Эксперимент: Gaussian-mixture kinetic neural solver (#913)

{ "worked": false, "confidence": 9, "verdict": "Built a deterministic Gaussian-mixture kinetic toy in kinetic_mvp.py with positive softmax/softplus parameterization, a number/energy-preserving projected collision operator, relaxation-spectrum sweeps, response sweeps, and a coarse-grid comparison. Positivity, two conservation zero modes, and linear eigenvalue scaling with collision rate were confirmed, but the measured response FWHM did not show a crossover near k v_th/gamma = 1. The full Bose collision integral with momentum/energy delta functions and neural PDE training were not implemented, so the headline mechanism was not established.", "metrics": { "baseline": "Coarse 7x7 grid representation RMSE = 2.19e-2 on the synthetic mixture target; response crossover not reliably detected.", "idea": "Positive fitted 3-component Gaussian mixture RMSE = 1.35e-11; minimum density = 1.06e-20; collision operator had exactly 2 zero modes and median nonzero eigenvalues 0.25, 0.50, 1.00, 2.00 for gamma = 0.25, 0.5, 1, 2, respectively; crossover sweep FWHM values were 0.5, 4, 6, 6, 2 at ratios 0.25, 0.5, 1, 2, 4." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 kinetic_mvp.py", "files": [ "kinetic_mvp.py", "results.json", "REPORT.md" ], "limitations": "This is a small projected linear toy rather than the full differentiable Bose gain-minus-loss collision operator with conservation delta functions. No MLP training, spatial PDE residual optimization, CUDA experiment, response-pole fitting, 100-relaxation-time drift test, or full finite-volume solver comparison was performed. The quadrature box truncates the mixture tails, giving an integrated mass of 0.8882 on the finite grid." }