# Эксперимент: Frozen-Diffusion Parametrix Preconditioner (#1160)

{
  "worked": false,
  "confidence": 8,
  "verdict": "Built a compact 1D variable-diffusion backward solver comparing raw backward Euler targets with frozen-diffusion parametrix targets. The Gaussian propagation check matched the exact Fourier multiplier to 2.2e-5 absolute error, and the correction vanished exactly for constant diffusion. However, after 700 matched Adam steps, parametrix relative L2 value error was 0.979 versus 0.840 for the raw baseline, so the claimed optimization/accuracy win was not observed in this test.",
  "metrics": {
    "baseline": "Raw backward target: final relative L2 value error 0.83998; final recorded training loss 0.70607.",
    "idea": "Frozen-diffusion parametrix target: final relative L2 value error 0.97901; final recorded training loss 0.78302. Gaussian multiplier Monte Carlo absolute error: 2.22e-5."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "This is a 1D diffusion-only periodic toy problem without drift, control Hamiltonian, multidimensional patch assignment, or a full PINN residual baseline. The experiment uses a short horizon, one fixed local patch rule, Monte Carlo Gaussian propagation, and one seed; broader tuning of timestep, patch size, sample count, and network architecture was not tested."
}