| """Reproduce VSCE continuous first-passage comparisons and monitoring study.""" |
| from pathlib import Path |
| import json |
| import math |
| import numpy as np |
| from risk_math import (ou_continuous_bounds, survival_fv, mean_exit_time, |
| mean_exit_fv, laplace_exit,laplace_exit_fv, |
| simulate_nested_sampled_exit,poisson_clearance) |
|
|
|
|
| def run(): |
| comparison=[] |
| for beta,T in ((2,.1),(2,1),(6.25,.03),(6.25,.2),(6.25,2), |
| (12.5,2),(12.5,10),(25,10)): |
| R=math.sqrt(2*beta) |
| bounds=ou_continuous_bounds(R,T,1,1) |
| estimates={} |
| if beta<=15: |
| for cells in (200,400,800): |
| numerical=survival_fv(R,[T],1,1,cells) |
| value=float(numerical['exit_probability'][0]) |
| estimates[str(cells)]={ |
| 'exit_probability':value if math.isfinite(value) else None, |
| 'resolved':bool(numerical['resolved'][0]), |
| 'principal_eigenvalue':numerical['principal_eigenvalue'], |
| 'roundoff_clip_max':numerical['roundoff_clip_max']} |
| comparison.append({'beta':beta,'T':T,'kappa':1,'diffusion':1,'radius':R, |
| 'bounds':bounds,'fv_estimates':estimates, |
| 'fv_status':'spatial estimates, not interval-certified' |
| if beta<=15 else 'unsupported beta>15'}) |
| refinement=[] |
| for beta in (0.5,2,6.25,12.5,15): |
| R=math.sqrt(2*beta) |
| exact_m=mean_exit_time(R,1,1) |
| exact_l=laplace_exit(.2,R,1,1) |
| row={'beta':beta,'exact_mean':exact_m,'exact_laplace_s0_2':exact_l, |
| 'grid_results':{}} |
| for n in (80,160,320,800): |
| m=mean_exit_fv(R,1,1,n) |
| l=laplace_exit_fv(.2,R,1,1,n) |
| row['grid_results'][str(n)]={'mean':m,'laplace_s0_2':l, |
| 'mean_relative_error':abs(m/exact_m-1), |
| 'laplace_relative_error':abs(l/exact_l-1)} |
| refinement.append(row) |
| monitoring=simulate_nested_sampled_exit( |
| 1,2,1,.08,.001,(1,5,10,50,100),trials=30000,seed=20261013) |
| continuous=survival_fv(1,[2],1,.08,800) |
| monitoring['continuous_pde_estimate']=float(continuous['exit_probability'][0]) |
| monitoring['continuous_pde_cells']=800 |
| radius=poisson_clearance(10,1,.04,.001) |
| design={'T':10,'kappa':1,'diffusion':.04,'events':1,'error_budget':.001, |
| 'poisson_radius':radius,'poisson_beta':radius*radius/.08, |
| 'v5_direct_beta':20+math.log(1000), |
| 'v5_direct_radius':math.sqrt(.08*(20+math.log(1000)))} |
| data={'schema':'VSCE continuous first-passage evidence 1.0', |
| 'scientific_scope':'conditional classical stochastic model; no exotic vacuum apparatus', |
| 'analytic_numeric_support':{'beta_max':650,'upper_underflow':'rounded upward to smallest positive float'}, |
| 'finite_volume_support':{'beta_max':15,'cells_min':8,'cells_max':2000, |
| 'exit_resolution_floor':1e-11, |
| 'below_resolution':'null/unresolved; never a zero probability claim', |
| 'interval_certified':False}, |
| 'comparison':comparison,'independent_fv_refinement':refinement, |
| 'nested_monitoring':monitoring,'clearance_design':design} |
| return data |
|
|
|
|
| if __name__=='__main__': |
| output=Path(__file__).resolve().parents[1]/'results/risk_results.json' |
| output.write_text(json.dumps(run(),indent=2,allow_nan=False)+'\n') |
| print(output) |
|
|
