File size: 3,588 Bytes
347a3de | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 | """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)
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