765725404024124
258
+ },
259
+ {
260
+ "stage": "stage2",
261
+ "epoch": 230,
262
+ "cosine_similarity": 0.9999306797981262,
263
+ "grad_magnitude_ratio": 0.918259471904662,
264
+ "physics_grad_norm": 0.6174400448799133,
265
+ "causal_grad_norm": 0.56697016954422,
266
+ "physics_loss": 0.04422111064195633,
267
+ "causal_loss": 0.04269907996058464
268
+ },
269
+ {
270
+ "stage": "stage2",
271
+ "epoch": 240,
272
+ "cosine_similarity": 0.9999527335166931,
273
+ "grad_magnitude_ratio": 0.9137341712624651,
274
+ "physics_grad_norm": 0.7395679354667664,
275
+ "causal_grad_norm": 0.6757684946060181,
276
+ "physics_loss": 0.0448484942317009,
277
+ "causal_loss": 0.04324014484882355
278
+ },
279
+ {
280
+ "stage": "stage2",
281
+ "epoch": 250,
282
+ "cosine_similarity": 0.9999762773513794,
283
+ "grad_magnitude_ratio": 0.9133715609809337,
284
+ "physics_grad_norm": 0.6389611959457397,
285
+ "causal_grad_norm": 0.5836089849472046,
286
+ "physics_loss": 0.04383711516857147,
287
+ "causal_loss": 0.04225538671016693
288
+ },
289
+ {
290
+ "stage": "stage2",
291
+ "epoch": 260,
292
+ "cosine_similarity": 0.9999442100524902,
293
+ "grad_magnitude_ratio": 0.911102178888148,
294
+ "physics_grad_norm": 0.6988846063613892,
295
+ "causal_grad_norm": 0.6367552876472473,
296
+ "physics_loss": 0.04445000737905502,
297
+ "causal_loss": 0.04272095486521721
298
+ },
299
+ {
300
+ "stage": "stage2",
301
+ "epoch": 270,
302
+ "cosine_similarity": 0.9999780654907227,
303
+ "grad_magnitude_ratio": 0.8997360871318981,
304
+ "physics_grad_norm": 0.7756356596946716,
305
+ "causal_grad_norm": 0.6978673934936523,
306
+ "physics_loss": 0.04578574001789093,
307
+ "causal_loss": 0.04382932558655739
308
+ },
309
+ {
310
+ "stage": "stage2",
311
+ "epoch": 280,
312
+ "cosine_similarity": 0.9999723434448242,
313
+ "grad_magnitude_ratio": 0.9015764518307645,
314
+ "physics_grad_norm": 0.7358685731887817,
315
+ "causal_grad_norm": 0.6634417772293091,
316
+ "physics_loss": 0.04494570195674896,
317
+ "causal_loss": 0.043037354946136475
318
+ },
319
+ {
320
+ "stage": "stage2",
321
+ "epoch": 290,
322
+ "cosine_similarity": 0.9999745488166809,
323
+ "grad_magnitude_ratio": 0.9060748624054917,
324
+ "physics_grad_norm": 0.6788421273231506,
325
+ "causal_grad_norm": 0.615081787109375,
326
+ "physics_loss": 0.04312191531062126,
327
+ "causal_loss": 0.04134276509284973
328
+ },
329
+ {
330
+ "stage": "stage3",
331
+ "epoch": 0,
332
+ "cosine_similarity": 0.9999999403953552,
333
+ "grad_magnitude_ratio": 0.9982615401341168,
334
+ "physics_grad_norm": 0.7001178860664368,
335
+ "causal_grad_norm": 0.6989007592201233,
336
+ "physics_loss": 0.044308703392744064,
337
+ "causal_loss": 0.04427751898765564
338
+ },
339
+ {
340
+ "stage": "stage3",
341
+ "epoch": 10,
342
+ "cosine_similarity": 0.9999999403953552,
343
+ "grad_magnitude_ratio": 0.9933540937316265,
344
+ "physics_grad_norm": 0.6333015561103821,
345
+ "causal_grad_norm": 0.6290926933288574,
346
+ "physics_loss": 0.04282544180750847,
347
+ "causal_loss": 0.04270695522427559
348
+ },
349
+ {
350
+ "stage": "stage3",
351
+ "epoch": 20,
352
+ "cosine_similarity": 0.999999463558197,
353
+ "grad_magnitude_ratio": 0.9882850783396225,
354
+ "physics_grad_norm": 0.6763531565666199,
355
+ "causal_grad_norm": 0.6684297323226929,
356
+ "physics_loss": 0.042618528008461,
357
+ "causal_loss": 0.04240940883755684
358
+ },
359
+ {
360
+ "stage": "stage3",
361
+ "epoch": 30,
362
+ "cosine_similarity": 0.999998927116394,
363
+ "grad_magnitude_ratio": 0.9830887024584454,
364
+ "physics_grad_norm": 0.6515440344810486,
365
+ "causal_grad_norm": 0.6405255794525146,
366
+ "physics_loss": 0.042896151542663574,
367
+ "causal_loss": 0.042592853307724
368
+ },
369
+ {
370
+ "stage": "stage3",
371
+ "epoch": 40,
372
+ "cosine_similarity": 0.9999986886978149,
373
+ "grad_magnitude_ratio": 0.9767355079996379,
374
+ "physics_grad_norm": 0.7393955588340759,
375
+ "causal_grad_norm": 0.7221938967704773,
376
+ "physics_loss": 0.04606733098626137,
377
+ "causal_loss": 0.04560099169611931
378
+ },
379
+ {
380
+ "stage": "stage3",
381
+ "epoch": 50,
382
+ "cosine_similarity": 0.9999974966049194,
383
+ "grad_magnitude_ratio": 0.97118263367917,
384
+ "physics_grad_norm": 0.7001683115959167,
385
+ "causal_grad_norm": 0.6799913048744202,
386
+ "physics_loss": 0.045983947813510895,
387
+ "causal_loss": 0.045426271855831146
388
+ },
389
+ {
390
+ "stage": "stage3",
391
+ "epoch": 60,
392
+ "cosine_similarity": 0.9999970197677612,
393
+ "grad_magnitude_ratio": 0.9692205452657506,
394
+ "physics_grad_norm": 0.6170719861984253,
395
+ "causal_grad_norm": 0.5980788469314575,
396
+ "physics_loss": 0.04294866323471069,
397
+ "causal_loss": 0.042390353977680206
398
+ },
399
+ {
400
+ "stage": "stage3",
401
+ "epoch": 70,
402
+ "cosine_similarity": 0.9999914169311523,
403
+ "grad_magnitude_ratio": 0.9600264610163318,
404
+ "physics_grad_norm": 0.6657623648643494,
405
+ "causal_grad_norm": 0.6391494870185852,
406
+ "physics_loss": 0.04482446610927582,
407
+ "causal_loss": 0.04410147666931152
408
+ },
409
+ {
410
+ "stage": "stage3",
411
+ "epoch": 80,
412
+ "cosine_similarity": 0.9999932050704956,
413
+ "grad_magnitude_ratio": 0.9566570512191559,
414
+ "physics_grad_norm": 0.6834223866462708,
415
+ "causal_grad_norm": 0.6538008451461792,
416
+ "physics_loss": 0.04623283073306084,
417
+ "causal_loss": 0.045379262417554855
418
+ },
419
+ {
420
+ "stage": "stage3",
421
+ "epoch": 90,
422
+ "cosine_similarity": 0.9999946355819702,
423
+ "grad_magnitude_ratio": 0.9532482056278844,
424
+ "physics_grad_norm": 0.7080071568489075,
425
+ "causal_grad_norm": 0.6749065518379211,
426
+ "physics_loss": 0.04521498829126358,
427
+ "causal_loss": 0.044295601546764374
428
+ },
429
+ {
430
+ "stage": "stage3",
431
+ "epoch": 100,
432
+ "cosine_similarity": 0.9999913573265076,
433
+ "grad_magnitude_ratio": 0.9432266719387628,
434
+ "physics_grad_norm": 0.695525586605072,
435
+ "causal_grad_norm": 0.6560382843017578,
436
+ "physics_loss": 0.044754963368177414,
437
+ "causal_loss": 0.04373271018266678
438
+ },
439
+ {
440
+ "stage": "stage3",
441
+ "epoch": 110,
442
+ "cosine_similarity": 0.9999872446060181,
443
+ "grad_magnitude_ratio": 0.9390058841784479,
444
+ "physics_grad_norm": 0.7323430180549622,
445
+ "causal_grad_norm": 0.6876744031906128,
446
+ "physics_loss": 0.04640015587210655,
447
+ "causal_loss": 0.045184724032878876
448
+ },
449
+ {
450
+ "stage": "stage3",
451
+ "epoch": 120,
452
+ "cosine_similarity": 0.9999969601631165,
453
+ "grad_magnitude_ratio": 0.9404587533088888,
454
+ "physics_grad_norm": 0.7167343497276306,
455
+ "causal_grad_norm": 0.6740590929985046,
456
+ "physics_loss": 0.045412126928567886,
457
+ "causal_loss": 0.04420420899987221
458
+ },
459
+ {
460
+ "stage": "stage3",
461
+ "epoch": 130,
462
+ "cosine_similarity": 0.9999827146530151,
463
+ "grad_magnitude_ratio": 0.9285862616359762,
464
+ "physics_grad_norm": 0.7109633088111877,
465
+ "causal_grad_norm": 0.660190761089325,
466
+ "physics_loss": 0.045627411454916,
467
+ "causal_loss": 0.04428752511739731
468
+ },
469
+ {
470
+ "stage": "stage3",
471
+ "epoch": 140,
472
+ "cosine_similarity": 0.999995768070221,
473
+ "grad_magnitude_ratio": 0.9293222498058229,
474
+ "physics_grad_norm": 0.7251167893409729,
475
+ "causal_grad_norm": 0.6738671660423279,
476
+ "physics_loss": 0.04282646253705025,
477
+ "causal_loss": 0.04154909402132034
478
+ },
479
+ {
480
+ "stage": "stage3",
481
+ "epoch": 150,
482
+ "cosine_similarity": 0.9999794960021973,
483
+ "grad_magnitude_ratio": 0.9182274204151067,
484
+ "physics_grad_norm": 0.7336264252662659,
485
+ "causal_grad_norm": 0.6736359000205994,
486
+ "physics_loss": 0.04431173950433731,
487
+ "causal_loss": 0.04277871549129486
488
+ },
489
+ {
490
+ "stage": "stage3",
491
+ "epoch": 160,
492
+ "cosine_similarity": 0.9999836683273315,
493
+ "grad_magnitude_ratio": 0.9177797435987315,
494
+ "physics_grad_norm": 0.7753958702087402,
495
+ "causal_grad_norm": 0.7116426229476929,
496
+ "physics_loss": 0.04464239627122879,
497
+ "causal_loss": 0.04303407669067383
498
+ },
499
+ {
500
+ "stage": "stage3",
501
+ "epoch": 170,
502
+ "cosine_similarity": 0.9999809265136719,
503
+ "grad_magnitude_ratio": 0.9119617638762987,
504
+ "physics_grad_norm": 0.6739000678062439,
505
+ "causal_grad_norm": 0.6145710945129395,
506
+ "physics_loss": 0.0432513952255249,
507
+ "causal_loss": 0.04165253788232803
508
+ },
509
+ {
510
+ "stage": "stage3",
511
+ "epoch": 180,
512
+ "cosine_similarity": 0.999973475933075,
513
+ "grad_magnitude_ratio": 0.8994237348599768,
514
+ "physics_grad_norm": 0.7391712665557861,
515
+ "causal_grad_norm": 0.6648281812667847,
516
+ "physics_loss": 0.04473922401666641,
517
+ "causal_loss": 0.042887549847364426
518
+ },
519
+ {
520
+ "stage": "stage3",
521
+ "epoch": 190,
522
+ "cosine_similarity": 0.999984860420227,
523
+ "grad_magnitude_ratio": 0.8990077300474821,
524
+ "physics_grad_norm": 0.7599506974220276,
525
+ "causal_grad_norm": 0.6832015514373779,
526
+ "physics_loss": 0.04525204375386238,
527
+ "causal_loss": 0.043319955468177795
528
+ }
529
+ ],
530
+ "wall_time_s": 75.96
531
+ },
532
+ "without_pretrain": {
533
+ "condition": "without_pretrain",
534
+ "probes": [
535
+ {
536
+ "stage": "stage2",
537
+ "epoch": 0,
538
+ "cosine_similarity": 1.0000001192092896,
539
+ "grad_magnitude_ratio": 1.0000007894806682,
540
+ "physics_grad_norm": 0.0004792388353962451,
541
+ "causal_grad_norm": 0.00047923921374604106,
542
+ "physics_loss": 3.7137635899853194e-06,
543
+ "causal_loss": 3.713763362611644e-06
544
+ },
545
+ {
546
+ "stage": "stage2",
547
+ "epoch": 10,
548
+ "cosine_similarity": 0.9999999403953552,
549
+ "grad_magnitude_ratio": 0.9999796440333171,
550
+ "physics_grad_norm": 0.03147725388407707,
551
+ "causal_grad_norm": 0.03147661313414574,
552
+ "physics_loss": 0.00020076784130651504,
553
+ "causal_loss": 0.0002007657749345526
554
+ },
555
+ {
556
+ "stage": "stage2",
557
+ "epoch": 20,
558
+ "cosine_similarity": 0.9999999403953552,
559
+ "grad_magnitude_ratio": 0.9999074185500586,
560
+ "physics_grad_norm": 0.04884890466928482,
561
+ "causal_grad_norm": 0.04884438216686249,
562
+ "physics_loss": 0.0005776846664957702,
563
+ "causal_loss": 0.0005776579491794109
564
+ },
565
+ {
566
+ "stage": "stage2",
567
+ "epoch": 30,
568
+ "cosine_similarity": 0.9999998807907104,
569
+ "grad_magnitude_ratio": 0.999754104070612,
570
+ "physics_grad_norm": 0.06176600232720375,
571
+ "causal_grad_norm": 0.06175081431865692,
572
+ "physics_loss": 0.0011018798686563969,
573
+ "causal_loss": 0.0011017454089596868
574
+ },
575
+ {
576
+ "stage": "stage2",
577
+ "epoch": 40,
578
+ "cosine_similarity": 1.0,
579
+ "grad_magnitude_ratio": 0.9995120045741328,
580
+ "physics_grad_norm": 0.07230795174837112,
581
+ "causal_grad_norm": 0.07227266579866409,
582
+ "physics_loss": 0.001746926223859191,
583
+ "causal_loss": 0.0017465013079345226
584
+ },
585
+ {
586
+ "stage": "stage2",
587
+ "epoch": 50,
588
+ "cosine_similarity": 0.9999998807907104,
589
+ "grad_magnitude_ratio": 0.9991100083482312,
590
+ "physics_grad_norm": 0.08170600980520248,
591
+ "causal_grad_norm": 0.08163329213857651,
592
+ "physics_loss": 0.0025422745384275913,
593
+ "causal_loss": 0.0025411585811525583
594
+ },
595
+ {
596
+ "stage": "stage2",
597
+ "epoch": 60,
598
+ "cosine_similarity": 1.0000001192092896,
599
+ "grad_magnitude_ratio": 0.9983814839130658,
600
+ "physics_grad_norm": 0.09295525401830673,
601
+ "causal_grad_norm": 0.09280480444431305,
602
+ "physics_loss": 0.003877741750329733,
603
+ "causal_loss": 0.0038746101781725883
604
+ },
605
+ {
606
+ "stage": "stage2",
607
+ "epoch": 70,
608
+ "cosine_similarity": 1.0,
609
+ "grad_magnitude_ratio": 0.997449907799605,
610
+ "physics_grad_norm": 0.1060895100235939,
611
+ "causal_grad_norm": 0.105818971991539,
612
+ "physics_loss": 0.005380403716117144,
613
+ "causal_loss": 0.005373532418161631
614
+ },
615
+ {
616
+ "stage": "stage2",
617
+ "epoch": 80,
618
+ "cosine_similarity": 1.0,
619
+ "grad_magnitude_ratio": 0.9956059260863372,
620
+ "physics_grad_norm": 0.1282617747783661,
621
+ "causal_grad_norm": 0.12769818305969238,
622
+ "physics_loss": 0.007923213765025139,
623
+ "causal_loss": 0.007906163111329079
624
+ },
625
+ {
626
+ "stage": "stage2",
627
+ "epoch": 90,
628
+ "cosine_similarity": 1.0,
629
+ "grad_magnitude_ratio": 0.993441872161522,
630
+ "physics_grad_norm": 0.1464797854423523,
631
+ "causal_grad_norm": 0.14551915228366852,
632
+ "physics_loss": 0.011197277344763279,
633
+ "causal_loss": 0.011160054244101048
634
+ },
635
+ {
636
+ "stage": "stage2",
637
+ "epoch": 100,
638
+ "cosine_similarity": 1.0,
639
+ "grad_magnitude_ratio": 0.9904552663099362,
640
+ "physics_grad_norm": 0.16701631247997284,
641
+ "causal_grad_norm": 0.16542218625545502,
642
+ "physics_loss": 0.014517954550683498,
643
+ "causal_loss": 0.014448716305196285
644
+ },
645
+ {
646
+ "stage": "stage2",
647
+ "epoch": 110,
648
+ "cosine_similarity": 1.0,
649
+ "grad_magnitude_ratio": 0.9853395770031275,
650
+ "physics_grad_norm": 0.18083450198173523,
651
+ "causal_grad_norm": 0.1781833916902542,
652
+ "physics_loss": 0.0200224369764328,
653
+ "causal_loss": 0.019877955317497253
654
+ },
655
+ {
656
+ "stage": "stage2",
657
+ "epoch": 120,
658
+ "cosine_similarity": 0.9999998807907104,
659
+ "grad_magnitude_ratio": 0.9805785907215071,
660
+ "physics_grad_norm": 0.18466661870479584,
661
+ "causal_grad_norm": 0.18108013272285461,
662
+ "physics_loss": 0.025005321949720383,
663
+ "causal_loss": 0.02476070076227188
664
+ },
665
+ {
666
+ "stage": "stage2",
667
+ "epoch": 130,
668
+ "cosine_similarity": 0.9999998807907104,
669
+ "grad_magnitude_ratio": 0.9740073890686621,
670
+ "physics_grad_norm": 0.18331746757030487,
671
+ "causal_grad_norm": 0.1785525679588318,
672
+ "physics_loss": 0.030870094895362854,
673
+ "causal_loss": 0.030468566343188286
674
+ },
675
+ {
676
+ "stage": "stage2",
677
+ "epoch": 140,
678
+ "cosine_similarity": 0.9999996423721313,
679
+ "grad_magnitude_ratio": 0.965926664338591,
680
+ "physics_grad_norm": 0.18664249777793884,
681
+ "causal_grad_norm": 0.18028296530246735,
682
+ "physics_loss": 0.038192734122276306,
683
+ "causal_loss": 0.03753706440329552
684
+ },
685
+ {
686
+ "stage": "stage2",
687
+ "epoch": 150,
688
+ "cosine_similarity": 0.9999992847442627,
689
+ "grad_magnitude_ratio": 0.9571787832996401,
690
+ "physics_grad_norm": 0.1798747330904007,
691
+ "causal_grad_norm": 0.17217227816581726,
692
+ "physics_loss": 0.042504098266363144,
693
+ "causal_loss": 0.041611362248659134
694
+ },
695
+ {
696
+ "stage": "stage2",
697
+ "epoch": 160,
698
+ "cosine_similarity": 0.9999963641166687,
699
+ "grad_magnitude_ratio": 0.9492246597367726,
700
+ "physics_grad_norm": 0.16242729127407074,
701
+ "causal_grad_norm": 0.15417999029159546,
702
+ "physics_loss": 0.04767782986164093,
703
+ "causal_loss": 0.046470362693071365
704
+ },
705
+ {
706
+ "stage": "stage2",
707
+ "epoch": 170,
708
+ "cosine_similarity": 0.9999962449073792,
709
+ "grad_magnitude_ratio": 0.9441143773152635,
710
+ "physics_grad_norm": 0.18513309955596924,
711
+ "causal_grad_norm": 0.17478682100772858,
712
+ "physics_loss": 0.05183972790837288,
713
+ "causal_loss": 0.05033285915851593
714
+ },
715
+ {
716
+ "stage": "stage2",
717
+ "epoch": 180,
718
+ "cosine_similarity": 0.9999988079071045,
719
+ "grad_magnitude_ratio": 0.9383557681154895,
720
+ "physics_grad_norm": 0.2137746810913086,
721
+ "causal_grad_norm": 0.20059670507907867,
722
+ "physics_loss": 0.05255147069692612,
723
+ "causal_loss": 0.050898097455501556
724
+ },
725
+ {
726
+ "stage": "stage2",
727
+ "epoch": 190,
728
+ "cosine_similarity": 0.9999973773956299,
729
+ "grad_magnitude_ratio": 0.9334897791923115,
730
+ "physics_grad_norm": 0.24750520288944244,
731
+ "causal_grad_norm": 0.23104357719421387,
732
+ "physics_loss": 0.05498194321990013,
733
+ "causal_loss": 0.053119104355573654
734
+ },
735
+ {
736
+ "stage": "stage2",
737
+ "epoch": 200,
738
+ "cosine_similarity": 0.9999964833259583,
739
+ "grad_magnitude_ratio": 0.9298753336453318,
740
+ "physics_grad_norm": 0.25911590456962585,
741
+ "causal_grad_norm": 0.2409454882144928,
742
+ "physics_loss": 0.05580781027674675,
743
+ "causal_loss": 0.053816378116607666
744
+ },
745
+ {
746
+ "stage": "stage2",
747
+ "epoch": 210,
748
+ "cosine_similarity": 0.9999914169311523,
749
+ "grad_magnitude_ratio": 0.9183742170660167,
750
+ "physics_grad_norm": 0.19449986517429352,
751
+ "causal_grad_norm": 0.17862366139888763,
752
+ "physics_loss": 0.056751374155282974,
753
+ "causal_loss": 0.05453530699014664
754
+ },
755
+ {
756
+ "stage": "stage2",
757
+ "epoch": 220,
758
+ "cosine_similarity": 0.9999777674674988,
759
+ "grad_magnitude_ratio": 0.9120892189334118,
760
+ "physics_grad_norm": 0.17617318034172058,
761
+ "causal_grad_norm": 0.16068565845489502,
762
+ "physics_loss": 0.056242212653160095,
763
+ "causal_loss": 0.05397667735815048
764
+ },
765
+ {
766
+ "stage": "stage2",
767
+ "epoch": 230,
768
+ "cosine_similarity": 0.999954342842102,
769
+ "grad_magnitude_ratio": 0.9064719413169217,
770
+ "physics_grad_norm": 0.16839155554771423,
771
+ "causal_grad_norm": 0.15264222025871277,
772
+ "physics_loss": 0.05647708848118782,
773
+ "causal_loss": 0.0540536604821682
774
+ },
775
+ {
776
+ "stage": "stage2",
777
+ "epoch": 240,
778
+ "cosine_similarity": 0.9999758005142212,
779
+ "grad_magnitude_ratio": 0.9118240952479634,
780
+ "physics_grad_norm": 0.18925708532333374,
781
+ "causal_grad_norm": 0.1725691705942154,
782
+ "physics_loss": 0.054281093180179596,
783
+ "causal_loss": 0.05196930095553398
784
+ },
785
+ {
786
+ "stage": "stage2",
787
+ "epoch": 250,
788
+ "cosine_similarity": 0.9999624490737915,
789
+ "grad_magnitude_ratio": 0.9101634154833095,
790
+ "physics_grad_norm": 0.19936302304267883,
791
+ "causal_grad_norm": 0.1814529299736023,
792
+ "physics_loss": 0.05273370444774628,
793
+ "causal_loss": 0.050439707934856415
794
+ },
795
+ {
796
+ "stage": "stage2",
797
+ "epoch": 260,
798
+ "cosine_similarity": 0.9999144077301025,
799
+ "grad_magnitude_ratio": 0.9066402418735077,
800
+ "physics_grad_norm": 0.23766104876995087,
801
+ "causal_grad_norm": 0.21547307074069977,
802
+ "physics_loss": 0.053496476262807846,
803
+ "causal_loss": 0.0510469526052475
804
+ },
805
+ {
806
+ "stage": "stage2",
807
+ "epoch": 270,
808
+ "cosine_similarity": 0.9998779296875,
809
+ "grad_magnitude_ratio": 0.9094283019373488,
810
+ "physics_grad_norm": 0.22634072601795197,
811
+ "causal_grad_norm": 0.20584066212177277,
812
+ "physics_loss": 0.050522707402706146,
813
+ "causal_loss": 0.04828266799449921
814
+ },
815
+ {
816
+ "stage": "stage2",
817
+ "epoch": 280,
818
+ "cosine_similarity": 0.9999082088470459,
819
+ "grad_magnitude_ratio": 0.9167229511927705,
820
+ "physics_grad_norm": 0.2755134105682373,
821
+ "causal_grad_norm": 0.2525694668292999,
822
+ "physics_loss": 0.05260825529694557,
823
+ "causal_loss": 0.050173766911029816
824
+ },
825
+ {
826
+ "stage": "stage2",
827
+ "epoch": 290,
828
+ "cosine_similarity": 0.9999412894248962,
829
+ "grad_magnitude_ratio": 0.9140871111293728,
830
+ "physics_grad_norm": 0.33074435591697693,
831
+ "causal_grad_norm": 0.3023291528224945,
832
+ "physics_loss": 0.05346252769231796,
833
+ "causal_loss": 0.05089973658323288
834
+ },
835
+ {
836
+ "stage": "stage3",
837
+ "epoch": 0,
838
+ "cosine_similarity": 1.0,
839
+ "grad_magnitude_ratio": 0.9986853569585982,
840
+ "physics_grad_norm": 0.2367490977048874,
841
+ "causal_grad_norm": 0.2364378571510315,
842
+ "physics_loss": 0.05100517347455025,
843
+ "causal_loss": 0.05096830055117607
844
+ },
845
+ {
846
+ "stage": "stage3",
847
+ "epoch": 10,
848
+ "cosine_similarity": 0.9999996423721313,
849
+ "grad_magnitude_ratio": 0.9943671983639533,
850
+ "physics_grad_norm": 0.39971861243247986,
851
+ "causal_grad_norm": 0.39746707677841187,
852
+ "physics_loss": 0.05461542680859566,
853
+ "causal_loss": 0.05443704500794411
854
+ },
855
+ {
856
+ "stage": "stage3",
857
+ "epoch": 20,
858
+ "cosine_similarity": 0.9999989867210388,
859
+ "grad_magnitude_ratio": 0.9900900693785609,
860
+ "physics_grad_norm": 0.3590829074382782,
861
+ "causal_grad_norm": 0.3555244207382202,
862
+ "physics_loss": 0.05250366032123566,
863
+ "causal_loss": 0.05220848694443703
864
+ },
865
+ {
866
+ "stage": "stage3",
867
+ "epoch": 30,
868
+ "cosine_similarity": 0.9999991655349731,
869
+ "grad_magnitude_ratio": 0.9836748583750083,
870
+ "physics_grad_norm": 0.341109037399292,
871
+ "causal_grad_norm": 0.33554038405418396,
872
+ "physics_loss": 0.05420675128698349,
873
+ "causal_loss": 0.05374656990170479
874
+ },
875
+ {
876
+ "stage": "stage3",
877
+ "epoch": 40,
878
+ "cosine_similarity": 0.9999984502792358,
879
+ "grad_magnitude_ratio": 0.9796337409284395,
880
+ "physics_grad_norm": 0.33858993649482727,
881
+ "causal_grad_norm": 0.3316941261291504,
882
+ "physics_loss": 0.05304212495684624,
883
+ "causal_loss": 0.05248739942908287
884
+ },
885
+ {
886
+ "stage": "stage3",
887
+ "epoch": 50,
888
+ "cosine_similarity": 0.9999983906745911,
889
+ "grad_magnitude_ratio": 0.9755987627493854,
890
+ "physics_grad_norm": 0.42131996154785156,
891
+ "causal_grad_norm": 0.41103923320770264,
892
+ "physics_loss": 0.05565572530031204,
893
+ "causal_loss": 0.0549265518784523
894
+ },
895
+ {
896
+ "stage": "stage3",
897
+ "epoch": 60,
898
+ "cosine_similarity": 0.9999954104423523,
899
+ "grad_magnitude_ratio": 0.971290264885484,
900
+ "physics_grad_norm": 0.4120720326900482,
901
+ "causal_grad_norm": 0.40024155378341675,
902
+ "physics_loss": 0.05529622733592987,
903
+ "causal_loss": 0.05440807715058327
904
+ },
905
+ {
906
+ "stage": "stage3",
907
+ "epoch": 70,
908
+ "cosine_similarity": 0.9999979138374329,
909
+ "grad_magnitude_ratio": 0.9685351954925496,
910
+ "physics_grad_norm": 0.4003519117832184,
911
+ "causal_grad_norm": 0.3877549171447754,
912
+ "physics_loss": 0.054538529366254807,
913
+ "causal_loss": 0.0535748153924942
914
+ },
915
+ {
916
+ "stage": "stage3",
917
+ "epoch": 80,
918
+ "cosine_similarity": 0.9999963641166687,
919
+ "grad_magnitude_ratio": 0.9624991929563279,
920
+ "physics_grad_norm": 0.3632769286632538,
921
+ "causal_grad_norm": 0.3496537506580353,
922
+ "physics_loss": 0.054632458835840225,
923
+ "causal_loss": 0.05352343991398811
924
+ },
925
+ {
926
+ "stage": "stage3",
927
+ "epoch": 90,
928
+ "cosine_similarity": 0.9999859929084778,
929
+ "grad_magnitude_ratio": 0.9573937283020989,
930
+ "physics_grad_norm": 0.4305787682533264,
931
+ "causal_grad_norm": 0.4122334122657776,
932
+ "physics_loss": 0.056385673582553864,
933
+ "causal_loss": 0.055050935596227646
934
+ },
935
+ {
936
+ "stage": "stage3",
937
+ "epoch": 100,
938
+ "cosine_similarity": 0.9999861717224121,
939
+ "grad_magnitude_ratio": 0.9532526003689006,
940
+ "physics_grad_norm": 0.3871144950389862,
941
+ "causal_grad_norm": 0.36901789903640747,
942
+ "physics_loss": 0.05586513504385948,
943
+ "causal_loss": 0.054406747221946716
944
+ },
945
+ {
946
+ "stage": "stage3",
947
+ "epoch": 110,
948
+ "cosine_similarity": 0.9999767541885376,
949
+ "grad_magnitude_ratio": 0.9504285575023982,
950
+ "physics_grad_norm": 0.32742342352867126,
951
+ "causal_grad_norm": 0.3111925721168518,
952
+ "physics_loss": 0.053127046674489975,
953
+ "causal_loss": 0.0516701266169548
954
+ },
955
+ {
956
+ "stage": "stage3",
957
+ "epoch": 120,
958
+ "cosine_similarity": 0.9999771118164062,
959
+ "grad_magnitude_ratio": 0.9482551316582968,
960
+ "physics_grad_norm": 0.3578418791294098,
961
+ "causal_grad_norm": 0.3393253982067108,
962
+ "physics_loss": 0.0537872388958931,
963
+ "causal_loss": 0.05216517299413681
964
+ },
965
+ {
966
+ "stage": "stage3",
967
+ "epoch": 130,
968
+ "cosine_similarity": 0.9999456405639648,
969
+ "grad_magnitude_ratio": 0.9404921022437905,
970
+ "physics_grad_norm": 0.3505805432796478,
971
+ "causal_grad_norm": 0.3297182321548462,
972
+ "physics_loss": 0.05556783825159073,
973
+ "causal_loss": 0.05369650572538376
974
+ },
975
+ {
976
+ "stage": "stage3",
977
+ "epoch": 140,
978
+ "cosine_similarity": 0.9999868869781494,
979
+ "grad_magnitude_ratio": 0.9348177278678765,
980
+ "physics_grad_norm": 0.3535548746585846,
981
+ "causal_grad_norm": 0.33050936460494995,
982
+ "physics_loss": 0.05561727657914162,
983
+ "causal_loss": 0.05365462601184845
984
+ },
985
+ {
986
+ "stage": "stage3",
987
+ "epoch": 150,
988
+ "cosine_similarity": 0.9999855756759644,
989
+ "grad_magnitude_ratio": 0.9301569293024268,
990
+ "physics_grad_norm": 0.44729509949684143,
991
+ "causal_grad_norm": 0.4160546362400055,
992
+ "physics_loss": 0.055762868374586105,
993
+ "causal_loss": 0.05362442135810852
994
+ },
995
+ {
996
+ "stage": "stage3",
997
+ "epoch": 160,
998
+ "cosine_similarity": 0.999966025352478,
999
+ "grad_magnitude_ratio": 0.9303893661815831,
1000
+ "physics_grad_norm": 0.3832900822162628,
1001
+ "causal_grad_norm": 0.3566090166568756,
1002
+ "physics_loss": 0.0554170086979866,
1003
+ "causal_loss": 0.05319099500775337
1004
+ },
1005
+ {
1006
+ "stage": "stage3",
1007
+ "epoch": 170,
1008
+ "cosine_similarity": 0.9999842047691345,
1009
+ "grad_magnitude_ratio": 0.9246074317324314,
1010
+ "physics_grad_norm": 0.3531397581100464,
1011
+ "causal_grad_norm": 0.32651564478874207,
1012
+ "physics_loss": 0.05328086391091347,
1013
+ "causal_loss": 0.05107120797038078
1014
+ },
1015
+ {
1016
+ "stage": "stage3",
1017
+ "epoch": 180,
1018
+ "cosine_similarity": 0.9999874234199524,
1019
+ "grad_magnitude_ratio": 0.9127072497767221,
1020
+ "physics_grad_norm": 0.36515793204307556,
1021
+ "causal_grad_norm": 0.3332822918891907,
1022
+ "physics_loss": 0.05485963076353073,
1023
+ "causal_loss": 0.052342433482408524
1024
+ },
1025
+ {
1026
+ "stage": "stage3",
1027
+ "epoch": 190,
1028
+ "cosine_similarity": 0.9999748468399048,
1029
+ "grad_magnitude_ratio": 0.9127649293547775,
1030
+ "physics_grad_norm": 0.38128459453582764,
1031
+ "causal_grad_norm": 0.3480232059955597,
1032
+ "physics_loss": 0.055660102516412735,
1033
+ "causal_loss": 0.05301564186811447
1034
+ }
1035
+ ],
1036
+ "wall_time_s": 69.65
1037
+ }
1038
+ }
1039
+ }
results/paper_c/gradient_flow_heat1d/fig_gradient_alignment.pdf ADDED
Binary file (18.8 kB). View file
 
results/paper_c/gradient_flow_heat1d/gradient_flow_results.json ADDED
@@ -0,0 +1,1039 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "experiment": "gradient_flow_analysis",
3
+ "pde": "heat1d",
4
+ "seed": 42,
5
+ "device": "cuda",
6
+ "hyperparameters": {
7
+ "stage1_epochs": 200,
8
+ "stage2_epochs": 300,
9
+ "stage3_epochs": 200,
10
+ "stage1_lr": 0.001,
11
+ "stage2_lr": 0.0001,
12
+ "stage3_lr": 1e-05,
13
+ "causal_epsilon": 1.0,
14
+ "num_collocation": 2000,
15
+ "num_boundary": 200,
16
+ "batch_size": 256,
17
+ "hidden_dims": [
18
+ 64,
19
+ 64,
20
+ 64,
21
+ 64
22
+ ],
23
+ "probe_every": 10
24
+ },
25
+ "conditions": {
26
+ "with_pretrain": {
27
+ "condition": "with_pretrain",
28
+ "probes": [
29
+ {
30
+ "stage": "stage2",
31
+ "epoch": 0,
32
+ "cosine_similarity": 1.0,
33
+ "grad_magnitude_ratio": 0.9994796848503216,
34
+ "physics_grad_norm": 0.32333117723464966,
35
+ "causal_grad_norm": 0.3231629431247711,
36
+ "physics_loss": 0.011444528587162495,
37
+ "causal_loss": 0.011440851725637913
38
+ },
39
+ {
40
+ "stage": "stage2",
41
+ "epoch": 10,
42
+ "cosine_similarity": 0.9999968409538269,
43
+ "grad_magnitude_ratio": 0.9984852295878843,
44
+ "physics_grad_norm": 0.30853521823883057,
45
+ "causal_grad_norm": 0.30806785821914673,
46
+ "physics_loss": 0.016559144482016563,
47
+ "causal_loss": 0.016530906781554222
48
+ },
49
+ {
50
+ "stage": "stage2",
51
+ "epoch": 20,
52
+ "cosine_similarity": 0.999999463558197,
53
+ "grad_magnitude_ratio": 0.9961949657183415,
54
+ "physics_grad_norm": 0.5394759178161621,
55
+ "causal_grad_norm": 0.5374231934547424,
56
+ "physics_loss": 0.018041346222162247,
57
+ "causal_loss": 0.017998017370700836
58
+ },
59
+ {
60
+ "stage": "stage2",
61
+ "epoch": 30,
62
+ "cosine_similarity": 0.9999740123748779,
63
+ "grad_magnitude_ratio": 0.9948957591768954,
64
+ "physics_grad_norm": 0.372873455286026,
65
+ "causal_grad_norm": 0.370970219373703,
66
+ "physics_loss": 0.019589228555560112,
67
+ "causal_loss": 0.019485408440232277
68
+ },
69
+ {
70
+ "stage": "stage2",
71
+ "epoch": 40,
72
+ "cosine_similarity": 0.999991774559021,
73
+ "grad_magnitude_ratio": 0.9943614117380314,
74
+ "physics_grad_norm": 0.3396465480327606,
75
+ "causal_grad_norm": 0.33773142099380493,
76
+ "physics_loss": 0.017780328169465065,
77
+ "causal_loss": 0.0176900215446949
78
+ },
79
+ {
80
+ "stage": "stage2",
81
+ "epoch": 50,
82
+ "cosine_similarity": 0.9999902844429016,
83
+ "grad_magnitude_ratio": 0.995681603751873,
84
+ "physics_grad_norm": 0.2784101366996765,
85
+ "causal_grad_norm": 0.2772078514099121,
86
+ "physics_loss": 0.01581607200205326,
87
+ "causal_loss": 0.015728861093521118
88
+ },
89
+ {
90
+ "stage": "stage2",
91
+ "epoch": 60,
92
+ "cosine_similarity": 0.999981701374054,
93
+ "grad_magnitude_ratio": 0.9947258881588674,
94
+ "physics_grad_norm": 0.30437391996383667,
95
+ "causal_grad_norm": 0.30276861786842346,
96
+ "physics_loss": 0.016007302328944206,
97
+ "causal_loss": 0.015894334763288498
98
+ },
99
+ {
100
+ "stage": "stage2",
101
+ "epoch": 70,
102
+ "cosine_similarity": 0.9997181296348572,
103
+ "grad_magnitude_ratio": 0.9851106152181356,
104
+ "physics_grad_norm": 0.19047152996063232,
105
+ "causal_grad_norm": 0.18763552606105804,
106
+ "physics_loss": 0.01645784080028534,
107
+ "causal_loss": 0.01629667729139328
108
+ },
109
+ {
110
+ "stage": "stage2",
111
+ "epoch": 80,
112
+ "cosine_similarity": 0.9998576641082764,
113
+ "grad_magnitude_ratio": 0.9937882570011494,
114
+ "physics_grad_norm": 0.2081691026687622,
115
+ "causal_grad_norm": 0.2068760097026825,
116
+ "physics_loss": 0.01547793298959732,
117
+ "causal_loss": 0.015325108543038368
118
+ },
119
+ {
120
+ "stage": "stage2",
121
+ "epoch": 90,
122
+ "cosine_similarity": 0.9999786615371704,
123
+ "grad_magnitude_ratio": 0.9877144686729173,
124
+ "physics_grad_norm": 0.2842681407928467,
125
+ "causal_grad_norm": 0.2807757556438446,
126
+ "physics_loss": 0.013632264919579029,
127
+ "causal_loss": 0.013499477878212929
128
+ },
129
+ {
130
+ "stage": "stage2",
131
+ "epoch": 100,
132
+ "cosine_similarity": 0.9999774694442749,
133
+ "grad_magnitude_ratio": 0.9880192940134765,
134
+ "physics_grad_norm": 0.24980859458446503,
135
+ "causal_grad_norm": 0.24681571125984192,
136
+ "physics_loss": 0.01139654777944088,
137
+ "causal_loss": 0.011291371658444405
138
+ },
139
+ {
140
+ "stage": "stage2",
141
+ "epoch": 110,
142
+ "cosine_similarity": 0.9997946619987488,
143
+ "grad_magnitude_ratio": 0.9865394942786195,
144
+ "physics_grad_norm": 0.16232356429100037,
145
+ "causal_grad_norm": 0.16013860702514648,
146
+ "physics_loss": 0.010706419125199318,
147
+ "causal_loss": 0.010574324056506157
148
+ },
149
+ {
150
+ "stage": "stage2",
151
+ "epoch": 120,
152
+ "cosine_similarity": 0.9999150037765503,
153
+ "grad_magnitude_ratio": 0.989826612568192,
154
+ "physics_grad_norm": 0.11540599912405014,
155
+ "causal_grad_norm": 0.11423192918300629,
156
+ "physics_loss": 0.008098816499114037,
157
+ "causal_loss": 0.008025840856134892
158
+ },
159
+ {
160
+ "stage": "stage2",
161
+ "epoch": 130,
162
+ "cosine_similarity": 0.9998161196708679,
163
+ "grad_magnitude_ratio": 0.9884792498998584,
164
+ "physics_grad_norm": 0.10886646062135696,
165
+ "causal_grad_norm": 0.1076122373342514,
166
+ "physics_loss": 0.0073507982306182384,
167
+ "causal_loss": 0.0072771781124174595
168
+ },
169
+ {
170
+ "stage": "stage2",
171
+ "epoch": 140,
172
+ "cosine_similarity": 0.9998558759689331,
173
+ "grad_magnitude_ratio": 0.9794225163260818,
174
+ "physics_grad_norm": 0.15226243436336517,
175
+ "causal_grad_norm": 0.149129256606102,
176
+ "physics_loss": 0.0070302593521773815,
177
+ "causal_loss": 0.006943168118596077
178
+ },
179
+ {
180
+ "stage": "stage2",
181
+ "epoch": 150,
182
+ "cosine_similarity": 0.9998636841773987,
183
+ "grad_magnitude_ratio": 0.9843070580202906,
184
+ "physics_grad_norm": 0.08256439864635468,
185
+ "causal_grad_norm": 0.08126872032880783,
186
+ "physics_loss": 0.005276232957839966,
187
+ "causal_loss": 0.005227019544690847
188
+ },
189
+ {
190
+ "stage": "stage2",
191
+ "epoch": 160,
192
+ "cosine_similarity": 0.9999596476554871,
193
+ "grad_magnitude_ratio": 0.9903036877616537,
194
+ "physics_grad_norm": 0.10383220762014389,
195
+ "causal_grad_norm": 0.10282541811466217,
196
+ "physics_loss": 0.004106142558157444,
197
+ "causal_loss": 0.004076830577105284
198
+ },
199
+ {
200
+ "stage": "stage2",
201
+ "epoch": 170,
202
+ "cosine_similarity": 0.9998334050178528,
203
+ "grad_magnitude_ratio": 0.9799607726025179,
204
+ "physics_grad_norm": 0.06811000406742096,
205
+ "causal_grad_norm": 0.06674513220787048,
206
+ "physics_loss": 0.003668186953291297,
207
+ "causal_loss": 0.0036437269300222397
208
+ },
209
+ {
210
+ "stage": "stage2",
211
+ "epoch": 180,
212
+ "cosine_similarity": 0.999983549118042,
213
+ "grad_magnitude_ratio": 0.9879723728579903,
214
+ "physics_grad_norm": 0.20202304422855377,
215
+ "causal_grad_norm": 0.199593186378479,
216
+ "physics_loss": 0.0035066131968051195,
217
+ "causal_loss": 0.003482623491436243
218
+ },
219
+ {
220
+ "stage": "stage2",
221
+ "epoch": 190,
222
+ "cosine_similarity": 0.9999862313270569,
223
+ "grad_magnitude_ratio": 0.9848956608817268,
224
+ "physics_grad_norm": 0.2361362725496292,
225
+ "causal_grad_norm": 0.2325695902109146,
226
+ "physics_loss": 0.0038125126156955957,
227
+ "causal_loss": 0.0037828076165169477
228
+ },
229
+ {
230
+ "stage": "stage2",
231
+ "epoch": 200,
232
+ "cosine_similarity": 0.9999841451644897,
233
+ "grad_magnitude_ratio": 0.9883376248227186,
234
+ "physics_grad_norm": 0.17144855856895447,
235
+ "causal_grad_norm": 0.1694490611553192,
236
+ "physics_loss": 0.0031273667700588703,
237
+ "causal_loss": 0.0031082627829164267
238
+ },
239
+ {
240
+ "stage": "stage2",
241
+ "epoch": 210,
242
+ "cosine_similarity": 0.9999420642852783,
243
+ "grad_magnitude_ratio": 0.9937903073637939,
244
+ "physics_grad_norm": 0.0673237070441246,
245
+ "causal_grad_norm": 0.06690564751625061,
246
+ "physics_loss": 0.0027480502612888813,
247
+ "causal_loss": 0.002733997767791152
248
+ },
249
+ {
250
+ "stage": "stage2",
251
+ "epoch": 220,
252
+ "cosine_similarity": 0.9999206066131592,
253
+ "grad_magnitude_ratio": 0.9926372953827896,
254
+ "physics_grad_norm": 0.07206901907920837,
255
+ "causal_grad_norm": 0.07153839617967606,
256
+ "physics_loss": 0.002840222790837288,
257
+ "causal_loss": 0.002825093222782016
258
+ },
259
+ {
260
+ "stage": "stage2",
261
+ "epoch": 230,
262
+ "cosine_similarity": 0.9999788403511047,
263
+ "grad_magnitude_ratio": 0.9979884953631502,
264
+ "physics_grad_norm": 0.06267881393432617,
265
+ "causal_grad_norm": 0.06255273520946503,
266
+ "physics_loss": 0.0024382229894399643,
267
+ "causal_loss": 0.0024290962610393763
268
+ },
269
+ {
270
+ "stage": "stage2",
271
+ "epoch": 240,
272
+ "cosine_similarity": 0.999923050403595,
273
+ "grad_magnitude_ratio": 0.9889954878726862,
274
+ "physics_grad_norm": 0.07763774693012238,
275
+ "causal_grad_norm": 0.07678338140249252,
276
+ "physics_loss": 0.0026584926526993513,
277
+ "causal_loss": 0.0026432867161929607
278
+ },
279
+ {
280
+ "stage": "stage2",
281
+ "epoch": 250,
282
+ "cosine_similarity": 0.9999872446060181,
283
+ "grad_magnitude_ratio": 0.9891128585551718,
284
+ "physics_grad_norm": 0.18387167155742645,
285
+ "causal_grad_norm": 0.18186983466148376,
286
+ "physics_loss": 0.0026910139713436365,
287
+ "causal_loss": 0.0026749703101813793
288
+ },
289
+ {
290
+ "stage": "stage2",
291
+ "epoch": 260,
292
+ "cosine_similarity": 0.9999933242797852,
293
+ "grad_magnitude_ratio": 0.9877147332783783,
294
+ "physics_grad_norm": 0.1916683167219162,
295
+ "causal_grad_norm": 0.1893136203289032,
296
+ "physics_loss": 0.002540862187743187,
297
+ "causal_loss": 0.0025276499800384045
298
+ },
299
+ {
300
+ "stage": "stage2",
301
+ "epoch": 270,
302
+ "cosine_similarity": 0.9999889135360718,
303
+ "grad_magnitude_ratio": 0.989242361005925,
304
+ "physics_grad_norm": 0.13113822042942047,
305
+ "causal_grad_norm": 0.12972748279571533,
306
+ "physics_loss": 0.0024866373278200626,
307
+ "causal_loss": 0.0024732486344873905
308
+ },
309
+ {
310
+ "stage": "stage2",
311
+ "epoch": 280,
312
+ "cosine_similarity": 0.9999841451644897,
313
+ "grad_magnitude_ratio": 0.9875132419635543,
314
+ "physics_grad_norm": 0.13465602695941925,
315
+ "causal_grad_norm": 0.13297460973262787,
316
+ "physics_loss": 0.0023069533053785563,
317
+ "causal_loss": 0.002295802114531398
318
+ },
319
+ {
320
+ "stage": "stage2",
321
+ "epoch": 290,
322
+ "cosine_similarity": 0.9999823570251465,
323
+ "grad_magnitude_ratio": 0.9781911882468476,
324
+ "physics_grad_norm": 0.17625665664672852,
325
+ "causal_grad_norm": 0.17241270840168,
326
+ "physics_loss": 0.0024413778446614742,
327
+ "causal_loss": 0.002424899721518159
328
+ },
329
+ {
330
+ "stage": "stage3",
331
+ "epoch": 0,
332
+ "cosine_similarity": 1.0,
333
+ "grad_magnitude_ratio": 0.999763194320115,
334
+ "physics_grad_norm": 0.07944368571043015,
335
+ "causal_grad_norm": 0.07942487299442291,
336
+ "physics_loss": 0.0023612608201801777,
337
+ "causal_loss": 0.00236104940995574
338
+ },
339
+ {
340
+ "stage": "stage3",
341
+ "epoch": 10,
342
+ "cosine_similarity": 1.0,
343
+ "grad_magnitude_ratio": 0.9990685228986583,
344
+ "physics_grad_norm": 0.2908317446708679,
345
+ "causal_grad_norm": 0.29056084156036377,
346
+ "physics_loss": 0.002630747389048338,
347
+ "causal_loss": 0.0026296020951122046
348
+ },
349
+ {
350
+ "stage": "stage3",
351
+ "epoch": 20,
352
+ "cosine_similarity": 0.9999998807907104,
353
+ "grad_magnitude_ratio": 0.9986145713931356,
354
+ "physics_grad_norm": 0.14093105494976044,
355
+ "causal_grad_norm": 0.14073580503463745,
356
+ "physics_loss": 0.0021903591696172953,
357
+ "causal_loss": 0.0021890688221901655
358
+ },
359
+ {
360
+ "stage": "stage3",
361
+ "epoch": 30,
362
+ "cosine_similarity": 0.9999997019767761,
363
+ "grad_magnitude_ratio": 0.9980981412491796,
364
+ "physics_grad_norm": 0.1831364929676056,
365
+ "causal_grad_norm": 0.1827881932258606,
366
+ "physics_loss": 0.002204042160883546,
367
+ "causal_loss": 0.002202059142291546
368
+ },
369
+ {
370
+ "stage": "stage3",
371
+ "epoch": 40,
372
+ "cosine_similarity": 0.9999997615814209,
373
+ "grad_magnitude_ratio": 0.9974243180196066,
374
+ "physics_grad_norm": 0.17689792811870575,
375
+ "causal_grad_norm": 0.17644229531288147,
376
+ "physics_loss": 0.0022595259360969067,
377
+ "causal_loss": 0.0022572430316358805
378
+ },
379
+ {
380
+ "stage": "stage3",
381
+ "epoch": 50,
382
+ "cosine_similarity": 0.9999971389770508,
383
+ "grad_magnitude_ratio": 0.9975902747766989,
384
+ "physics_grad_norm": 0.13713105022907257,
385
+ "causal_grad_norm": 0.1368006020784378,
386
+ "physics_loss": 0.0024006846360862255,
387
+ "causal_loss": 0.00239626900292933
388
+ },
389
+ {
390
+ "stage": "stage3",
391
+ "epoch": 60,
392
+ "cosine_similarity": 0.9999988079071045,
393
+ "grad_magnitude_ratio": 0.9965287982857624,
394
+ "physics_grad_norm": 0.1611258089542389,
395
+ "causal_grad_norm": 0.160566508769989,
396
+ "physics_loss": 0.002307700924575329,
397
+ "causal_loss": 0.002303451532498002
398
+ },
399
+ {
400
+ "stage": "stage3",
401
+ "epoch": 70,
402
+ "cosine_similarity": 0.9999964833259583,
403
+ "grad_magnitude_ratio": 0.9969244291737349,
404
+ "physics_grad_norm": 0.11183971166610718,
405
+ "causal_grad_norm": 0.111495740711689,
406
+ "physics_loss": 0.002288483316078782,
407
+ "causal_loss": 0.002283424371853471
408
+ },
409
+ {
410
+ "stage": "stage3",
411
+ "epoch": 80,
412
+ "cosine_similarity": 0.9999992251396179,
413
+ "grad_magnitude_ratio": 0.9951443110947598,
414
+ "physics_grad_norm": 0.17448610067367554,
415
+ "causal_grad_norm": 0.17363885045051575,
416
+ "physics_loss": 0.0022205431014299393,
417
+ "causal_loss": 0.0022161740344017744
418
+ },
419
+ {
420
+ "stage": "stage3",
421
+ "epoch": 90,
422
+ "cosine_similarity": 0.9999994039535522,
423
+ "grad_magnitude_ratio": 0.994346165654128,
424
+ "physics_grad_norm": 0.21715375781059265,
425
+ "causal_grad_norm": 0.21592600643634796,
426
+ "physics_loss": 0.002217289060354233,
427
+ "causal_loss": 0.0022123600356280804
428
+ },
429
+ {
430
+ "stage": "stage3",
431
+ "epoch": 100,
432
+ "cosine_similarity": 0.9999959468841553,
433
+ "grad_magnitude_ratio": 0.9959024742721783,
434
+ "physics_grad_norm": 0.13495148718357086,
435
+ "causal_grad_norm": 0.13439851999282837,
436
+ "physics_loss": 0.0021600781474262476,
437
+ "causal_loss": 0.0021540841553360224
438
+ },
439
+ {
440
+ "stage": "stage3",
441
+ "epoch": 110,
442
+ "cosine_similarity": 0.999997615814209,
443
+ "grad_magnitude_ratio": 0.9923992946332796,
444
+ "physics_grad_norm": 0.20407991111278534,
445
+ "causal_grad_norm": 0.20252875983715057,
446
+ "physics_loss": 0.0025637445505708456,
447
+ "causal_loss": 0.002554674632847309
448
+ },
449
+ {
450
+ "stage": "stage3",
451
+ "epoch": 120,
452
+ "cosine_similarity": 0.999997615814209,
453
+ "grad_magnitude_ratio": 0.9941186223762818,
454
+ "physics_grad_norm": 0.1437954604625702,
455
+ "causal_grad_norm": 0.14294974505901337,
456
+ "physics_loss": 0.0022186744026839733,
457
+ "causal_loss": 0.002211965387687087
458
+ },
459
+ {
460
+ "stage": "stage3",
461
+ "epoch": 130,
462
+ "cosine_similarity": 0.9999939799308777,
463
+ "grad_magnitude_ratio": 0.9938297894016138,
464
+ "physics_grad_norm": 0.14187981188297272,
465
+ "causal_grad_norm": 0.14100438356399536,
466
+ "physics_loss": 0.0022837358992546797,
467
+ "causal_loss": 0.002275709295645356
468
+ },
469
+ {
470
+ "stage": "stage3",
471
+ "epoch": 140,
472
+ "cosine_similarity": 0.9999952912330627,
473
+ "grad_magnitude_ratio": 0.9921674676191345,
474
+ "physics_grad_norm": 0.20921467244625092,
475
+ "causal_grad_norm": 0.2075759917497635,
476
+ "physics_loss": 0.002616866724565625,
477
+ "causal_loss": 0.002604421693831682
478
+ },
479
+ {
480
+ "stage": "stage3",
481
+ "epoch": 150,
482
+ "cosine_similarity": 0.999992847442627,
483
+ "grad_magnitude_ratio": 0.9953614135461566,
484
+ "physics_grad_norm": 0.08494322746992111,
485
+ "causal_grad_norm": 0.08454921096563339,
486
+ "physics_loss": 0.0019863839261233807,
487
+ "causal_loss": 0.001979128923267126
488
+ },
489
+ {
490
+ "stage": "stage3",
491
+ "epoch": 160,
492
+ "cosine_similarity": 0.999982476234436,
493
+ "grad_magnitude_ratio": 0.9883436956151774,
494
+ "physics_grad_norm": 0.19324342906475067,
495
+ "causal_grad_norm": 0.19099092483520508,
496
+ "physics_loss": 0.002701425924897194,
497
+ "causal_loss": 0.0026835124008357525
498
+ },
499
+ {
500
+ "stage": "stage3",
501
+ "epoch": 170,
502
+ "cosine_similarity": 0.9999954700469971,
503
+ "grad_magnitude_ratio": 0.9890497357391418,
504
+ "physics_grad_norm": 0.20878812670707703,
505
+ "causal_grad_norm": 0.20650184154510498,
506
+ "physics_loss": 0.0023093693889677525,
507
+ "causal_loss": 0.0022974421735852957
508
+ },
509
+ {
510
+ "stage": "stage3",
511
+ "epoch": 180,
512
+ "cosine_similarity": 0.9999920129776001,
513
+ "grad_magnitude_ratio": 0.9926090016567897,
514
+ "physics_grad_norm": 0.109470434486866,
515
+ "causal_grad_norm": 0.10866133868694305,
516
+ "physics_loss": 0.0021147222723811865,
517
+ "causal_loss": 0.0021052786614745855
518
+ },
519
+ {
520
+ "stage": "stage3",
521
+ "epoch": 190,
522
+ "cosine_similarity": 0.9999966621398926,
523
+ "grad_magnitude_ratio": 0.9897969674209683,
524
+ "physics_grad_norm": 0.20291978120803833,
525
+ "causal_grad_norm": 0.20084938406944275,
526
+ "physics_loss": 0.0023312505800276995,
527
+ "causal_loss": 0.0023205294273793697
528
+ }
529
+ ],
530
+ "wall_time_s": 85.26
531
+ },
532
+ "without_pretrain": {
533
+ "condition": "without_pretrain",
534
+ "probes": [
535
+ {
536
+ "stage": "stage2",
537
+ "epoch": 0,
538
+ "cosine_similarity": 1.0,
539
+ "grad_magnitude_ratio": 0.9999994884635225,
540
+ "physics_grad_norm": 0.0022757970727980137,
541
+ "causal_grad_norm": 0.0022757959086447954,
542
+ "physics_loss": 3.544172432157211e-05,
543
+ "causal_loss": 3.544171340763569e-05
544
+ },
545
+ {
546
+ "stage": "stage2",
547
+ "epoch": 10,
548
+ "cosine_similarity": 1.0,
549
+ "grad_magnitude_ratio": 0.9999871311141048,
550
+ "physics_grad_norm": 0.0032385620288550854,
551
+ "causal_grad_norm": 0.0032385203521698713,
552
+ "physics_loss": 5.556490577873774e-05,
553
+ "causal_loss": 5.556453106692061e-05
554
+ },
555
+ {
556
+ "stage": "stage2",
557
+ "epoch": 20,
558
+ "cosine_similarity": 1.0,
559
+ "grad_magnitude_ratio": 0.9999487483680847,
560
+ "physics_grad_norm": 0.0075684585608541965,
561
+ "causal_grad_norm": 0.007568070665001869,
562
+ "physics_loss": 0.00017420860240235925,
563
+ "causal_loss": 0.00017420340736862272
564
+ },
565
+ {
566
+ "stage": "stage2",
567
+ "epoch": 30,
568
+ "cosine_similarity": 1.0000001192092896,
569
+ "grad_magnitude_ratio": 0.9998803843301277,
570
+ "physics_grad_norm": 0.011032702401280403,
571
+ "causal_grad_norm": 0.011031382717192173,
572
+ "physics_loss": 0.000317765778163448,
573
+ "causal_loss": 0.00031774386297911406
574
+ },
575
+ {
576
+ "stage": "stage2",
577
+ "epoch": 40,
578
+ "cosine_similarity": 1.0,
579
+ "grad_magnitude_ratio": 0.9997934134359097,
580
+ "physics_grad_norm": 0.013258459977805614,
581
+ "causal_grad_norm": 0.01325572095811367,
582
+ "physics_loss": 0.0004226307210046798,
583
+ "causal_loss": 0.0004225802840664983
584
+ },
585
+ {
586
+ "stage": "stage2",
587
+ "epoch": 50,
588
+ "cosine_similarity": 0.9999999403953552,
589
+ "grad_magnitude_ratio": 0.9997276221482657,
590
+ "physics_grad_norm": 0.013475186191499233,
591
+ "causal_grad_norm": 0.013471515849232674,
592
+ "physics_loss": 0.00042341966764070094,
593
+ "causal_loss": 0.0004233529034536332
594
+ },
595
+ {
596
+ "stage": "stage2",
597
+ "epoch": 60,
598
+ "cosine_similarity": 1.0,
599
+ "grad_magnitude_ratio": 0.9997036444118942,
600
+ "physics_grad_norm": 0.011002189479768276,
601
+ "causal_grad_norm": 0.010998928919434547,
602
+ "physics_loss": 0.00032947357976809144,
603
+ "causal_loss": 0.0003294190391898155
604
+ },
605
+ {
606
+ "stage": "stage2",
607
+ "epoch": 70,
608
+ "cosine_similarity": 1.0,
609
+ "grad_magnitude_ratio": 0.9996889567160482,
610
+ "physics_grad_norm": 0.005823698826134205,
611
+ "causal_grad_norm": 0.005821887403726578,
612
+ "physics_loss": 0.00022465373331215233,
613
+ "causal_loss": 0.0002246264775749296
614
+ },
615
+ {
616
+ "stage": "stage2",
617
+ "epoch": 80,
618
+ "cosine_similarity": 1.0,
619
+ "grad_magnitude_ratio": 0.9999786827475972,
620
+ "physics_grad_norm": 0.004783910233527422,
621
+ "causal_grad_norm": 0.0047838082537055016,
622
+ "physics_loss": 0.00023390715068671852,
623
+ "causal_loss": 0.00023389517446048558
624
+ },
625
+ {
626
+ "stage": "stage2",
627
+ "epoch": 90,
628
+ "cosine_similarity": 1.0,
629
+ "grad_magnitude_ratio": 0.9997226350600497,
630
+ "physics_grad_norm": 0.01960255391895771,
631
+ "causal_grad_norm": 0.019597116857767105,
632
+ "physics_loss": 0.0007215060759335756,
633
+ "causal_loss": 0.0007214088109321892
634
+ },
635
+ {
636
+ "stage": "stage2",
637
+ "epoch": 100,
638
+ "cosine_similarity": 0.9999998807907104,
639
+ "grad_magnitude_ratio": 0.9991213450495027,
640
+ "physics_grad_norm": 0.03870481252670288,
641
+ "causal_grad_norm": 0.03867080435156822,
642
+ "physics_loss": 0.0018610046245157719,
643
+ "causal_loss": 0.0018602308118715882
644
+ },
645
+ {
646
+ "stage": "stage2",
647
+ "epoch": 110,
648
+ "cosine_similarity": 0.9999998807907104,
649
+ "grad_magnitude_ratio": 0.9978435296256818,
650
+ "physics_grad_norm": 0.06168882176280022,
651
+ "causal_grad_norm": 0.06155579164624214,
652
+ "physics_loss": 0.0038336380384862423,
653
+ "causal_loss": 0.003829744178801775
654
+ },
655
+ {
656
+ "stage": "stage2",
657
+ "epoch": 120,
658
+ "cosine_similarity": 1.0,
659
+ "grad_magnitude_ratio": 0.9960124716517482,
660
+ "physics_grad_norm": 0.08493134379386902,
661
+ "causal_grad_norm": 0.08459267765283585,
662
+ "physics_loss": 0.006289852783083916,
663
+ "causal_loss": 0.00627800403162837
664
+ },
665
+ {
666
+ "stage": "stage2",
667
+ "epoch": 130,
668
+ "cosine_similarity": 1.0,
669
+ "grad_magnitude_ratio": 0.9934892121529685,
670
+ "physics_grad_norm": 0.10880536586046219,
671
+ "causal_grad_norm": 0.10809695720672607,
672
+ "physics_loss": 0.009131738916039467,
673
+ "causal_loss": 0.009103531017899513
674
+ },
675
+ {
676
+ "stage": "stage2",
677
+ "epoch": 140,
678
+ "cosine_similarity": 0.9999998211860657,
679
+ "grad_magnitude_ratio": 0.9909496024395709,
680
+ "physics_grad_norm": 0.12894947826862335,
681
+ "causal_grad_norm": 0.1277824342250824,
682
+ "physics_loss": 0.011682460084557533,
683
+ "causal_loss": 0.011632158420979977
684
+ },
685
+ {
686
+ "stage": "stage2",
687
+ "epoch": 150,
688
+ "cosine_similarity": 0.9999998807907104,
689
+ "grad_magnitude_ratio": 0.9889506182602904,
690
+ "physics_grad_norm": 0.14225943386554718,
691
+ "causal_grad_norm": 0.14068755507469177,
692
+ "physics_loss": 0.013175363652408123,
693
+ "causal_loss": 0.013105973601341248
694
+ },
695
+ {
696
+ "stage": "stage2",
697
+ "epoch": 160,
698
+ "cosine_similarity": 0.9999997615814209,
699
+ "grad_magnitude_ratio": 0.9879517938581499,
700
+ "physics_grad_norm": 0.1476992964744568,
701
+ "causal_grad_norm": 0.1459197849035263,
702
+ "physics_loss": 0.0134408138692379,
703
+ "causal_loss": 0.013363644480705261
704
+ },
705
+ {
706
+ "stage": "stage2",
707
+ "epoch": 170,
708
+ "cosine_similarity": 0.9999997019767761,
709
+ "grad_magnitude_ratio": 0.9870115872100009,
710
+ "physics_grad_norm": 0.153041809797287,
711
+ "causal_grad_norm": 0.1510540395975113,
712
+ "physics_loss": 0.013742067851126194,
713
+ "causal_loss": 0.013656970113515854
714
+ },
715
+ {
716
+ "stage": "stage2",
717
+ "epoch": 180,
718
+ "cosine_similarity": 0.9999997615814209,
719
+ "grad_magnitude_ratio": 0.9861619387463435,
720
+ "physics_grad_norm": 0.1568136215209961,
721
+ "causal_grad_norm": 0.15464362502098083,
722
+ "physics_loss": 0.01376590970903635,
723
+ "causal_loss": 0.013675066642463207
724
+ },
725
+ {
726
+ "stage": "stage2",
727
+ "epoch": 190,
728
+ "cosine_similarity": 0.9999997615814209,
729
+ "grad_magnitude_ratio": 0.9852609357460117,
730
+ "physics_grad_norm": 0.16138961911201477,
731
+ "causal_grad_norm": 0.1590108871459961,
732
+ "physics_loss": 0.013848919421434402,
733
+ "causal_loss": 0.01375141367316246
734
+ },
735
+ {
736
+ "stage": "stage2",
737
+ "epoch": 200,
738
+ "cosine_similarity": 0.9999996423721313,
739
+ "grad_magnitude_ratio": 0.9845329282120944,
740
+ "physics_grad_norm": 0.16568565368652344,
741
+ "causal_grad_norm": 0.1631229817867279,
742
+ "physics_loss": 0.01389279030263424,
743
+ "causal_loss": 0.013790265657007694
744
+ },
745
+ {
746
+ "stage": "stage2",
747
+ "epoch": 210,
748
+ "cosine_similarity": 0.9999996423721313,
749
+ "grad_magnitude_ratio": 0.9839286191286115,
750
+ "physics_grad_norm": 0.1690269559621811,
751
+ "causal_grad_norm": 0.16631045937538147,
752
+ "physics_loss": 0.01361975446343422,
753
+ "causal_loss": 0.013514954596757889
754
+ },
755
+ {
756
+ "stage": "stage2",
757
+ "epoch": 220,
758
+ "cosine_similarity": 0.9999996423721313,
759
+ "grad_magnitude_ratio": 0.9826292489881284,
760
+ "physics_grad_norm": 0.1767233908176422,
761
+ "causal_grad_norm": 0.17365357279777527,
762
+ "physics_loss": 0.014065449126064777,
763
+ "causal_loss": 0.013948477804660797
764
+ },
765
+ {
766
+ "stage": "stage2",
767
+ "epoch": 230,
768
+ "cosine_similarity": 0.9999995827674866,
769
+ "grad_magnitude_ratio": 0.9825425831521097,
770
+ "physics_grad_norm": 0.17720238864421844,
771
+ "causal_grad_norm": 0.17410889267921448,
772
+ "physics_loss": 0.013500860892236233,
773
+ "causal_loss": 0.01338779367506504
774
+ },
775
+ {
776
+ "stage": "stage2",
777
+ "epoch": 240,
778
+ "cosine_similarity": 0.9999996423721313,
779
+ "grad_magnitude_ratio": 0.982902763411873,
780
+ "physics_grad_norm": 0.1756424903869629,
781
+ "causal_grad_norm": 0.17263948917388916,
782
+ "physics_loss": 0.012757726013660431,
783
+ "causal_loss": 0.012653104029595852
784
+ },
785
+ {
786
+ "stage": "stage2",
787
+ "epoch": 250,
788
+ "cosine_similarity": 0.9999996423721313,
789
+ "grad_magnitude_ratio": 0.9836474723947813,
790
+ "physics_grad_norm": 0.17069534957408905,
791
+ "causal_grad_norm": 0.1679040491580963,
792
+ "physics_loss": 0.011561302468180656,
793
+ "causal_loss": 0.01147026289254427
794
+ },
795
+ {
796
+ "stage": "stage2",
797
+ "epoch": 260,
798
+ "cosine_similarity": 0.9999996423721313,
799
+ "grad_magnitude_ratio": 0.9835348673295707,
800
+ "physics_grad_norm": 0.17183846235275269,
801
+ "causal_grad_norm": 0.16900911927223206,
802
+ "physics_loss": 0.011226456612348557,
803
+ "causal_loss": 0.011137180030345917
804
+ },
805
+ {
806
+ "stage": "stage2",
807
+ "epoch": 270,
808
+ "cosine_similarity": 0.9999996423721313,
809
+ "grad_magnitude_ratio": 0.9837657215106906,
810
+ "physics_grad_norm": 0.171419158577919,
811
+ "causal_grad_norm": 0.168636292219162,
812
+ "physics_loss": 0.01084563322365284,
813
+ "causal_loss": 0.010760230012238026
814
+ },
815
+ {
816
+ "stage": "stage2",
817
+ "epoch": 280,
818
+ "cosine_similarity": 0.9999997615814209,
819
+ "grad_magnitude_ratio": 0.9836862876491791,
820
+ "physics_grad_norm": 0.16989029943943024,
821
+ "causal_grad_norm": 0.16711875796318054,
822
+ "physics_loss": 0.010373719036579132,
823
+ "causal_loss": 0.010291113518178463
824
+ },
825
+ {
826
+ "stage": "stage2",
827
+ "epoch": 290,
828
+ "cosine_similarity": 0.9999997019767761,
829
+ "grad_magnitude_ratio": 0.9833734678849106,
830
+ "physics_grad_norm": 0.16872206330299377,
831
+ "causal_grad_norm": 0.1659168004989624,
832
+ "physics_loss": 0.010052061639726162,
833
+ "causal_loss": 0.009969815611839294
834
+ },
835
+ {
836
+ "stage": "stage3",
837
+ "epoch": 0,
838
+ "cosine_similarity": 0.9999999403953552,
839
+ "grad_magnitude_ratio": 0.9997714307446923,
840
+ "physics_grad_norm": 0.1582890897989273,
841
+ "causal_grad_norm": 0.15825290977954865,
842
+ "physics_loss": 0.009080103598535061,
843
+ "causal_loss": 0.00907907821238041
844
+ },
845
+ {
846
+ "stage": "stage3",
847
+ "epoch": 10,
848
+ "cosine_similarity": 1.0000001192092896,
849
+ "grad_magnitude_ratio": 0.9990241415176903,
850
+ "physics_grad_norm": 0.15301863849163055,
851
+ "causal_grad_norm": 0.152869313955307,
852
+ "physics_loss": 0.009140199981629848,
853
+ "causal_loss": 0.009135782718658447
854
+ },
855
+ {
856
+ "stage": "stage3",
857
+ "epoch": 20,
858
+ "cosine_similarity": 1.0,
859
+ "grad_magnitude_ratio": 0.9981685718904909,
860
+ "physics_grad_norm": 0.15733282268047333,
861
+ "causal_grad_norm": 0.1570446789264679,
862
+ "physics_loss": 0.009180361405014992,
863
+ "causal_loss": 0.0091720474883914
864
+ },
865
+ {
866
+ "stage": "stage3",
867
+ "epoch": 30,
868
+ "cosine_similarity": 1.0000001192092896,
869
+ "grad_magnitude_ratio": 0.997505767266452,
870
+ "physics_grad_norm": 0.154081791639328,
871
+ "causal_grad_norm": 0.15369747579097748,
872
+ "physics_loss": 0.008927350863814354,
873
+ "causal_loss": 0.008916286751627922
874
+ },
875
+ {
876
+ "stage": "stage3",
877
+ "epoch": 40,
878
+ "cosine_similarity": 0.9999998807907104,
879
+ "grad_magnitude_ratio": 0.9967648911095572,
880
+ "physics_grad_norm": 0.15446019172668457,
881
+ "causal_grad_norm": 0.15396049618721008,
882
+ "physics_loss": 0.00902617909014225,
883
+ "causal_loss": 0.009011521935462952
884
+ },
885
+ {
886
+ "stage": "stage3",
887
+ "epoch": 50,
888
+ "cosine_similarity": 1.0,
889
+ "grad_magnitude_ratio": 0.9962274920556033,
890
+ "physics_grad_norm": 0.1473957747220993,
891
+ "causal_grad_norm": 0.14683972299098969,
892
+ "physics_loss": 0.008508026599884033,
893
+ "causal_loss": 0.008492054417729378
894
+ },
895
+ {
896
+ "stage": "stage3",
897
+ "epoch": 60,
898
+ "cosine_similarity": 1.0,
899
+ "grad_magnitude_ratio": 0.9950659283345845,
900
+ "physics_grad_norm": 0.15708205103874207,
901
+ "causal_grad_norm": 0.15630699694156647,
902
+ "physics_loss": 0.009157667867839336,
903
+ "causal_loss": 0.009135149419307709
904
+ },
905
+ {
906
+ "stage": "stage3",
907
+ "epoch": 70,
908
+ "cosine_similarity": 0.9999999403953552,
909
+ "grad_magnitude_ratio": 0.9945406319123118,
910
+ "physics_grad_norm": 0.15222233533859253,
911
+ "causal_grad_norm": 0.15139129757881165,
912
+ "physics_loss": 0.008964071981608868,
913
+ "causal_loss": 0.008939478546380997
914
+ },
915
+ {
916
+ "stage": "stage3",
917
+ "epoch": 80,
918
+ "cosine_similarity": 0.9999998807907104,
919
+ "grad_magnitude_ratio": 0.9938133934639659,
920
+ "physics_grad_norm": 0.14937515556812286,
921
+ "causal_grad_norm": 0.148451030254364,
922
+ "physics_loss": 0.008734101429581642,
923
+ "causal_loss": 0.008707092143595219
924
+ },
925
+ {
926
+ "stage": "stage3",
927
+ "epoch": 90,
928
+ "cosine_similarity": 0.9999999403953552,
929
+ "grad_magnitude_ratio": 0.9933483535758965,
930
+ "physics_grad_norm": 0.14573536813259125,
931
+ "causal_grad_norm": 0.14476598799228668,
932
+ "physics_loss": 0.008640279993414879,
933
+ "causal_loss": 0.008611132390797138
934
+ },
935
+ {
936
+ "stage": "stage3",
937
+ "epoch": 100,
938
+ "cosine_similarity": 0.9999998807907104,
939
+ "grad_magnitude_ratio": 0.9924725775225761,
940
+ "physics_grad_norm": 0.14681778848171234,
941
+ "causal_grad_norm": 0.14571262896060944,
942
+ "physics_loss": 0.008504576049745083,
943
+ "causal_loss": 0.008472257293760777
944
+ },
945
+ {
946
+ "stage": "stage3",
947
+ "epoch": 110,
948
+ "cosine_similarity": 0.9999999403953552,
949
+ "grad_magnitude_ratio": 0.9918229763450171,
950
+ "physics_grad_norm": 0.14772097766399384,
951
+ "causal_grad_norm": 0.14651305973529816,
952
+ "physics_loss": 0.008644085377454758,
953
+ "causal_loss": 0.008608398959040642
954
+ },
955
+ {
956
+ "stage": "stage3",
957
+ "epoch": 120,
958
+ "cosine_similarity": 0.9999998807907104,
959
+ "grad_magnitude_ratio": 0.9914868935445922,
960
+ "physics_grad_norm": 0.14443425834178925,
961
+ "causal_grad_norm": 0.1432046741247177,
962
+ "physics_loss": 0.00838481541723013,
963
+ "causal_loss": 0.008348679170012474
964
+ },
965
+ {
966
+ "stage": "stage3",
967
+ "epoch": 130,
968
+ "cosine_similarity": 0.9999998211860657,
969
+ "grad_magnitude_ratio": 0.9905924845195724,
970
+ "physics_grad_norm": 0.14431491494178772,
971
+ "causal_grad_norm": 0.14295727014541626,
972
+ "physics_loss": 0.008324045687913895,
973
+ "causal_loss": 0.008284557610750198
974
+ },
975
+ {
976
+ "stage": "stage3",
977
+ "epoch": 140,
978
+ "cosine_similarity": 0.9999998807907104,
979
+ "grad_magnitude_ratio": 0.9899381770982862,
980
+ "physics_grad_norm": 0.14195449650287628,
981
+ "causal_grad_norm": 0.1405261754989624,
982
+ "physics_loss": 0.008363154716789722,
983
+ "causal_loss": 0.00832019280642271
984
+ },
985
+ {
986
+ "stage": "stage3",
987
+ "epoch": 150,
988
+ "cosine_similarity": 0.9999998211860657,
989
+ "grad_magnitude_ratio": 0.9888867814861269,
990
+ "physics_grad_norm": 0.1461312174797058,
991
+ "causal_grad_norm": 0.14450722932815552,
992
+ "physics_loss": 0.008684198372066021,
993
+ "causal_loss": 0.008635187521576881
994
+ },
995
+ {
996
+ "stage": "stage3",
997
+ "epoch": 160,
998
+ "cosine_similarity": 0.9999998211860657,
999
+ "grad_magnitude_ratio": 0.9880044537834135,
1000
+ "physics_grad_norm": 0.14756011962890625,
1001
+ "causal_grad_norm": 0.14579005539417267,
1002
+ "physics_loss": 0.008742680773139,
1003
+ "causal_loss": 0.008690222166478634
1004
+ },
1005
+ {
1006
+ "stage": "stage3",
1007
+ "epoch": 170,
1008
+ "cosine_similarity": 0.9999997615814209,
1009
+ "grad_magnitude_ratio": 0.9876508988721416,
1010
+ "physics_grad_norm": 0.1449306756258011,
1011
+ "causal_grad_norm": 0.14314091205596924,
1012
+ "physics_loss": 0.008542116731405258,
1013
+ "causal_loss": 0.008488398976624012
1014
+ },
1015
+ {
1016
+ "stage": "stage3",
1017
+ "epoch": 180,
1018
+ "cosine_similarity": 0.9999998211860657,
1019
+ "grad_magnitude_ratio": 0.9867379552661963,
1020
+ "physics_grad_norm": 0.1436425745487213,
1021
+ "causal_grad_norm": 0.14173758029937744,
1022
+ "physics_loss": 0.00850664358586073,
1023
+ "causal_loss": 0.008449172601103783
1024
+ },
1025
+ {
1026
+ "stage": "stage3",
1027
+ "epoch": 190,
1028
+ "cosine_similarity": 0.9999996423721313,
1029
+ "grad_magnitude_ratio": 0.9859424413077561,
1030
+ "physics_grad_norm": 0.14140011370182037,
1031
+ "causal_grad_norm": 0.13941237330436707,
1032
+ "physics_loss": 0.008413869887590408,
1033
+ "causal_loss": 0.00835377536714077
1034
+ }
1035
+ ],
1036
+ "wall_time_s": 83.86
1037
+ }
1038
+ }
1039
+ }
results/paper_c/gradient_flow_kdv1d/fig_gradient_alignment.pdf ADDED
Binary file (19.1 kB). View file
 
results/paper_c/gradient_flow_kdv1d/gradient_flow_results.json ADDED
@@ -0,0 +1,1039 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "experiment": "gradient_flow_analysis",
3
+ "pde": "kdv1d",
4
+ "seed": 42,
5
+ "device": "cuda",
6
+ "hyperparameters": {
7
+ "stage1_epochs": 200,
8
+ "stage2_epochs": 300,
9
+ "stage3_epochs": 200,
10
+ "stage1_lr": 0.001,
11
+ "stage2_lr": 0.0001,
12
+ "stage3_lr": 1e-05,
13
+ "causal_epsilon": 1.0,
14
+ "num_collocation": 2000,
15
+ "num_boundary": 200,
16
+ "batch_size": 256,
17
+ "hidden_dims": [
18
+ 64,
19
+ 64,
20
+ 64,
21
+ 64
22
+ ],
23
+ "probe_every": 10
24
+ },
25
+ "conditions": {
26
+ "with_pretrain": {
27
+ "condition": "with_pretrain",
28
+ "probes": [
29
+ {
30
+ "stage": "stage2",
31
+ "epoch": 0,
32
+ "cosine_similarity": 1.0,
33
+ "grad_magnitude_ratio": 0.9999592168012155,
34
+ "physics_grad_norm": 0.11819881200790405,
35
+ "causal_grad_norm": 0.11819399148225784,
36
+ "physics_loss": 0.002024286426603794,
37
+ "causal_loss": 0.0020242284517735243
38
+ },
39
+ {
40
+ "stage": "stage2",
41
+ "epoch": 10,
42
+ "cosine_similarity": 1.0,
43
+ "grad_magnitude_ratio": 0.9997688521566171,
44
+ "physics_grad_norm": 0.20970767736434937,
45
+ "causal_grad_norm": 0.20965920388698578,
46
+ "physics_loss": 0.0024616208393126726,
47
+ "causal_loss": 0.0024613323621451855
48
+ },
49
+ {
50
+ "stage": "stage2",
51
+ "epoch": 20,
52
+ "cosine_similarity": 0.9999998807907104,
53
+ "grad_magnitude_ratio": 0.9995085050934766,
54
+ "physics_grad_norm": 0.13688594102859497,
55
+ "causal_grad_norm": 0.13681866228580475,
56
+ "physics_loss": 0.0025930970441550016,
57
+ "causal_loss": 0.0025925354566425085
58
+ },
59
+ {
60
+ "stage": "stage2",
61
+ "epoch": 30,
62
+ "cosine_similarity": 0.9999999403953552,
63
+ "grad_magnitude_ratio": 0.9992774640437077,
64
+ "physics_grad_norm": 0.12082229554653168,
65
+ "causal_grad_norm": 0.12073499709367752,
66
+ "physics_loss": 0.002552424557507038,
67
+ "causal_loss": 0.002551636192947626
68
+ },
69
+ {
70
+ "stage": "stage2",
71
+ "epoch": 40,
72
+ "cosine_similarity": 0.9999999403953552,
73
+ "grad_magnitude_ratio": 0.9992165391770294,
74
+ "physics_grad_norm": 0.11769367754459381,
75
+ "causal_grad_norm": 0.11760146915912628,
76
+ "physics_loss": 0.002533592749387026,
77
+ "causal_loss": 0.002532667014747858
78
+ },
79
+ {
80
+ "stage": "stage2",
81
+ "epoch": 50,
82
+ "cosine_similarity": 0.9999998807907104,
83
+ "grad_magnitude_ratio": 0.9991560880601795,
84
+ "physics_grad_norm": 0.06583504378795624,
85
+ "causal_grad_norm": 0.06577948480844498,
86
+ "physics_loss": 0.002193423919379711,
87
+ "causal_loss": 0.0021925480104982853
88
+ },
89
+ {
90
+ "stage": "stage2",
91
+ "epoch": 60,
92
+ "cosine_similarity": 0.9999999403953552,
93
+ "grad_magnitude_ratio": 0.998997859543723,
94
+ "physics_grad_norm": 0.06488977372646332,
95
+ "causal_grad_norm": 0.06482474505901337,
96
+ "physics_loss": 0.002100002020597458,
97
+ "causal_loss": 0.0020990418270230293
98
+ },
99
+ {
100
+ "stage": "stage2",
101
+ "epoch": 70,
102
+ "cosine_similarity": 1.0,
103
+ "grad_magnitude_ratio": 0.998853546225293,
104
+ "physics_grad_norm": 0.06999213993549347,
105
+ "causal_grad_norm": 0.0699118971824646,
106
+ "physics_loss": 0.0019214375643059611,
107
+ "causal_loss": 0.001920417184010148
108
+ },
109
+ {
110
+ "stage": "stage2",
111
+ "epoch": 80,
112
+ "cosine_similarity": 1.0,
113
+ "grad_magnitude_ratio": 0.9989756911149992,
114
+ "physics_grad_norm": 0.05204014107584953,
115
+ "causal_grad_norm": 0.05198683589696884,
116
+ "physics_loss": 0.0016818580916151404,
117
+ "causal_loss": 0.001681031077168882
118
+ },
119
+ {
120
+ "stage": "stage2",
121
+ "epoch": 90,
122
+ "cosine_similarity": 0.9999998807907104,
123
+ "grad_magnitude_ratio": 0.9988801432913772,
124
+ "physics_grad_norm": 0.05452926084399223,
125
+ "causal_grad_norm": 0.054468195885419846,
126
+ "physics_loss": 0.001546658342704177,
127
+ "causal_loss": 0.0015458432026207447
128
+ },
129
+ {
130
+ "stage": "stage2",
131
+ "epoch": 100,
132
+ "cosine_similarity": 0.9999998211860657,
133
+ "grad_magnitude_ratio": 0.9986245511406237,
134
+ "physics_grad_norm": 0.05004885420203209,
135
+ "causal_grad_norm": 0.04998001456260681,
136
+ "physics_loss": 0.0013552362797781825,
137
+ "causal_loss": 0.0013545422116294503
138
+ },
139
+ {
140
+ "stage": "stage2",
141
+ "epoch": 110,
142
+ "cosine_similarity": 0.9999998807907104,
143
+ "grad_magnitude_ratio": 0.9988848662173261,
144
+ "physics_grad_norm": 0.04631500318646431,
145
+ "causal_grad_norm": 0.046263355761766434,
146
+ "physics_loss": 0.001136549049988389,
147
+ "causal_loss": 0.0011360046919435263
148
+ },
149
+ {
150
+ "stage": "stage2",
151
+ "epoch": 120,
152
+ "cosine_similarity": 0.9999998807907104,
153
+ "grad_magnitude_ratio": 0.9989608344120292,
154
+ "physics_grad_norm": 0.04016147926449776,
155
+ "causal_grad_norm": 0.04011974483728409,
156
+ "physics_loss": 0.0009449823410250247,
157
+ "causal_loss": 0.0009445770410820842
158
+ },
159
+ {
160
+ "stage": "stage2",
161
+ "epoch": 130,
162
+ "cosine_similarity": 0.9999999403953552,
163
+ "grad_magnitude_ratio": 0.9990681758795786,
164
+ "physics_grad_norm": 0.03266241028904915,
165
+ "causal_grad_norm": 0.032631974667310715,
166
+ "physics_loss": 0.0008698305464349687,
167
+ "causal_loss": 0.0008694697171449661
168
+ },
169
+ {
170
+ "stage": "stage2",
171
+ "epoch": 140,
172
+ "cosine_similarity": 0.9999998807907104,
173
+ "grad_magnitude_ratio": 0.9991936159035145,
174
+ "physics_grad_norm": 0.03154825046658516,
175
+ "causal_grad_norm": 0.03152281045913696,
176
+ "physics_loss": 0.0007923531229607761,
177
+ "causal_loss": 0.0007920302450656891
178
+ },
179
+ {
180
+ "stage": "stage2",
181
+ "epoch": 150,
182
+ "cosine_similarity": 0.9999998807907104,
183
+ "grad_magnitude_ratio": 0.9991718468663399,
184
+ "physics_grad_norm": 0.026342108845710754,
185
+ "causal_grad_norm": 0.02632029354572296,
186
+ "physics_loss": 0.0006486708298325539,
187
+ "causal_loss": 0.0006484432378783822
188
+ },
189
+ {
190
+ "stage": "stage2",
191
+ "epoch": 160,
192
+ "cosine_similarity": 0.9999998807907104,
193
+ "grad_magnitude_ratio": 0.9993166946596317,
194
+ "physics_grad_norm": 0.028960321098566055,
195
+ "causal_grad_norm": 0.028940532356500626,
196
+ "physics_loss": 0.0005571252549998462,
197
+ "causal_loss": 0.0005569419590756297
198
+ },
199
+ {
200
+ "stage": "stage2",
201
+ "epoch": 170,
202
+ "cosine_similarity": 0.9999998807907104,
203
+ "grad_magnitude_ratio": 0.9993261672468411,
204
+ "physics_grad_norm": 0.02568821609020233,
205
+ "causal_grad_norm": 0.025670906528830528,
206
+ "physics_loss": 0.0004951822920702398,
207
+ "causal_loss": 0.0004950151778757572
208
+ },
209
+ {
210
+ "stage": "stage2",
211
+ "epoch": 180,
212
+ "cosine_similarity": 0.9999998211860657,
213
+ "grad_magnitude_ratio": 0.9990766083112973,
214
+ "physics_grad_norm": 0.021712901070713997,
215
+ "causal_grad_norm": 0.021692851558327675,
216
+ "physics_loss": 0.00044343573972582817,
217
+ "causal_loss": 0.0004432957503013313
218
+ },
219
+ {
220
+ "stage": "stage2",
221
+ "epoch": 190,
222
+ "cosine_similarity": 1.0,
223
+ "grad_magnitude_ratio": 0.999390717636822,
224
+ "physics_grad_norm": 0.029177088290452957,
225
+ "causal_grad_norm": 0.029159311205148697,
226
+ "physics_loss": 0.00037398963468149304,
227
+ "causal_loss": 0.0003738825616892427
228
+ },
229
+ {
230
+ "stage": "stage2",
231
+ "epoch": 200,
232
+ "cosine_similarity": 0.9999998807907104,
233
+ "grad_magnitude_ratio": 0.9994437351198495,
234
+ "physics_grad_norm": 0.02150062844157219,
235
+ "causal_grad_norm": 0.021488668397068977,
236
+ "physics_loss": 0.00035980853135697544,
237
+ "causal_loss": 0.0003597069007810205
238
+ },
239
+ {
240
+ "stage": "stage2",
241
+ "epoch": 210,
242
+ "cosine_similarity": 0.9999998807907104,
243
+ "grad_magnitude_ratio": 0.9992817934052436,
244
+ "physics_grad_norm": 0.02426188439130783,
245
+ "causal_grad_norm": 0.024244459345936775,
246
+ "physics_loss": 0.00032361637568101287,
247
+ "causal_loss": 0.00032353063579648733
248
+ },
249
+ {
250
+ "stage": "stage2",
251
+ "epoch": 220,
252
+ "cosine_similarity": 1.0,
253
+ "grad_magnitude_ratio": 0.9993424497884299,
254
+ "physics_grad_norm": 0.031862255185842514,
255
+ "causal_grad_norm": 0.031841304153203964,
256
+ "physics_loss": 0.00030714261811226606,
257
+ "causal_loss": 0.0003070640086662024
258
+ },
259
+ {
260
+ "stage": "stage2",
261
+ "epoch": 230,
262
+ "cosine_similarity": 0.9999997615814209,
263
+ "grad_magnitude_ratio": 0.9989795584937425,
264
+ "physics_grad_norm": 0.016929959878325462,
265
+ "causal_grad_norm": 0.016912683844566345,
266
+ "physics_loss": 0.0003096368454862386,
267
+ "causal_loss": 0.00030954982503317297
268
+ },
269
+ {
270
+ "stage": "stage2",
271
+ "epoch": 240,
272
+ "cosine_similarity": 0.9999995827674866,
273
+ "grad_magnitude_ratio": 0.9992118881556796,
274
+ "physics_grad_norm": 0.011689512059092522,
275
+ "causal_grad_norm": 0.011680299416184425,
276
+ "physics_loss": 0.0002884274290408939,
277
+ "causal_loss": 0.0002883506822399795
278
+ },
279
+ {
280
+ "stage": "stage2",
281
+ "epoch": 250,
282
+ "cosine_similarity": 0.9999998211860657,
283
+ "grad_magnitude_ratio": 0.9991881717473673,
284
+ "physics_grad_norm": 0.021034905686974525,
285
+ "causal_grad_norm": 0.021017828956246376,
286
+ "physics_loss": 0.0002795044856611639,
287
+ "causal_loss": 0.00027942360611632466
288
+ },
289
+ {
290
+ "stage": "stage2",
291
+ "epoch": 260,
292
+ "cosine_similarity": 0.9999999403953552,
293
+ "grad_magnitude_ratio": 0.9991265486136407,
294
+ "physics_grad_norm": 0.020924203097820282,
295
+ "causal_grad_norm": 0.020905926823616028,
296
+ "physics_loss": 0.0002549265045672655,
297
+ "causal_loss": 0.0002548538031987846
298
+ },
299
+ {
300
+ "stage": "stage2",
301
+ "epoch": 270,
302
+ "cosine_similarity": 0.9999997615814209,
303
+ "grad_magnitude_ratio": 0.9991854872333331,
304
+ "physics_grad_norm": 0.014099396765232086,
305
+ "causal_grad_norm": 0.014087912626564503,
306
+ "physics_loss": 0.00024897654657252133,
307
+ "causal_loss": 0.0002489082107786089
308
+ },
309
+ {
310
+ "stage": "stage2",
311
+ "epoch": 280,
312
+ "cosine_similarity": 0.9999997019767761,
313
+ "grad_magnitude_ratio": 0.999134464348898,
314
+ "physics_grad_norm": 0.011154966428875923,
315
+ "causal_grad_norm": 0.011145311407744884,
316
+ "physics_loss": 0.00022054863802623004,
317
+ "causal_loss": 0.00022049368999432772
318
+ },
319
+ {
320
+ "stage": "stage2",
321
+ "epoch": 290,
322
+ "cosine_similarity": 0.9999998807907104,
323
+ "grad_magnitude_ratio": 0.9991663185871762,
324
+ "physics_grad_norm": 0.01525539718568325,
325
+ "causal_grad_norm": 0.015242679044604301,
326
+ "physics_loss": 0.00022069187252782285,
327
+ "causal_loss": 0.0002206366480095312
328
+ },
329
+ {
330
+ "stage": "stage3",
331
+ "epoch": 0,
332
+ "cosine_similarity": 0.9999999403953552,
333
+ "grad_magnitude_ratio": 0.9999799169344817,
334
+ "physics_grad_norm": 0.013309202156960964,
335
+ "causal_grad_norm": 0.01330893486738205,
336
+ "physics_loss": 0.0002213681727880612,
337
+ "causal_loss": 0.00022136713960208
338
+ },
339
+ {
340
+ "stage": "stage3",
341
+ "epoch": 10,
342
+ "cosine_similarity": 1.0,
343
+ "grad_magnitude_ratio": 0.9999467388520843,
344
+ "physics_grad_norm": 0.02605408802628517,
345
+ "causal_grad_norm": 0.026052700355648994,
346
+ "physics_loss": 0.00023315814905799925,
347
+ "causal_loss": 0.00023315382713917643
348
+ },
349
+ {
350
+ "stage": "stage3",
351
+ "epoch": 20,
352
+ "cosine_similarity": 1.0,
353
+ "grad_magnitude_ratio": 0.9999037646313063,
354
+ "physics_grad_norm": 0.01140983123332262,
355
+ "causal_grad_norm": 0.011408733204007149,
356
+ "physics_loss": 0.0002161241282010451,
357
+ "causal_loss": 0.0002161180746043101
358
+ },
359
+ {
360
+ "stage": "stage3",
361
+ "epoch": 30,
362
+ "cosine_similarity": 1.0,
363
+ "grad_magnitude_ratio": 0.9998828757563715,
364
+ "physics_grad_norm": 0.011792190372943878,
365
+ "causal_grad_norm": 0.011790809221565723,
366
+ "physics_loss": 0.00021280757209751755,
367
+ "causal_loss": 0.00021279843349475414
368
+ },
369
+ {
370
+ "stage": "stage3",
371
+ "epoch": 40,
372
+ "cosine_similarity": 1.0,
373
+ "grad_magnitude_ratio": 0.9997465618114373,
374
+ "physics_grad_norm": 0.01996125467121601,
375
+ "causal_grad_norm": 0.0199561957269907,
376
+ "physics_loss": 0.0002246476215077564,
377
+ "causal_loss": 0.00022463251661974937
378
+ },
379
+ {
380
+ "stage": "stage3",
381
+ "epoch": 50,
382
+ "cosine_similarity": 1.0,
383
+ "grad_magnitude_ratio": 0.9997893496794243,
384
+ "physics_grad_norm": 0.01726912148296833,
385
+ "causal_grad_norm": 0.017265483736991882,
386
+ "physics_loss": 0.0002204008196713403,
387
+ "causal_loss": 0.0002203843032475561
388
+ },
389
+ {
390
+ "stage": "stage3",
391
+ "epoch": 60,
392
+ "cosine_similarity": 1.0,
393
+ "grad_magnitude_ratio": 0.99975731052979,
394
+ "physics_grad_norm": 0.0070015317760407925,
395
+ "causal_grad_norm": 0.0069998325780034065,
396
+ "physics_loss": 0.00019787038036156446,
397
+ "causal_loss": 0.00019785754557233304
398
+ },
399
+ {
400
+ "stage": "stage3",
401
+ "epoch": 70,
402
+ "cosine_similarity": 0.9999999403953552,
403
+ "grad_magnitude_ratio": 0.9998428791224305,
404
+ "physics_grad_norm": 0.01349675189703703,
405
+ "causal_grad_norm": 0.01349463127553463,
406
+ "physics_loss": 0.00019742622680496424,
407
+ "causal_loss": 0.00019741056894417852
408
+ },
409
+ {
410
+ "stage": "stage3",
411
+ "epoch": 80,
412
+ "cosine_similarity": 0.9999997615814209,
413
+ "grad_magnitude_ratio": 0.999750763346381,
414
+ "physics_grad_norm": 0.008859715424478054,
415
+ "causal_grad_norm": 0.00885750725865364,
416
+ "physics_loss": 0.00021947571076452732,
417
+ "causal_loss": 0.00021945314074400812
418
+ },
419
+ {
420
+ "stage": "stage3",
421
+ "epoch": 90,
422
+ "cosine_similarity": 0.9999999403953552,
423
+ "grad_magnitude_ratio": 0.9996678059741,
424
+ "physics_grad_norm": 0.015301776118576527,
425
+ "causal_grad_norm": 0.015296692959964275,
426
+ "physics_loss": 0.0002109828346874565,
427
+ "causal_loss": 0.0002109594497596845
428
+ },
429
+ {
430
+ "stage": "stage3",
431
+ "epoch": 100,
432
+ "cosine_similarity": 0.9999998807907104,
433
+ "grad_magnitude_ratio": 0.9995499057617422,
434
+ "physics_grad_norm": 0.006516858469694853,
435
+ "causal_grad_norm": 0.006513925269246101,
436
+ "physics_loss": 0.00019689950568135828,
437
+ "causal_loss": 0.0001968774595297873
438
+ },
439
+ {
440
+ "stage": "stage3",
441
+ "epoch": 110,
442
+ "cosine_similarity": 0.9999998807907104,
443
+ "grad_magnitude_ratio": 0.9995662848582001,
444
+ "physics_grad_norm": 0.012806580401957035,
445
+ "causal_grad_norm": 0.012801025994122028,
446
+ "physics_loss": 0.00021183936041779816,
447
+ "causal_loss": 0.00021180666226428002
448
+ },
449
+ {
450
+ "stage": "stage3",
451
+ "epoch": 120,
452
+ "cosine_similarity": 0.9999999403953552,
453
+ "grad_magnitude_ratio": 0.999824339159814,
454
+ "physics_grad_norm": 0.017241526395082474,
455
+ "causal_grad_norm": 0.017238497734069824,
456
+ "physics_loss": 0.00020098530512768775,
457
+ "causal_loss": 0.00020095625950489193
458
+ },
459
+ {
460
+ "stage": "stage3",
461
+ "epoch": 130,
462
+ "cosine_similarity": 0.9999998807907104,
463
+ "grad_magnitude_ratio": 0.999488405462993,
464
+ "physics_grad_norm": 0.015852313488721848,
465
+ "causal_grad_norm": 0.015844203531742096,
466
+ "physics_loss": 0.00020262245379853994,
467
+ "causal_loss": 0.00020258838776499033
468
+ },
469
+ {
470
+ "stage": "stage3",
471
+ "epoch": 140,
472
+ "cosine_similarity": 1.0,
473
+ "grad_magnitude_ratio": 0.999809362677798,
474
+ "physics_grad_norm": 0.010073510929942131,
475
+ "causal_grad_norm": 0.010071590542793274,
476
+ "physics_loss": 0.0001745590998325497,
477
+ "causal_loss": 0.00017453500186093152
478
+ },
479
+ {
480
+ "stage": "stage3",
481
+ "epoch": 150,
482
+ "cosine_similarity": 1.0,
483
+ "grad_magnitude_ratio": 0.9995219089988671,
484
+ "physics_grad_norm": 0.02869408018887043,
485
+ "causal_grad_norm": 0.028680361807346344,
486
+ "physics_loss": 0.00019484524091240019,
487
+ "causal_loss": 0.0001948086137417704
488
+ },
489
+ {
490
+ "stage": "stage3",
491
+ "epoch": 160,
492
+ "cosine_similarity": 0.9999996423721313,
493
+ "grad_magnitude_ratio": 0.9999732518617795,
494
+ "physics_grad_norm": 0.00853046402335167,
495
+ "causal_grad_norm": 0.008530235849320889,
496
+ "physics_loss": 0.000177969312062487,
497
+ "causal_loss": 0.00017793962615542114
498
+ },
499
+ {
500
+ "stage": "stage3",
501
+ "epoch": 170,
502
+ "cosine_similarity": 0.9999998807907104,
503
+ "grad_magnitude_ratio": 0.9993789376819278,
504
+ "physics_grad_norm": 0.016618166118860245,
505
+ "causal_grad_norm": 0.016607845202088356,
506
+ "physics_loss": 0.00018510379595682025,
507
+ "causal_loss": 0.00018506818742025644
508
+ },
509
+ {
510
+ "stage": "stage3",
511
+ "epoch": 180,
512
+ "cosine_similarity": 0.9999996423721313,
513
+ "grad_magnitude_ratio": 0.9994314728305904,
514
+ "physics_grad_norm": 0.00898351613432169,
515
+ "causal_grad_norm": 0.008978408761322498,
516
+ "physics_loss": 0.0001801902981242165,
517
+ "causal_loss": 0.00018015565001405776
518
+ },
519
+ {
520
+ "stage": "stage3",
521
+ "epoch": 190,
522
+ "cosine_similarity": 0.9999998807907104,
523
+ "grad_magnitude_ratio": 0.9989517103950173,
524
+ "physics_grad_norm": 0.012357048690319061,
525
+ "causal_grad_norm": 0.012344094924628735,
526
+ "physics_loss": 0.0001838373573264107,
527
+ "causal_loss": 0.00018379546236246824
528
+ }
529
+ ],
530
+ "wall_time_s": 89.27
531
+ },
532
+ "without_pretrain": {
533
+ "condition": "without_pretrain",
534
+ "probes": [
535
+ {
536
+ "stage": "stage2",
537
+ "epoch": 0,
538
+ "cosine_similarity": 1.0,
539
+ "grad_magnitude_ratio": 0.9999977841682366,
540
+ "physics_grad_norm": 0.008406076580286026,
541
+ "causal_grad_norm": 0.008406057953834534,
542
+ "physics_loss": 6.629204290220514e-05,
543
+ "causal_loss": 6.629197741858661e-05
544
+ },
545
+ {
546
+ "stage": "stage2",
547
+ "epoch": 10,
548
+ "cosine_similarity": 0.9999999403953552,
549
+ "grad_magnitude_ratio": 0.999971694533383,
550
+ "physics_grad_norm": 0.039877913892269135,
551
+ "causal_grad_norm": 0.0398767851293087,
552
+ "physics_loss": 0.00030635649454779923,
553
+ "causal_loss": 0.0003063521580770612
554
+ },
555
+ {
556
+ "stage": "stage2",
557
+ "epoch": 20,
558
+ "cosine_similarity": 1.0,
559
+ "grad_magnitude_ratio": 0.9999197455261096,
560
+ "physics_grad_norm": 0.04711475223302841,
561
+ "causal_grad_norm": 0.04711097106337547,
562
+ "physics_loss": 0.0004883746150881052,
563
+ "causal_loss": 0.000488354591652751
564
+ },
565
+ {
566
+ "stage": "stage2",
567
+ "epoch": 30,
568
+ "cosine_similarity": 0.9999999403953552,
569
+ "grad_magnitude_ratio": 0.9999220034662666,
570
+ "physics_grad_norm": 0.03701574727892876,
571
+ "causal_grad_norm": 0.03701286017894745,
572
+ "physics_loss": 0.0003136149316560477,
573
+ "causal_loss": 0.00031360203865915537
574
+ },
575
+ {
576
+ "stage": "stage2",
577
+ "epoch": 40,
578
+ "cosine_similarity": 1.0,
579
+ "grad_magnitude_ratio": 0.9999365774930856,
580
+ "physics_grad_norm": 0.018590472638607025,
581
+ "causal_grad_norm": 0.018589293584227562,
582
+ "physics_loss": 0.00018458197882864624,
583
+ "causal_loss": 0.00018457576516084373
584
+ },
585
+ {
586
+ "stage": "stage2",
587
+ "epoch": 50,
588
+ "cosine_similarity": 1.0,
589
+ "grad_magnitude_ratio": 0.9999012205592943,
590
+ "physics_grad_norm": 0.011398819275200367,
591
+ "causal_grad_norm": 0.011397693306207657,
592
+ "physics_loss": 0.00023562512069474906,
593
+ "causal_loss": 0.00023561320267617702
594
+ },
595
+ {
596
+ "stage": "stage2",
597
+ "epoch": 60,
598
+ "cosine_similarity": 1.0,
599
+ "grad_magnitude_ratio": 0.999829440206264,
600
+ "physics_grad_norm": 0.02349058724939823,
601
+ "causal_grad_norm": 0.023486580699682236,
602
+ "physics_loss": 0.0004235631204210222,
603
+ "causal_loss": 0.00042352185118943453
604
+ },
605
+ {
606
+ "stage": "stage2",
607
+ "epoch": 70,
608
+ "cosine_similarity": 1.0,
609
+ "grad_magnitude_ratio": 0.9995712395350586,
610
+ "physics_grad_norm": 0.057934995740652084,
611
+ "causal_grad_norm": 0.05791015550494194,
612
+ "physics_loss": 0.0009275780175812542,
613
+ "causal_loss": 0.000927366316318512
614
+ },
615
+ {
616
+ "stage": "stage2",
617
+ "epoch": 80,
618
+ "cosine_similarity": 0.9999998807907104,
619
+ "grad_magnitude_ratio": 0.9991961648488358,
620
+ "physics_grad_norm": 0.08636660128831863,
621
+ "causal_grad_norm": 0.0862971767783165,
622
+ "physics_loss": 0.0015279916115105152,
623
+ "causal_loss": 0.0015273542376235127
624
+ },
625
+ {
626
+ "stage": "stage2",
627
+ "epoch": 90,
628
+ "cosine_similarity": 1.0,
629
+ "grad_magnitude_ratio": 0.998476583561125,
630
+ "physics_grad_norm": 0.13368253409862518,
631
+ "causal_grad_norm": 0.13347887992858887,
632
+ "physics_loss": 0.0026282984763383865,
633
+ "causal_loss": 0.0026262393221259117
634
+ },
635
+ {
636
+ "stage": "stage2",
637
+ "epoch": 100,
638
+ "cosine_similarity": 0.9999999403953552,
639
+ "grad_magnitude_ratio": 0.9975018585186783,
640
+ "physics_grad_norm": 0.15901227295398712,
641
+ "causal_grad_norm": 0.15861503779888153,
642
+ "physics_loss": 0.0036369378212839365,
643
+ "causal_loss": 0.003632216714322567
644
+ },
645
+ {
646
+ "stage": "stage2",
647
+ "epoch": 110,
648
+ "cosine_similarity": 0.9999999403953552,
649
+ "grad_magnitude_ratio": 0.9964932319871611,
650
+ "physics_grad_norm": 0.18089090287685394,
651
+ "causal_grad_norm": 0.18025656044483185,
652
+ "physics_loss": 0.004737340845167637,
653
+ "causal_loss": 0.0047288197092711926
654
+ },
655
+ {
656
+ "stage": "stage2",
657
+ "epoch": 120,
658
+ "cosine_similarity": 1.0,
659
+ "grad_magnitude_ratio": 0.9951767391598021,
660
+ "physics_grad_norm": 0.20285244286060333,
661
+ "causal_grad_norm": 0.2018740326166153,
662
+ "physics_loss": 0.006069636438041925,
663
+ "causal_loss": 0.0060547287575900555
664
+ },
665
+ {
666
+ "stage": "stage2",
667
+ "epoch": 130,
668
+ "cosine_similarity": 0.9999998807907104,
669
+ "grad_magnitude_ratio": 0.9934326001230106,
670
+ "physics_grad_norm": 0.21736854314804077,
671
+ "causal_grad_norm": 0.21594099700450897,
672
+ "physics_loss": 0.007210241165012121,
673
+ "causal_loss": 0.007186318747699261
674
+ },
675
+ {
676
+ "stage": "stage2",
677
+ "epoch": 140,
678
+ "cosine_similarity": 0.9999999403953552,
679
+ "grad_magnitude_ratio": 0.9924782269895481,
680
+ "physics_grad_norm": 0.2058173567056656,
681
+ "causal_grad_norm": 0.20426924526691437,
682
+ "physics_loss": 0.0076875239610672,
683
+ "causal_loss": 0.007658554706722498
684
+ },
685
+ {
686
+ "stage": "stage2",
687
+ "epoch": 150,
688
+ "cosine_similarity": 0.9999998807907104,
689
+ "grad_magnitude_ratio": 0.9902909407162303,
690
+ "physics_grad_norm": 0.24350488185882568,
691
+ "causal_grad_norm": 0.241140678524971,
692
+ "physics_loss": 0.009436768479645252,
693
+ "causal_loss": 0.009390776045620441
694
+ },
695
+ {
696
+ "stage": "stage2",
697
+ "epoch": 160,
698
+ "cosine_similarity": 0.9999998807907104,
699
+ "grad_magnitude_ratio": 0.9899236960156501,
700
+ "physics_grad_norm": 0.23211008310317993,
701
+ "causal_grad_norm": 0.22977127134799957,
702
+ "physics_loss": 0.009470558725297451,
703
+ "causal_loss": 0.009422815404832363
704
+ },
705
+ {
706
+ "stage": "stage2",
707
+ "epoch": 170,
708
+ "cosine_similarity": 1.0,
709
+ "grad_magnitude_ratio": 0.9881025757798351,
710
+ "physics_grad_norm": 0.23349037766456604,
711
+ "causal_grad_norm": 0.23071244359016418,
712
+ "physics_loss": 0.010156689211726189,
713
+ "causal_loss": 0.010096704587340355
714
+ },
715
+ {
716
+ "stage": "stage2",
717
+ "epoch": 180,
718
+ "cosine_similarity": 0.9999998807907104,
719
+ "grad_magnitude_ratio": 0.9853137321001949,
720
+ "physics_grad_norm": 0.2744986116886139,
721
+ "causal_grad_norm": 0.27046725153923035,
722
+ "physics_loss": 0.011608390137553215,
723
+ "causal_loss": 0.011524069122970104
724
+ },
725
+ {
726
+ "stage": "stage2",
727
+ "epoch": 190,
728
+ "cosine_similarity": 0.9999999403953552,
729
+ "grad_magnitude_ratio": 0.9851797399667083,
730
+ "physics_grad_norm": 0.2627907395362854,
731
+ "causal_grad_norm": 0.2588961124420166,
732
+ "physics_loss": 0.011185036040842533,
733
+ "causal_loss": 0.011103439144790173
734
+ },
735
+ {
736
+ "stage": "stage2",
737
+ "epoch": 200,
738
+ "cosine_similarity": 0.9999997615814209,
739
+ "grad_magnitude_ratio": 0.9824736088266268,
740
+ "physics_grad_norm": 0.2897014915943146,
741
+ "causal_grad_norm": 0.2846240699291229,
742
+ "physics_loss": 0.011972111649811268,
743
+ "causal_loss": 0.011870373971760273
744
+ },
745
+ {
746
+ "stage": "stage2",
747
+ "epoch": 210,
748
+ "cosine_similarity": 1.0,
749
+ "grad_magnitude_ratio": 0.9844412975110608,
750
+ "physics_grad_norm": 0.2801307141780853,
751
+ "causal_grad_norm": 0.27577224373817444,
752
+ "physics_loss": 0.011492785066366196,
753
+ "causal_loss": 0.01140268798917532
754
+ },
755
+ {
756
+ "stage": "stage2",
757
+ "epoch": 220,
758
+ "cosine_similarity": 0.9999997615814209,
759
+ "grad_magnitude_ratio": 0.9822436479701964,
760
+ "physics_grad_norm": 0.266612708568573,
761
+ "causal_grad_norm": 0.26187863945961,
762
+ "physics_loss": 0.011489767581224442,
763
+ "causal_loss": 0.011389329098165035
764
+ },
765
+ {
766
+ "stage": "stage2",
767
+ "epoch": 230,
768
+ "cosine_similarity": 0.9999997019767761,
769
+ "grad_magnitude_ratio": 0.9814452140540793,
770
+ "physics_grad_norm": 0.30302348732948303,
771
+ "causal_grad_norm": 0.29740095138549805,
772
+ "physics_loss": 0.011890760622918606,
773
+ "causal_loss": 0.011780405417084694
774
+ },
775
+ {
776
+ "stage": "stage2",
777
+ "epoch": 240,
778
+ "cosine_similarity": 1.0,
779
+ "grad_magnitude_ratio": 0.9806410160750632,
780
+ "physics_grad_norm": 0.303956538438797,
781
+ "causal_grad_norm": 0.2980722486972809,
782
+ "physics_loss": 0.011711680330336094,
783
+ "causal_loss": 0.011599436402320862
784
+ },
785
+ {
786
+ "stage": "stage2",
787
+ "epoch": 250,
788
+ "cosine_similarity": 1.0,
789
+ "grad_magnitude_ratio": 0.9794725257375871,
790
+ "physics_grad_norm": 0.3427993655204773,
791
+ "causal_grad_norm": 0.33576256036758423,
792
+ "physics_loss": 0.011594258248806,
793
+ "causal_loss": 0.011475291103124619
794
+ },
795
+ {
796
+ "stage": "stage2",
797
+ "epoch": 260,
798
+ "cosine_similarity": 0.9999998807907104,
799
+ "grad_magnitude_ratio": 0.9790945395114803,
800
+ "physics_grad_norm": 0.3315861225128174,
801
+ "causal_grad_norm": 0.32465416193008423,
802
+ "physics_loss": 0.011505494825541973,
803
+ "causal_loss": 0.01138637587428093
804
+ },
805
+ {
806
+ "stage": "stage2",
807
+ "epoch": 270,
808
+ "cosine_similarity": 0.9999996423721313,
809
+ "grad_magnitude_ratio": 0.9807794646800561,
810
+ "physics_grad_norm": 0.2996678054332733,
811
+ "causal_grad_norm": 0.293908029794693,
812
+ "physics_loss": 0.010979090817272663,
813
+ "causal_loss": 0.010872878134250641
814
+ },
815
+ {
816
+ "stage": "stage2",
817
+ "epoch": 280,
818
+ "cosine_similarity": 1.0,
819
+ "grad_magnitude_ratio": 0.9780514327730572,
820
+ "physics_grad_norm": 0.34630250930786133,
821
+ "causal_grad_norm": 0.33870166540145874,
822
+ "physics_loss": 0.011557349003851414,
823
+ "causal_loss": 0.011432092636823654
824
+ },
825
+ {
826
+ "stage": "stage2",
827
+ "epoch": 290,
828
+ "cosine_similarity": 0.9999999403953552,
829
+ "grad_magnitude_ratio": 0.9754427650954186,
830
+ "physics_grad_norm": 0.38003817200660706,
831
+ "causal_grad_norm": 0.3707054853439331,
832
+ "physics_loss": 0.012468194589018822,
833
+ "causal_loss": 0.012315720319747925
834
+ },
835
+ {
836
+ "stage": "stage3",
837
+ "epoch": 0,
838
+ "cosine_similarity": 1.0,
839
+ "grad_magnitude_ratio": 0.9995690308050741,
840
+ "physics_grad_norm": 0.43620994687080383,
841
+ "causal_grad_norm": 0.43602195382118225,
842
+ "physics_loss": 0.013604261912405491,
843
+ "causal_loss": 0.013601357117295265
844
+ },
845
+ {
846
+ "stage": "stage3",
847
+ "epoch": 10,
848
+ "cosine_similarity": 1.0,
849
+ "grad_magnitude_ratio": 0.9982693448386983,
850
+ "physics_grad_norm": 0.36742857098579407,
851
+ "causal_grad_norm": 0.3667926788330078,
852
+ "physics_loss": 0.012182917445898056,
853
+ "causal_loss": 0.012172874994575977
854
+ },
855
+ {
856
+ "stage": "stage3",
857
+ "epoch": 20,
858
+ "cosine_similarity": 1.0,
859
+ "grad_magnitude_ratio": 0.9971377625514067,
860
+ "physics_grad_norm": 0.37050938606262207,
861
+ "causal_grad_norm": 0.3694489002227783,
862
+ "physics_loss": 0.012593756429851055,
863
+ "causal_loss": 0.012575511820614338
864
+ },
865
+ {
866
+ "stage": "stage3",
867
+ "epoch": 30,
868
+ "cosine_similarity": 1.0000001192092896,
869
+ "grad_magnitude_ratio": 0.9958621560167862,
870
+ "physics_grad_norm": 0.3914637267589569,
871
+ "causal_grad_norm": 0.3898439109325409,
872
+ "physics_loss": 0.01252305880188942,
873
+ "causal_loss": 0.012497065588831902
874
+ },
875
+ {
876
+ "stage": "stage3",
877
+ "epoch": 40,
878
+ "cosine_similarity": 0.9999999403953552,
879
+ "grad_magnitude_ratio": 0.9944419450977557,
880
+ "physics_grad_norm": 0.40237027406692505,
881
+ "causal_grad_norm": 0.40013387799263,
882
+ "physics_loss": 0.012568428181111813,
883
+ "causal_loss": 0.012534420937299728
884
+ },
885
+ {
886
+ "stage": "stage3",
887
+ "epoch": 50,
888
+ "cosine_similarity": 1.0,
889
+ "grad_magnitude_ratio": 0.993028946927179,
890
+ "physics_grad_norm": 0.4011633098125458,
891
+ "causal_grad_norm": 0.398366779088974,
892
+ "physics_loss": 0.012641211040318012,
893
+ "causal_loss": 0.01259805541485548
894
+ },
895
+ {
896
+ "stage": "stage3",
897
+ "epoch": 60,
898
+ "cosine_similarity": 1.0,
899
+ "grad_magnitude_ratio": 0.9916983056115007,
900
+ "physics_grad_norm": 0.3922046720981598,
901
+ "causal_grad_norm": 0.3889487087726593,
902
+ "physics_loss": 0.012513640336692333,
903
+ "causal_loss": 0.012462528422474861
904
+ },
905
+ {
906
+ "stage": "stage3",
907
+ "epoch": 70,
908
+ "cosine_similarity": 0.9999999403953552,
909
+ "grad_magnitude_ratio": 0.9906369450305695,
910
+ "physics_grad_norm": 0.38038718700408936,
911
+ "causal_grad_norm": 0.37682560086250305,
912
+ "physics_loss": 0.01219366304576397,
913
+ "causal_loss": 0.01213786005973816
914
+ },
915
+ {
916
+ "stage": "stage3",
917
+ "epoch": 80,
918
+ "cosine_similarity": 1.0,
919
+ "grad_magnitude_ratio": 0.9897401085084669,
920
+ "physics_grad_norm": 0.3933599591255188,
921
+ "causal_grad_norm": 0.3893241286277771,
922
+ "physics_loss": 0.012070046737790108,
923
+ "causal_loss": 0.012009061872959137
924
+ },
925
+ {
926
+ "stage": "stage3",
927
+ "epoch": 90,
928
+ "cosine_similarity": 0.9999998807907104,
929
+ "grad_magnitude_ratio": 0.9878257294627887,
930
+ "physics_grad_norm": 0.3817373812198639,
931
+ "causal_grad_norm": 0.3770900070667267,
932
+ "physics_loss": 0.01263386569917202,
933
+ "causal_loss": 0.01255928073078394
934
+ },
935
+ {
936
+ "stage": "stage3",
937
+ "epoch": 100,
938
+ "cosine_similarity": 0.9999999403953552,
939
+ "grad_magnitude_ratio": 0.9863813796626999,
940
+ "physics_grad_norm": 0.4212685227394104,
941
+ "causal_grad_norm": 0.4155314266681671,
942
+ "physics_loss": 0.013203107751905918,
943
+ "causal_loss": 0.013114635832607746
944
+ },
945
+ {
946
+ "stage": "stage3",
947
+ "epoch": 110,
948
+ "cosine_similarity": 1.0,
949
+ "grad_magnitude_ratio": 0.9851608370796959,
950
+ "physics_grad_norm": 0.3793342709541321,
951
+ "causal_grad_norm": 0.37370526790618896,
952
+ "physics_loss": 0.012840031646192074,
953
+ "causal_loss": 0.012746474705636501
954
+ },
955
+ {
956
+ "stage": "stage3",
957
+ "epoch": 120,
958
+ "cosine_similarity": 0.9999999403953552,
959
+ "grad_magnitude_ratio": 0.9841690927191897,
960
+ "physics_grad_norm": 0.4134378731250763,
961
+ "causal_grad_norm": 0.4068927764892578,
962
+ "physics_loss": 0.013167422264814377,
963
+ "causal_loss": 0.013063681311905384
964
+ },
965
+ {
966
+ "stage": "stage3",
967
+ "epoch": 130,
968
+ "cosine_similarity": 0.9999998807907104,
969
+ "grad_magnitude_ratio": 0.9827298638030152,
970
+ "physics_grad_norm": 0.3993358910083771,
971
+ "causal_grad_norm": 0.3924393057823181,
972
+ "physics_loss": 0.012849428690969944,
973
+ "causal_loss": 0.012738684192299843
974
+ },
975
+ {
976
+ "stage": "stage3",
977
+ "epoch": 140,
978
+ "cosine_similarity": 0.9999998807907104,
979
+ "grad_magnitude_ratio": 0.9819113139447541,
980
+ "physics_grad_norm": 0.41583767533302307,
981
+ "causal_grad_norm": 0.4083157181739807,
982
+ "physics_loss": 0.012703648768365383,
983
+ "causal_loss": 0.012588806450366974
984
+ },
985
+ {
986
+ "stage": "stage3",
987
+ "epoch": 150,
988
+ "cosine_similarity": 0.9999998211860657,
989
+ "grad_magnitude_ratio": 0.9788188413653486,
990
+ "physics_grad_norm": 0.4241448938846588,
991
+ "causal_grad_norm": 0.41516101360321045,
992
+ "physics_loss": 0.013339745812118053,
993
+ "causal_loss": 0.013201874680817127
994
+ },
995
+ {
996
+ "stage": "stage3",
997
+ "epoch": 160,
998
+ "cosine_similarity": 0.9999997615814209,
999
+ "grad_magnitude_ratio": 0.9779486806682995,
1000
+ "physics_grad_norm": 0.41282328963279724,
1001
+ "causal_grad_norm": 0.4037199914455414,
1002
+ "physics_loss": 0.012891106307506561,
1003
+ "causal_loss": 0.012750637717545033
1004
+ },
1005
+ {
1006
+ "stage": "stage3",
1007
+ "epoch": 170,
1008
+ "cosine_similarity": 0.9999996423721313,
1009
+ "grad_magnitude_ratio": 0.9753016792725326,
1010
+ "physics_grad_norm": 0.40076109766960144,
1011
+ "causal_grad_norm": 0.39086297154426575,
1012
+ "physics_loss": 0.012956085614860058,
1013
+ "causal_loss": 0.01280244067311287
1014
+ },
1015
+ {
1016
+ "stage": "stage3",
1017
+ "epoch": 180,
1018
+ "cosine_similarity": 1.0,
1019
+ "grad_magnitude_ratio": 0.9750830296978227,
1020
+ "physics_grad_norm": 0.4011375606060028,
1021
+ "causal_grad_norm": 0.39114242792129517,
1022
+ "physics_loss": 0.012997531332075596,
1023
+ "causal_loss": 0.012838414870202541
1024
+ },
1025
+ {
1026
+ "stage": "stage3",
1027
+ "epoch": 190,
1028
+ "cosine_similarity": 0.9999998807907104,
1029
+ "grad_magnitude_ratio": 0.9747385367734573,
1030
+ "physics_grad_norm": 0.41891545057296753,
1031
+ "causal_grad_norm": 0.40833303332328796,
1032
+ "physics_loss": 0.012914137914776802,
1033
+ "causal_loss": 0.012751063331961632
1034
+ }
1035
+ ],
1036
+ "wall_time_s": 79.78
1037
+ }
1038
+ }
1039
+ }
results/paper_c/heat1d_ablation/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_c/kdv1d_ablation/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_c/navier_stokes2d_ablation/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_c/pinn_only_ablation_heat1d/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_c/reaction_diffusion_stiff_ablation/results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_c/temporal_error_analysis/fig_temporal_error.pdf ADDED
Binary file (37.3 kB). View file
 
results/paper_c/temporal_error_analysis/fig_temporal_error.png ADDED

Git LFS Details

  • SHA256: 7ba57dbe1945a1bccc12df83f554af99fddfd20fe60259509cb5ec70c43f4bbc
  • Pointer size: 131 Bytes
  • Size of remote file: 188 kB
results/paper_c/temporal_error_analysis/results.json ADDED
@@ -0,0 +1,988 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ {
2
+ "experiment": "paper_c_temporal_error_analysis",
3
+ "pdes": [
4
+ "heat1d",
5
+ "advdiff1d",
6
+ "kdv1d",
7
+ "allencahn1d_sharp"
8
+ ],
9
+ "seed": 42,
10
+ "n_time_slices": 10,
11
+ "n_spatial": 200,
12
+ "conditions": [
13
+ "full_pipeline_no_causal",
14
+ "full_pipeline_with_causal",
15
+ "no_pretrain_no_causal",
16
+ "no_pretrain_with_causal"
17
+ ],
18
+ "results": {
19
+ "heat1d": [
20
+ {
21
+ "pde": "heat1d",
22
+ "condition": "full_pipeline_no_causal",
23
+ "skip_stage1": false,
24
+ "skip_stage3": true,
25
+ "seed": 42,
26
+ "training_time": 54.81971836090088,
27
+ "temporal_errors": [
28
+ {
29
+ "t_fraction": 0.1,
30
+ "t_value": 0.1,
31
+ "rel_l2": 0.04104175046086311
32
+ },
33
+ {
34
+ "t_fraction": 0.2,
35
+ "t_value": 0.2,
36
+ "rel_l2": 0.044689029455184937
37
+ },
38
+ {
39
+ "t_fraction": 0.3,
40
+ "t_value": 0.3,
41
+ "rel_l2": 0.09314703196287155
42
+ },
43
+ {
44
+ "t_fraction": 0.4,
45
+ "t_value": 0.4,
46
+ "rel_l2": 0.25617220997810364
47
+ },
48
+ {
49
+ "t_fraction": 0.5,
50
+ "t_value": 0.5,
51
+ "rel_l2": 0.49994584918022156
52
+ },
53
+ {
54
+ "t_fraction": 0.6,
55
+ "t_value": 0.6,
56
+ "rel_l2": 0.7969224452972412
57
+ },
58
+ {
59
+ "t_fraction": 0.7,
60
+ "t_value": 0.7,
61
+ "rel_l2": 1.1033254861831665
62
+ },
63
+ {
64
+ "t_fraction": 0.8,
65
+ "t_value": 0.8,
66
+ "rel_l2": 4.2106404304504395
67
+ },
68
+ {
69
+ "t_fraction": 0.9,
70
+ "t_value": 0.9,
71
+ "rel_l2": 22.006336212158203
72
+ },
73
+ {
74
+ "t_fraction": 1.0,
75
+ "t_value": 1.0,
76
+ "rel_l2": 93.99164581298828
77
+ }
78
+ ]
79
+ },
80
+ {
81
+ "pde": "heat1d",
82
+ "condition": "full_pipeline_with_causal",
83
+ "skip_stage1": false,
84
+ "skip_stage3": false,
85
+ "seed": 42,
86
+ "training_time": 93.93927550315857,
87
+ "temporal_errors": [
88
+ {
89
+ "t_fraction": 0.1,
90
+ "t_value": 0.1,
91
+ "rel_l2": 0.037900086492300034
92
+ },
93
+ {
94
+ "t_fraction": 0.2,
95
+ "t_value": 0.2,
96
+ "rel_l2": 0.039169199764728546
97
+ },
98
+ {
99
+ "t_fraction": 0.3,
100
+ "t_value": 0.3,
101
+ "rel_l2": 0.0872415229678154
102
+ },
103
+ {
104
+ "t_fraction": 0.4,
105
+ "t_value": 0.4,
106
+ "rel_l2": 0.22859923541545868
107
+ },
108
+ {
109
+ "t_fraction": 0.5,
110
+ "t_value": 0.5,
111
+ "rel_l2": 0.40989387035369873
112
+ },
113
+ {
114
+ "t_fraction": 0.6,
115
+ "t_value": 0.6,
116
+ "rel_l2": 0.5636295080184937
117
+ },
118
+ {
119
+ "t_fraction": 0.7,
120
+ "t_value": 0.7,
121
+ "rel_l2": 0.8257966041564941
122
+ },
123
+ {
124
+ "t_fraction": 0.8,
125
+ "t_value": 0.8,
126
+ "rel_l2": 4.600002765655518
127
+ },
128
+ {
129
+ "t_fraction": 0.9,
130
+ "t_value": 0.9,
131
+ "rel_l2": 22.087692260742188
132
+ },
133
+ {
134
+ "t_fraction": 1.0,
135
+ "t_value": 1.0,
136
+ "rel_l2": 88.26752471923828
137
+ }
138
+ ]
139
+ },
140
+ {
141
+ "pde": "heat1d",
142
+ "condition": "no_pretrain_no_causal",
143
+ "skip_stage1": true,
144
+ "skip_stage3": true,
145
+ "seed": 42,
146
+ "training_time": 39.43369650840759,
147
+ "temporal_errors": [
148
+ {
149
+ "t_fraction": 0.1,
150
+ "t_value": 0.1,
151
+ "rel_l2": 0.6483362913131714
152
+ },
153
+ {
154
+ "t_fraction": 0.2,
155
+ "t_value": 0.2,
156
+ "rel_l2": 1.7052363157272339
157
+ },
158
+ {
159
+ "t_fraction": 0.3,
160
+ "t_value": 0.3,
161
+ "rel_l2": 3.191932439804077
162
+ },
163
+ {
164
+ "t_fraction": 0.4,
165
+ "t_value": 0.4,
166
+ "rel_l2": 4.569985866546631
167
+ },
168
+ {
169
+ "t_fraction": 0.5,
170
+ "t_value": 0.5,
171
+ "rel_l2": 4.485414981842041
172
+ },
173
+ {
174
+ "t_fraction": 0.6,
175
+ "t_value": 0.6,
176
+ "rel_l2": 14.816030502319336
177
+ },
178
+ {
179
+ "t_fraction": 0.7,
180
+ "t_value": 0.7,
181
+ "rel_l2": 71.4526138305664
182
+ },
183
+ {
184
+ "t_fraction": 0.8,
185
+ "t_value": 0.8,
186
+ "rel_l2": 262.6552734375
187
+ },
188
+ {
189
+ "t_fraction": 0.9,
190
+ "t_value": 0.9,
191
+ "rel_l2": 861.85546875
192
+ },
193
+ {
194
+ "t_fraction": 1.0,
195
+ "t_value": 1.0,
196
+ "rel_l2": 2681.93603515625
197
+ }
198
+ ]
199
+ },
200
+ {
201
+ "pde": "heat1d",
202
+ "condition": "no_pretrain_with_causal",
203
+ "skip_stage1": true,
204
+ "skip_stage3": false,
205
+ "seed": 42,
206
+ "training_time": 77.87091994285583,
207
+ "temporal_errors": [
208
+ {
209
+ "t_fraction": 0.1,
210
+ "t_value": 0.1,
211
+ "rel_l2": 0.612163782119751
212
+ },
213
+ {
214
+ "t_fraction": 0.2,
215
+ "t_value": 0.2,
216
+ "rel_l2": 1.5834559202194214
217
+ },
218
+ {
219
+ "t_fraction": 0.3,
220
+ "t_value": 0.3,
221
+ "rel_l2": 2.8930206298828125
222
+ },
223
+ {
224
+ "t_fraction": 0.4,
225
+ "t_value": 0.4,
226
+ "rel_l2": 4.0013108253479
227
+ },
228
+ {
229
+ "t_fraction": 0.5,
230
+ "t_value": 0.5,
231
+ "rel_l2": 3.8991830348968506
232
+ },
233
+ {
234
+ "t_fraction": 0.6,
235
+ "t_value": 0.6,
236
+ "rel_l2": 14.644547462463379
237
+ },
238
+ {
239
+ "t_fraction": 0.7,
240
+ "t_value": 0.7,
241
+ "rel_l2": 67.54417419433594
242
+ },
243
+ {
244
+ "t_fraction": 0.8,
245
+ "t_value": 0.8,
246
+ "rel_l2": 244.23899841308594
247
+ },
248
+ {
249
+ "t_fraction": 0.9,
250
+ "t_value": 0.9,
251
+ "rel_l2": 798.2197875976562
252
+ },
253
+ {
254
+ "t_fraction": 1.0,
255
+ "t_value": 1.0,
256
+ "rel_l2": 2490.378173828125
257
+ }
258
+ ]
259
+ }
260
+ ],
261
+ "advdiff1d": [
262
+ {
263
+ "pde": "advdiff1d",
264
+ "condition": "full_pipeline_no_causal",
265
+ "skip_stage1": false,
266
+ "skip_stage3": true,
267
+ "seed": 42,
268
+ "training_time": 54.05611324310303,
269
+ "temporal_errors": [
270
+ {
271
+ "t_fraction": 0.1,
272
+ "t_value": 0.1,
273
+ "rel_l2": 0.010905697010457516
274
+ },
275
+ {
276
+ "t_fraction": 0.2,
277
+ "t_value": 0.2,
278
+ "rel_l2": 0.017594339326024055
279
+ },
280
+ {
281
+ "t_fraction": 0.3,
282
+ "t_value": 0.3,
283
+ "rel_l2": 0.019924551248550415
284
+ },
285
+ {
286
+ "t_fraction": 0.4,
287
+ "t_value": 0.4,
288
+ "rel_l2": 0.02781406231224537
289
+ },
290
+ {
291
+ "t_fraction": 0.5,
292
+ "t_value": 0.5,
293
+ "rel_l2": 0.03024555929005146
294
+ },
295
+ {
296
+ "t_fraction": 0.6,
297
+ "t_value": 0.6,
298
+ "rel_l2": 0.06709657609462738
299
+ },
300
+ {
301
+ "t_fraction": 0.7,
302
+ "t_value": 0.7,
303
+ "rel_l2": 0.13510915637016296
304
+ },
305
+ {
306
+ "t_fraction": 0.8,
307
+ "t_value": 0.8,
308
+ "rel_l2": 0.16575609147548676
309
+ },
310
+ {
311
+ "t_fraction": 0.9,
312
+ "t_value": 0.9,
313
+ "rel_l2": 0.22930265963077545
314
+ },
315
+ {
316
+ "t_fraction": 1.0,
317
+ "t_value": 1.0,
318
+ "rel_l2": 0.608425498008728
319
+ }
320
+ ]
321
+ },
322
+ {
323
+ "pde": "advdiff1d",
324
+ "condition": "full_pipeline_with_causal",
325
+ "skip_stage1": false,
326
+ "skip_stage3": false,
327
+ "seed": 42,
328
+ "training_time": 96.62131547927856,
329
+ "temporal_errors": [
330
+ {
331
+ "t_fraction": 0.1,
332
+ "t_value": 0.1,
333
+ "rel_l2": 0.008018957450985909
334
+ },
335
+ {
336
+ "t_fraction": 0.2,
337
+ "t_value": 0.2,
338
+ "rel_l2": 0.016648899763822556
339
+ },
340
+ {
341
+ "t_fraction": 0.3,
342
+ "t_value": 0.3,
343
+ "rel_l2": 0.020414035767316818
344
+ },
345
+ {
346
+ "t_fraction": 0.4,
347
+ "t_value": 0.4,
348
+ "rel_l2": 0.028999218717217445
349
+ },
350
+ {
351
+ "t_fraction": 0.5,
352
+ "t_value": 0.5,
353
+ "rel_l2": 0.03198612853884697
354
+ },
355
+ {
356
+ "t_fraction": 0.6,
357
+ "t_value": 0.6,
358
+ "rel_l2": 0.06586858630180359
359
+ },
360
+ {
361
+ "t_fraction": 0.7,
362
+ "t_value": 0.7,
363
+ "rel_l2": 0.13195450603961945
364
+ },
365
+ {
366
+ "t_fraction": 0.8,
367
+ "t_value": 0.8,
368
+ "rel_l2": 0.163643017411232
369
+ },
370
+ {
371
+ "t_fraction": 0.9,
372
+ "t_value": 0.9,
373
+ "rel_l2": 0.22099189460277557
374
+ },
375
+ {
376
+ "t_fraction": 1.0,
377
+ "t_value": 1.0,
378
+ "rel_l2": 0.5738446116447449
379
+ }
380
+ ]
381
+ },
382
+ {
383
+ "pde": "advdiff1d",
384
+ "condition": "no_pretrain_no_causal",
385
+ "skip_stage1": true,
386
+ "skip_stage3": true,
387
+ "seed": 42,
388
+ "training_time": 39.37109684944153,
389
+ "temporal_errors": [
390
+ {
391
+ "t_fraction": 0.1,
392
+ "t_value": 0.1,
393
+ "rel_l2": 0.362369567155838
394
+ },
395
+ {
396
+ "t_fraction": 0.2,
397
+ "t_value": 0.2,
398
+ "rel_l2": 0.4733711779117584
399
+ },
400
+ {
401
+ "t_fraction": 0.3,
402
+ "t_value": 0.3,
403
+ "rel_l2": 0.5978535413742065
404
+ },
405
+ {
406
+ "t_fraction": 0.4,
407
+ "t_value": 0.4,
408
+ "rel_l2": 0.6486167311668396
409
+ },
410
+ {
411
+ "t_fraction": 0.5,
412
+ "t_value": 0.5,
413
+ "rel_l2": 0.7314143180847168
414
+ },
415
+ {
416
+ "t_fraction": 0.6,
417
+ "t_value": 0.6,
418
+ "rel_l2": 1.0739532709121704
419
+ },
420
+ {
421
+ "t_fraction": 0.7,
422
+ "t_value": 0.7,
423
+ "rel_l2": 1.7182822227478027
424
+ },
425
+ {
426
+ "t_fraction": 0.8,
427
+ "t_value": 0.8,
428
+ "rel_l2": 2.6114306449890137
429
+ },
430
+ {
431
+ "t_fraction": 0.9,
432
+ "t_value": 0.9,
433
+ "rel_l2": 3.7681596279144287
434
+ },
435
+ {
436
+ "t_fraction": 1.0,
437
+ "t_value": 1.0,
438
+ "rel_l2": 5.288578033447266
439
+ }
440
+ ]
441
+ },
442
+ {
443
+ "pde": "advdiff1d",
444
+ "condition": "no_pretrain_with_causal",
445
+ "skip_stage1": true,
446
+ "skip_stage3": false,
447
+ "seed": 42,
448
+ "training_time": 79.32475543022156,
449
+ "temporal_errors": [
450
+ {
451
+ "t_fraction": 0.1,
452
+ "t_value": 0.1,
453
+ "rel_l2": 0.32900771498680115
454
+ },
455
+ {
456
+ "t_fraction": 0.2,
457
+ "t_value": 0.2,
458
+ "rel_l2": 0.4508853554725647
459
+ },
460
+ {
461
+ "t_fraction": 0.3,
462
+ "t_value": 0.3,
463
+ "rel_l2": 0.5835698843002319
464
+ },
465
+ {
466
+ "t_fraction": 0.4,
467
+ "t_value": 0.4,
468
+ "rel_l2": 0.6464436054229736
469
+ },
470
+ {
471
+ "t_fraction": 0.5,
472
+ "t_value": 0.5,
473
+ "rel_l2": 0.7454095482826233
474
+ },
475
+ {
476
+ "t_fraction": 0.6,
477
+ "t_value": 0.6,
478
+ "rel_l2": 1.0810928344726562
479
+ },
480
+ {
481
+ "t_fraction": 0.7,
482
+ "t_value": 0.7,
483
+ "rel_l2": 1.6860203742980957
484
+ },
485
+ {
486
+ "t_fraction": 0.8,
487
+ "t_value": 0.8,
488
+ "rel_l2": 2.50706148147583
489
+ },
490
+ {
491
+ "t_fraction": 0.9,
492
+ "t_value": 0.9,
493
+ "rel_l2": 3.5459303855895996
494
+ },
495
+ {
496
+ "t_fraction": 1.0,
497
+ "t_value": 1.0,
498
+ "rel_l2": 4.881657123565674
499
+ }
500
+ ]
501
+ }
502
+ ],
503
+ "kdv1d": [
504
+ {
505
+ "pde": "kdv1d",
506
+ "condition": "full_pipeline_no_causal",
507
+ "skip_stage1": false,
508
+ "skip_stage3": true,
509
+ "seed": 42,
510
+ "training_time": 85.86685729026794,
511
+ "temporal_errors": [
512
+ {
513
+ "t_fraction": 0.1,
514
+ "t_value": 0.05,
515
+ "rel_l2": 0.006645157001912594
516
+ },
517
+ {
518
+ "t_fraction": 0.2,
519
+ "t_value": 0.1,
520
+ "rel_l2": 0.0065646120347082615
521
+ },
522
+ {
523
+ "t_fraction": 0.3,
524
+ "t_value": 0.15,
525
+ "rel_l2": 0.006537383887916803
526
+ },
527
+ {
528
+ "t_fraction": 0.4,
529
+ "t_value": 0.2,
530
+ "rel_l2": 0.0065580569207668304
531
+ },
532
+ {
533
+ "t_fraction": 0.5,
534
+ "t_value": 0.25,
535
+ "rel_l2": 0.00662814499810338
536
+ },
537
+ {
538
+ "t_fraction": 0.6,
539
+ "t_value": 0.3,
540
+ "rel_l2": 0.006754877977073193
541
+ },
542
+ {
543
+ "t_fraction": 0.7,
544
+ "t_value": 0.35,
545
+ "rel_l2": 0.006949341390281916
546
+ },
547
+ {
548
+ "t_fraction": 0.8,
549
+ "t_value": 0.4,
550
+ "rel_l2": 0.007223880384117365
551
+ },
552
+ {
553
+ "t_fraction": 0.9,
554
+ "t_value": 0.45,
555
+ "rel_l2": 0.007590568158775568
556
+ },
557
+ {
558
+ "t_fraction": 1.0,
559
+ "t_value": 0.5,
560
+ "rel_l2": 0.008059190586209297
561
+ }
562
+ ]
563
+ },
564
+ {
565
+ "pde": "kdv1d",
566
+ "condition": "full_pipeline_with_causal",
567
+ "skip_stage1": false,
568
+ "skip_stage3": false,
569
+ "seed": 42,
570
+ "training_time": 135.2579312324524,
571
+ "temporal_errors": [
572
+ {
573
+ "t_fraction": 0.1,
574
+ "t_value": 0.05,
575
+ "rel_l2": 0.006147101055830717
576
+ },
577
+ {
578
+ "t_fraction": 0.2,
579
+ "t_value": 0.1,
580
+ "rel_l2": 0.00605774624273181
581
+ },
582
+ {
583
+ "t_fraction": 0.3,
584
+ "t_value": 0.15,
585
+ "rel_l2": 0.00601684907451272
586
+ },
587
+ {
588
+ "t_fraction": 0.4,
589
+ "t_value": 0.2,
590
+ "rel_l2": 0.006021728739142418
591
+ },
592
+ {
593
+ "t_fraction": 0.5,
594
+ "t_value": 0.25,
595
+ "rel_l2": 0.006075634155422449
596
+ },
597
+ {
598
+ "t_fraction": 0.6,
599
+ "t_value": 0.3,
600
+ "rel_l2": 0.006186927203088999
601
+ },
602
+ {
603
+ "t_fraction": 0.7,
604
+ "t_value": 0.35,
605
+ "rel_l2": 0.00636699516326189
606
+ },
607
+ {
608
+ "t_fraction": 0.8,
609
+ "t_value": 0.4,
610
+ "rel_l2": 0.006627767346799374
611
+ },
612
+ {
613
+ "t_fraction": 0.9,
614
+ "t_value": 0.45,
615
+ "rel_l2": 0.006980705074965954
616
+ },
617
+ {
618
+ "t_fraction": 1.0,
619
+ "t_value": 0.5,
620
+ "rel_l2": 0.007434645667672157
621
+ }
622
+ ]
623
+ },
624
+ {
625
+ "pde": "kdv1d",
626
+ "condition": "no_pretrain_no_causal",
627
+ "skip_stage1": true,
628
+ "skip_stage3": true,
629
+ "seed": 42,
630
+ "training_time": 61.04188060760498,
631
+ "temporal_errors": [
632
+ {
633
+ "t_fraction": 0.1,
634
+ "t_value": 0.05,
635
+ "rel_l2": 0.25605130195617676
636
+ },
637
+ {
638
+ "t_fraction": 0.2,
639
+ "t_value": 0.1,
640
+ "rel_l2": 0.2581954598426819
641
+ },
642
+ {
643
+ "t_fraction": 0.3,
644
+ "t_value": 0.15,
645
+ "rel_l2": 0.26054656505584717
646
+ },
647
+ {
648
+ "t_fraction": 0.4,
649
+ "t_value": 0.2,
650
+ "rel_l2": 0.263087660074234
651
+ },
652
+ {
653
+ "t_fraction": 0.5,
654
+ "t_value": 0.25,
655
+ "rel_l2": 0.2658027112483978
656
+ },
657
+ {
658
+ "t_fraction": 0.6,
659
+ "t_value": 0.3,
660
+ "rel_l2": 0.2686768174171448
661
+ },
662
+ {
663
+ "t_fraction": 0.7,
664
+ "t_value": 0.35,
665
+ "rel_l2": 0.27169594168663025
666
+ },
667
+ {
668
+ "t_fraction": 0.8,
669
+ "t_value": 0.4,
670
+ "rel_l2": 0.27484723925590515
671
+ },
672
+ {
673
+ "t_fraction": 0.9,
674
+ "t_value": 0.45,
675
+ "rel_l2": 0.2781187891960144
676
+ },
677
+ {
678
+ "t_fraction": 1.0,
679
+ "t_value": 0.5,
680
+ "rel_l2": 0.28150010108947754
681
+ }
682
+ ]
683
+ },
684
+ {
685
+ "pde": "kdv1d",
686
+ "condition": "no_pretrain_with_causal",
687
+ "skip_stage1": true,
688
+ "skip_stage3": false,
689
+ "seed": 42,
690
+ "training_time": 110.6938624382019,
691
+ "temporal_errors": [
692
+ {
693
+ "t_fraction": 0.1,
694
+ "t_value": 0.05,
695
+ "rel_l2": 0.2289496511220932
696
+ },
697
+ {
698
+ "t_fraction": 0.2,
699
+ "t_value": 0.1,
700
+ "rel_l2": 0.2312389314174652
701
+ },
702
+ {
703
+ "t_fraction": 0.3,
704
+ "t_value": 0.15,
705
+ "rel_l2": 0.23374919593334198
706
+ },
707
+ {
708
+ "t_fraction": 0.4,
709
+ "t_value": 0.2,
710
+ "rel_l2": 0.23646394908428192
711
+ },
712
+ {
713
+ "t_fraction": 0.5,
714
+ "t_value": 0.25,
715
+ "rel_l2": 0.23936735093593597
716
+ },
717
+ {
718
+ "t_fraction": 0.6,
719
+ "t_value": 0.3,
720
+ "rel_l2": 0.24244435131549835
721
+ },
722
+ {
723
+ "t_fraction": 0.7,
724
+ "t_value": 0.35,
725
+ "rel_l2": 0.24568109214305878
726
+ },
727
+ {
728
+ "t_fraction": 0.8,
729
+ "t_value": 0.4,
730
+ "rel_l2": 0.2490645945072174
731
+ },
732
+ {
733
+ "t_fraction": 0.9,
734
+ "t_value": 0.45,
735
+ "rel_l2": 0.252582848072052
736
+ },
737
+ {
738
+ "t_fraction": 1.0,
739
+ "t_value": 0.5,
740
+ "rel_l2": 0.25622451305389404
741
+ }
742
+ ]
743
+ }
744
+ ],
745
+ "allencahn1d_sharp": [
746
+ {
747
+ "pde": "allencahn1d_sharp",
748
+ "condition": "full_pipeline_no_causal",
749
+ "skip_stage1": false,
750
+ "skip_stage3": true,
751
+ "seed": 42,
752
+ "training_time": 55.12654089927673,
753
+ "temporal_errors": [
754
+ {
755
+ "t_fraction": 0.1,
756
+ "t_value": 0.05,
757
+ "rel_l2": 0.0882662981748581
758
+ },
759
+ {
760
+ "t_fraction": 0.2,
761
+ "t_value": 0.1,
762
+ "rel_l2": 0.08798334747552872
763
+ },
764
+ {
765
+ "t_fraction": 0.3,
766
+ "t_value": 0.15,
767
+ "rel_l2": 0.08771905303001404
768
+ },
769
+ {
770
+ "t_fraction": 0.4,
771
+ "t_value": 0.2,
772
+ "rel_l2": 0.08745966106653214
773
+ },
774
+ {
775
+ "t_fraction": 0.5,
776
+ "t_value": 0.25,
777
+ "rel_l2": 0.08719503879547119
778
+ },
779
+ {
780
+ "t_fraction": 0.6,
781
+ "t_value": 0.3,
782
+ "rel_l2": 0.08691807836294174
783
+ },
784
+ {
785
+ "t_fraction": 0.7,
786
+ "t_value": 0.35,
787
+ "rel_l2": 0.08662562072277069
788
+ },
789
+ {
790
+ "t_fraction": 0.8,
791
+ "t_value": 0.4,
792
+ "rel_l2": 0.08631708472967148
793
+ },
794
+ {
795
+ "t_fraction": 0.9,
796
+ "t_value": 0.45,
797
+ "rel_l2": 0.08599593490362167
798
+ },
799
+ {
800
+ "t_fraction": 1.0,
801
+ "t_value": 0.5,
802
+ "rel_l2": 0.08566892892122269
803
+ }
804
+ ]
805
+ },
806
+ {
807
+ "pde": "allencahn1d_sharp",
808
+ "condition": "full_pipeline_with_causal",
809
+ "skip_stage1": false,
810
+ "skip_stage3": false,
811
+ "seed": 42,
812
+ "training_time": 94.01985311508179,
813
+ "temporal_errors": [
814
+ {
815
+ "t_fraction": 0.1,
816
+ "t_value": 0.05,
817
+ "rel_l2": 0.08819203078746796
818
+ },
819
+ {
820
+ "t_fraction": 0.2,
821
+ "t_value": 0.1,
822
+ "rel_l2": 0.08791384100914001
823
+ },
824
+ {
825
+ "t_fraction": 0.3,
826
+ "t_value": 0.15,
827
+ "rel_l2": 0.0876200869679451
828
+ },
829
+ {
830
+ "t_fraction": 0.4,
831
+ "t_value": 0.2,
832
+ "rel_l2": 0.08730193972587585
833
+ },
834
+ {
835
+ "t_fraction": 0.5,
836
+ "t_value": 0.25,
837
+ "rel_l2": 0.08695367723703384
838
+ },
839
+ {
840
+ "t_fraction": 0.6,
841
+ "t_value": 0.3,
842
+ "rel_l2": 0.0865732729434967
843
+ },
844
+ {
845
+ "t_fraction": 0.7,
846
+ "t_value": 0.35,
847
+ "rel_l2": 0.08616193383932114
848
+ },
849
+ {
850
+ "t_fraction": 0.8,
851
+ "t_value": 0.4,
852
+ "rel_l2": 0.08572438359260559
853
+ },
854
+ {
855
+ "t_fraction": 0.9,
856
+ "t_value": 0.45,
857
+ "rel_l2": 0.08526898920536041
858
+ },
859
+ {
860
+ "t_fraction": 1.0,
861
+ "t_value": 0.5,
862
+ "rel_l2": 0.08480710536241531
863
+ }
864
+ ]
865
+ },
866
+ {
867
+ "pde": "allencahn1d_sharp",
868
+ "condition": "no_pretrain_no_causal",
869
+ "skip_stage1": true,
870
+ "skip_stage3": true,
871
+ "seed": 42,
872
+ "training_time": 39.21727156639099,
873
+ "temporal_errors": [
874
+ {
875
+ "t_fraction": 0.1,
876
+ "t_value": 0.05,
877
+ "rel_l2": 0.3401981592178345
878
+ },
879
+ {
880
+ "t_fraction": 0.2,
881
+ "t_value": 0.1,
882
+ "rel_l2": 0.33840498328208923
883
+ },
884
+ {
885
+ "t_fraction": 0.3,
886
+ "t_value": 0.15,
887
+ "rel_l2": 0.3369213342666626
888
+ },
889
+ {
890
+ "t_fraction": 0.4,
891
+ "t_value": 0.2,
892
+ "rel_l2": 0.3357868790626526
893
+ },
894
+ {
895
+ "t_fraction": 0.5,
896
+ "t_value": 0.25,
897
+ "rel_l2": 0.3350406587123871
898
+ },
899
+ {
900
+ "t_fraction": 0.6,
901
+ "t_value": 0.3,
902
+ "rel_l2": 0.3347201347351074
903
+ },
904
+ {
905
+ "t_fraction": 0.7,
906
+ "t_value": 0.35,
907
+ "rel_l2": 0.3348594605922699
908
+ },
909
+ {
910
+ "t_fraction": 0.8,
911
+ "t_value": 0.4,
912
+ "rel_l2": 0.3354886472225189
913
+ },
914
+ {
915
+ "t_fraction": 0.9,
916
+ "t_value": 0.45,
917
+ "rel_l2": 0.33663225173950195
918
+ },
919
+ {
920
+ "t_fraction": 1.0,
921
+ "t_value": 0.5,
922
+ "rel_l2": 0.33830881118774414
923
+ }
924
+ ]
925
+ },
926
+ {
927
+ "pde": "allencahn1d_sharp",
928
+ "condition": "no_pretrain_with_causal",
929
+ "skip_stage1": true,
930
+ "skip_stage3": false,
931
+ "seed": 42,
932
+ "training_time": 78.3809654712677,
933
+ "temporal_errors": [
934
+ {
935
+ "t_fraction": 0.1,
936
+ "t_value": 0.05,
937
+ "rel_l2": 0.3146457076072693
938
+ },
939
+ {
940
+ "t_fraction": 0.2,
941
+ "t_value": 0.1,
942
+ "rel_l2": 0.31246957182884216
943
+ },
944
+ {
945
+ "t_fraction": 0.3,
946
+ "t_value": 0.15,
947
+ "rel_l2": 0.3106701076030731
948
+ },
949
+ {
950
+ "t_fraction": 0.4,
951
+ "t_value": 0.2,
952
+ "rel_l2": 0.3092934787273407
953
+ },
954
+ {
955
+ "t_fraction": 0.5,
956
+ "t_value": 0.25,
957
+ "rel_l2": 0.30838391184806824
958
+ },
959
+ {
960
+ "t_fraction": 0.6,
961
+ "t_value": 0.3,
962
+ "rel_l2": 0.30798283219337463
963
+ },
964
+ {
965
+ "t_fraction": 0.7,
966
+ "t_value": 0.35,
967
+ "rel_l2": 0.3081277906894684
968
+ },
969
+ {
970
+ "t_fraction": 0.8,
971
+ "t_value": 0.4,
972
+ "rel_l2": 0.3088511526584625
973
+ },
974
+ {
975
+ "t_fraction": 0.9,
976
+ "t_value": 0.45,
977
+ "rel_l2": 0.3101797103881836
978
+ },
979
+ {
980
+ "t_fraction": 1.0,
981
+ "t_value": 0.5,
982
+ "rel_l2": 0.3121335506439209
983
+ }
984
+ ]
985
+ }
986
+ ]
987
+ }
988
+ }
results/paper_c/wang_comparison/advdiff1d_results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_c/wang_comparison/allencahn1d_sharp_results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_c/wang_comparison/heat1d_results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_c/wang_comparison/kdv1d.log ADDED
@@ -0,0 +1,10 @@
 
 
 
 
 
 
 
 
 
 
 
1
+ Wang et al. 2024 Comparison: kdv1d
2
+ Conditions: ['single_pinn_no_causal', 'single_pinn_with_causal', 'hybrid_full_pipeline']
3
+ Seeds: [42, 123, 456, 789, 1024, 2048, 3072, 4096, 5120, 6144]
4
+ Total runs: 30
5
+
6
+ --- single_pinn_no_causal (PINN-only, stages=2) ---
7
+ kdv1d/single_pinn_no_causal/seed=42... /projects/PINN/.venv/lib/python3.12/site-packages/torch/autograd/graph.py:825: UserWarning: Attempting to run cuBLAS, but there was no current CUDA context! Attempting to set the primary context... (Triggered internally at ../aten/src/ATen/cuda/CublasHandlePool.cpp:135.)
8
+ return Variable._execution_engine.run_backward( # Calls into the C++ engine to run the backward pass
9
+ rel_l2=3.3290e-01 pde_res=1.4128e-01 time=13.4s
10
+ kdv1d/single_pinn_no_causal/seed=123...
results/paper_c/wang_comparison/kdv1d_results.json ADDED
The diff for this file is too large to render. See raw diff
 
results/paper_combined/adaptive_epsilon/fig_epsilon_trajectories.pdf ADDED
Binary file (33 kB). View file