Эксперимент: Walk-on-Spheres stochastic target layer (#825)

{ "worked": true, "confidence": 8, "verdict": "Built a readable Walk-on-Spheres stochastic target generator and MLP training MVP in wos_experiment.py. The mechanism manifested: target variance followed the predicted 1/K law, with K times variance approximately 0.016 to 0.018, and finite-depth estimates approached the reference from 0.734 at M=2 to 0.9995 at M=64. The learning comparison gave relative RMSE 0.345 for WOS versus 0.350 for exact targets, but WOS took 4.31 seconds versus 1.70 seconds, so no practical win was demonstrated. The checks also identified that the supplied Delta-t formula is half the standard Brownian ball mean exit time under the usual convention.", "metrics": { "baseline": "Exact analytic square-Poisson targets: relative RMSE 0.3503, 1.70 seconds", "idea": "WOS square-Poisson targets with K=8 and M=25: relative RMSE 0.3450, 4.31 seconds; variance ratio at K=128 was 0.00692 versus predicted 1/128 = 0.0078125" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 wos_experiment.py", "files": [ "wos_experiment.py" ], "limitations": "Only a tiny 2D square learning experiment was run. Higher dimensions, unit-ball learning, screened Poisson, a true PINN residual baseline, FLOP-normalized comparisons, boundary projection, and corrected-versus-supplied time-step conventions were not fully benchmarked." }