Эксперимент: KPZ latent evolution block (#589)

{ "worked": true, "confidence": 9, "verdict": "Built a periodic 3-D KPZ simulator and differentiable PyTorch KPZCell with explicit diffusion, gradient-square nonlinearity, and stochastic forcing. Noise variance matched 2Ddt/dx^3 within 1.2–1.4%, nonlinear drift matched the predicted linear dependence on lambda to numerical precision, and the checkerboard mode became unstable above the predicted explicit diffusion bound. This validates the mechanism, but no end-to-end learning win was tested.", "metrics": { "baseline": "Diffusion-only rollout: final mean 0.003486 and RMS 0.169412; at the stability-bound factor 1.0, final checkerboard amplitude was 1.0.", "idea": "Noise observed/predicted ratios were 0.125753/0.124320, 0.015317/0.015540, and 0.001969/0.001943 for dx 0.5, 1.0, and 2.0. Nonlinear drift relative error was below 6e-16 for lambda in [-2,2]. At 1.2 times the predicted stability bound, amplification was 1.4 and final amplitude grew to 14.758; KPZ rollout final mean was 0.030622 and RMS 0.169710." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 kpz_experiment.py", "files": [ "kpz_experiment.py", "results.json" ], "limitations": "The 3+1-D exponents beta=0.1845 and chi=0.3135 were not estimated because that requires longer and larger ensembles. No encoder/decoder, ConvGRU, training-loss, FLOP, or long-horizon forecasting comparison was performed." }