Эксперимент: Input-Aware Contracting Neural ODE (#770)

{ "worked": true, "confidence": 8, "verdict": "Built an input-aware contracting Neural ODE prototype with a positive-definite learned metric and total derivative dM/dt=(∂M/∂x)f+(∂M/∂u)u_dot. The scalar checks confirmed three predictions essentially exactly: boundary q*=0.8, sensitivity dμ/dq=1.5, and zero input-rate effect when the metric is input-independent. The adaptive model reduced mean certificate eigenvalue and violation fraction, but its worst-case violation remained large, so this is a promising mechanism signal rather than a complete stability certificate.", "metrics": { "baseline": "Unconstrained: mean_mu=1.675, max_mu=2.295, violation_fraction=1.000; fixed M=I: mean_mu=0.748, max_mu=1.589, violation_fraction=1.000.", "idea": "Adaptive input-aware metric with total derivative: mean_mu=-0.402, max_mu=22.465, violation_fraction=0.438. Analytic predictions: q boundary 0.800 predicted/observed, dmu/dq 1.500 predicted/observed, k=0 variation 0." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "The mini-experiment uses a small short-horizon Duffing-inspired vector-field fitting task rather than full NODE trajectory optimization, omits robust B/E disturbance terms, does not separately train a frozen-metric neural model, and does not test long rollouts or the input-mismatch plateau. The learned metric still has substantial worst-case certificate violations." }