Эксперимент: Weak Koopman Latent Dynamics (#365)

{ "worked": true, "confidence": 9, "verdict": "Built a reproducible weak Koopman generator MVP with Hann test functions, quadrature-based G/B construction, integration-by-parts verification, analytic noise-variance predictions, and a finite-difference baseline. The weak identity error was 1.13e-6; measured weak and finite-difference noise variances matched theory within about 2.3%, with scaling slopes weak-vs-dt=+1.000, finite-difference-vs-dt=-1.999, and weak-vs-window=-0.995. In the oscillator generator fit at sigma=0.15, weak regression error was 0.223 versus 0.408 for finite differences, a 45.4% reduction, so the proposed noise-averaging mechanism manifested clearly in this toy setting.", "metrics": { "baseline": "Finite-difference derivative regression: variance followed 2sigma^2/dt^2; oscillator generator Frobenius error 0.4081 at sigma=0.15.", "idea": "Weak Hann-form regression: variance matched sigma^2sum(weights^2), weak variance scaled as dt^1 and window^-1; oscillator generator Frobenius error 0.2228, ratio 0.546 of baseline." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 weak_koopman_experiment.py", "files": [ "weak_koopman_experiment.py", "results.json" ], "limitations": "This is a small linear oscillator experiment with directly observed two-dimensional observables, not a learned neural encoder or Lorenz-63/world-model task. It does not test decoder reconstruction, nonlinear latent representations, multi-step forecasting, stability projection, correlated or colored noise, or computational cost at neural-network scale." }