Эксперимент: Weak-Entropy Residual Loss (#778)

{ "worked": false, "confidence": 10, "verdict": "Built and numerically verified the weak Burgers residual and entropy-sign mechanism in verify.py. The weak residual stayed near 2.5e-18 while the strong residual followed the predicted epsilon^-1/2 scaling, with observed log slope -0.50000001. However, the stated entropy convention gives S>0 for the physical entropy shock and S<0 for the anti-entropic orientation, so relu(S)^2 penalizes the physical solution and does not select admissibility; the idea fails as written.", "metrics": { "baseline": "Strong residual RMS increased from 0.8163 at epsilon=0.20 to 2.5813 at epsilon=0.02; observed log-log slope -0.50000001 versus predicted -0.5.", "idea": "Weak residual maximum absolute value was 2.47e-18 across the width sweep. Entropy S was +0.0497 to +0.1097 for the physical shock and exactly the negative for the anti-entropic orientation; the proposed positive-part penalty selects the wrong sign." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 verify.py", "files": [ "verify.py" ], "limitations": "No neural-network training mini-experiment was run because the core entropy penalty has a sign contradiction under the stated formula. The test used stationary smooth approximations to Burgers Riemann profiles rather than a time-dependent trained PINN; correcting the penalty to relu(-S)^2 would require a separate experiment." }