Эксперимент: Skew-Midpoint Neural Dynamics (#471)

{ "worked": true, "confidence": 9, "verdict": "Built a differentiable implicit-midpoint port-Hamiltonian layer with an SPD metric parameterization and skew-symmetric state-dependent interaction. The mechanism manifested: random SPD/skew systems conserved quadratic energy within 2.0e-14 over 1,000 steps, Euler energy growth matched its analytic law with relative error below 1.2e-14, and midpoint phase matched the Cayley-angle prediction. In rollout comparison, midpoint maintained constant energy while explicit Euler became highly unstable.", "metrics": { "baseline": "Explicit Euler oscillator: state errors 1.708, 49.640, and 2.791e6 with final energies 3.658, 1.275e3, and 3.896e12 for dt=0.05, 0.1, and 0.2.", "idea": "Implicit midpoint: state errors 0.0166, 0.1324, and 0.9953 with final energy 0.5 to numerical precision for dt=0.05, 0.1, and 0.2; nonlinear residual 4.61e-16 and finite gradients." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py > results.json && /home/maxwelhelp/main/bin/python3 nonlinear_check.py", "files": [ "skew_midpoint.py", "experiment.py", "nonlinear_check.py", "results.json" ], "limitations": "The benchmark is a low-dimensional harmonic oscillator rather than a learned GRU, Lorenz system, or sequential prediction task. The MVP handles one latent vector at a time, uses unoptimized per-component autograd Jacobians, and does not test training speed, batching, adaptive damping, or nonlinear model-learning accuracy." }