# Эксперимент: Quasipotential PINN for Optimization Dynamics (#354)

{
  "worked": false,
  "confidence": 9,
  "verdict": "Built a reproducible toy quasipotential experiment for a bistable diffusion, including exact HJ verification, empirical covariance estimation, a scalar PINN, and transition-rate sweeps. The inverse-noise transition slope was -0.2493 versus the predicted -0.25, but the PINN learned a near-constant potential with barrier 0.000535 versus the exact 0.25. Because the core learned-monitor effect was not recovered, this is not a demonstrated win.",
  "metrics": {
    "baseline": "Exact barrier=0.25; exact HJ residual=0; empirical transition slope=-0.2493 versus predicted -0.25.",
    "idea": "Estimated covariance mean=2.0057; PINN barrier=0.000535 versus exact 0.25; PINN HJ RMS=0.000499. Covariance-scale slopes: c=0.5, -0.4923 versus -0.5; c=1, -0.2733 versus -0.25; c=2, -0.1804 versus -0.125."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 quasipotential_experiment.py",
  "files": [
    "quasipotential_experiment.py",
    "results.json"
  ],
  "limitations": "Only a one-dimensional analytic bistable diffusion was tested. No neural-network optimizer trajectory, MNIST or two-moons task, SGD-versus-Adam comparison, basin clustering, learned transition path, or optimization intervention was tested."
}