Эксперимент: Tropical support-restricted PINN (#1262)

{ "worked": true, "confidence": 8, "verdict": "Built a coefficient-based tropical support-restricted PINN for u'=1+u^2, u(0)=0, using the formally derived odd-power support of tan(t). The recurrence check exactly produced zero even coefficients, and across three fixed seeds the restricted model used 8 rather than 16 coefficients, reduced mean residual loss from 4.55e-6 to 8.42e-9, and reduced relative solution error from 2.25e-4 to 7.86e-6 at equal optimization steps. This is a clear toy-system signal for the claimed structural-sparsity effect, but it is not evidence yet for general PDEs or MLP coefficient heads.", "metrics": { "baseline": "Dense exponents 0..15; 16 parameters; mean final residual 4.554e-6; mean relative tan(t) error 2.246e-4 over 3 seeds.", "idea": "Odd exponents {1,3,...,15}; 8 parameters; mean final residual 8.419e-9; mean relative error 7.865e-6 over 3 seeds; exact formal-series check max even coefficient 0.0." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "run_experiment.py", "results.json" ], "limitations": "Only a one-dimensional Riccati ODE on t in [0,1] was tested, with one trainable scalar coefficient per basis exponent rather than the proposed nonlinear MLP coefficient head. No Van der Pol, Burgers, wall-clock speed, FLOP-normalized comparison, or broader support-analysis implementation was tested." }