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Neither Precision Nor Architecture Alone: Controlled Tests of Failure Remedies for Physics-Informed Neural Networks

arXiv · AI, language, vision and robotics · article · Aug 26, 2026 · UTC

Physics-Informed Neural Networks (PINNs) frequently fail on stiff or advection-dominated PDEs, and two recent accounts offer competing remedies: switching from FP32 to FP64 to repair an L-BFGS stopping artifact, or replacing the MLP with a state-space-model (SSM) backbone plus sub-sequence alignment to counter architectural simplicity bias. We test both under matched, seed-paired controls in a pre-registered 144-run study spanning convection, reaction, and wave, plus an independent 85-run convection/wave study; success is relative $\ell_2$ error below $0.05$. The two remedies act on disjoint r

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