Эксперимент: Value-Gradient Trajectory Collocation (#857)

{ "worked": true, "confidence": 6, "verdict": "Built Value-Gradient Trajectory Collocation with affine bounded min/max actions, stochastic steering, uniform-reservoir mixing, and a small PINN experiment. The checks confirmed zero-error affine corner selection, deterministic displacement scaling as gamma·dt, Brownian variance scaling as 2·sigma²·dt, and exact trajectory mixture fractions. The trajectory sampler did not improve this toy PINN: global residual MSE was 0.000706 versus 0.000359 for uniform sampling, and top-error MSE was 0.00246 versus 0.00116, so the mechanism was validated but the promised accuracy win was not observed.", "metrics": { "baseline": "Uniform PINN: global residual MSE 3.5895e-4; top-error residual MSE 1.1628e-3.", "idea": "Trajectory PINN: global residual MSE 7.0623e-4; top-error residual MSE 2.4586e-3. Math checks: affine max error 0; gamma displacement/prediction ratios approximately 1.0; sigma variance/prediction ratios 1.002, 0.999, 0.997; mixture trajectory fractions exactly matched alpha." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a small 1D toy steering field and 1D Hamilton-Jacobi PINN were tested; no 2D Burgers, double-integrator reachability, Sobol baseline, residual-based adaptive baseline, FLOP-normalized study, or extensive alpha/sigma/gain sweeps were run." }