Эксперимент: Nonlinear Hydrodynamic Optimizer (#1157)

{ "worked": true, "confidence": 8, "verdict": "Built a small nonlinear hydrodynamic block-allocation optimizer with density-dependent diffusivity, mobility-scaled interface noise, positivity projection, and conservative renormalization. The math verification reproduced the predicted Fourier decay slope exactly, conserved total allocation to numerical precision, and showed highest-mode growth above the predicted Euler boundary with observed/theoretical growth 1.45681117. On the fixed toy MLP, noiseless hydrodynamic allocation improved final loss versus the Adam-like baseline, but the noisy variant did not, so the optimization benefit is promising but not established broadly.", "metrics": { "baseline": "Adam-like update: final full loss 0.008514; last-50 minibatch loss mean 0.006773; 9.04 sec.", "idea": "Hydro without noise: final full loss 0.004646; last-50 mean 0.003269; 9.39 sec. Hydro plus mobility noise: final full loss 0.007940; last-50 mean 0.006978; 6.35 sec. Math: mass error 5.33e-15; decay slope ratio 1.0000000000000009; above-boundary highest-mode growth 1.45681117." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 hydro_experiment.py && /home/maxwelhelp/main/bin/python3 verify_math.py", "files": [ "hydro_experiment.py", "verify_math.py", "results.json", "math_verification.json" ], "limitations": "Only a four-block, 500-step toy MLP experiment was tested, with one fixed seed and one synthetic dataset. No Transformer, multiple-seed study, wall-clock-matched hyperparameter sweep, or rigorous matched-loss block-activity-variance comparison was performed; the noise coefficient was not tuned." }