Эксперимент: FFT Weak-Residual Engine (#838)

{ "worked": false, "confidence": 9, "verdict": "Built fft_weak_engine.py implementing FFT weak Burgers residuals, Fourier test-function differentiation, Parseval accounting, quadratic-flux 3/2 dealiasing, frequency truncation, and projection timing. The core predictions manifested: Parseval error was 3.39e-16, Fourier derivative error was 1.89e-14, aliasing stayed about 3e-16 through kmax/N=0.333 then rose to 0.100 and 0.205 at 0.4 and 0.45 while dealiasing stayed below 5e-16; truncated spectral and physical projection energies agreed to about 2e-16. However, the PyTorch Burgers training comparison failed with “One of the differentiated Tensors does not require grad,” so there is no valid baseline-versus-idea training result or demonstrated end-to-end win.", "metrics": { "baseline": "Direct trigonometric projection: 19.46 ms; FFT selected projection: 0.307 ms; direct/FFT=63.4x. Strong-vs-weak training benchmark: failed before producing metrics.", "idea": "FFT projection relative numerical check 6.97e-15; dealiasing relative error 3.60e-16 to 4.96e-16 across tested cutoffs, versus raw alias error 0.100-0.205 above the 2/3 transition; Parseval and derivative checks at machine precision." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 fft_weak_engine.py", "files": [ "fft_weak_engine.py", "run.out", "results.json" ], "limitations": "The neural training benchmark was not successfully executed, so loss reduction, wall-clock training speed, memory, shock position, and solution error were not tested. The speed comparison is NumPy CPU projection timing rather than a matched GPU PINN workload; random weak quadrature was also not implemented." }