FluxNet shallow-water LAP pushforward reproduction
Source: https://arxiv.org/pdf/2602.01941v2 (Sections 3.2–3.7, Appendix C.2).
One independent training run (seed 42), 300 complete epochs. This is not a five-seed mean/std replication. 64 channels, 6 residual blocks, kernel 5, transport stencil 3×3, detached pushforward length 5. AdamW lr=1e-3, weight_decay=1e-2; ReduceLROnPlateau factor=0.5, patience=15; float32 states.
Selected checkpoint epoch: 283; validation MSE: 1.11785405e-06.
Checkpoint SHA256: 47fb0a029b0c5baa10b2452c70b12f54c958b548cb9aff300b85183d55f1ae70.
| Split | Horizon | MAE h | MAE mx | MAE my | Negative h (%) |
|---|---|---|---|---|---|
| test | 2.4 | 1.30214413e-03 | 1.79798426e-03 | 1.72321738e-03 | 0.00000000e+00 |
| test_long | 4.8 | 1.40631581e-03 | 1.85576825e-03 | 1.76324718e-03 | 0.00000000e+00 |
MAE averages all forecast steps, grid cells, and 50 trajectories, excluding the initial frame. Final-time and T=2/T=2.4/T=4.8 prefix metrics are separately stored in metrics.json. The paper labels Table 3 as T=2 while Appendix C.1 specifies 2.4/4.8; both time conventions are retained.
Conservation is computed using float64 reductions of float32 predictions relative to the initial state. Relative drift divides by |initial signed total|+1e-8; zero-total momentum makes this statistic ill-conditioned. Absolute sum drift and initial-L1-scaled drift are therefore also reported. No postprocessing correction is used.
test maximum absolute sum drift [h,mx,my]: [2.2027743398211896e-05, 3.510061651468277e-05, 3.0668867111671716e-05] test maximum relative drift [h,mx,my]: [2.168669351450529e-08, 3510.061651468277, 2132.3561668395996] test minimum depth: 0.00000000e+00
test_long maximum absolute sum drift [h,mx,my]: [2.8165319235995412e-05, 4.894798621535301e-05, 3.981318513979204e-05] test_long maximum relative drift [h,mx,my]: [2.574266788559366e-08, 4894.798621535301, 2548.028714954853] test_long minimum depth: 0.00000000e+00
All arrays, checkpoints, training history, and saved-case MAE recomputations were checked. The original numerical-generator datasets were read directly; no data generation or official repository code was downloaded.
Reference data contains small negative roundoff depths (about 1e-11); these are retained unchanged. Data validation tolerates reference values down to -1e-9; model violation metrics use the strict condition h<0, with no tolerance or clipping.