Эксперимент: Lyapunov-sign-preserving neural time stepping (#1064)

{ "worked": true, "confidence": 9, "verdict": "Built a reusable Lyapunov exponent estimator with exact PyTorch JVP support, Euler and semi-implicit stepping, and a controller that halves the step when a nominally stable mode appears expanding. The mechanism manifested: the scalar Euler sign-flip boundary matched h*=2/a within 0.1% across a=0.5,1,2,4, and Euler exponent error showed first-order scaling with successive ratios 2.39, 2.16, and 2.07. Implicit stepping preserved the stable sign in the oscillator sweep, while the controller corrected h=2.5 to h=1.25.", "metrics": { "baseline": "Explicit Euler: scalar sign boundary observed at 1.001x the predicted boundary across all tested damping values; oscillator exponent became positive at h=0.1, with lambda_h=+0.0020 despite continuous lambda=-0.2.", "idea": "Semi-implicit/controller: implicit oscillator exponent stayed negative for h=0.05, 0.1, 0.2, 0.4, and 0.8; the controller halved h=2.5 after lambda_hat=+0.1622 and stopped at h=1.25 with lambda_hat=-1.1090; exact JVP log error was 0.0." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 lyapunov_controller.py", "files": [ "lyapunov_controller.py", "results.json", "run_output.txt" ], "limitations": "This MVP verifies the mechanism on analytically defined linear deterministic systems and a synthetic PyTorch JVP, not on a trained neural ODE, recurrent model, or genuinely stochastic diffusion process. It does not benchmark wall-clock speed, training loss, memory, or adaptive estimation of the continuous exponent and error constant C." }