Neither Precision Nor Architecture Alone: Controlled Tests of Failure Remedies for Physics-Informed Neural Networks
Read the original on arXiv Machine Learning →Physics‑Informed Neural Networks (PINNs) often fail on stiff or advection‑dominated partial differential equations. This study compares two proposed fixes—switching from FP32 to FP64 precision to address an L‑BFGS stopping artifact, and replacing the MLP with a state‑space‑model (SSM) backbone plus sub‑sequence alignment to mitigate architectural simplicity bias—using a pre‑registered, seed‑paired 144‑run experiment across convection, reaction, and wave problems, plus an independent 85‑run study. The results show that the remedies act on disjoint subsets of regimes and seeds: precision changes affect some seeds in opposite directions, alignment improves success in hard convection cases, and the SSM backbone alone succeeds on many reaction seeds, but none of the remedies fully substitutes for the other, and all must be evaluated jointly and reported per seed.
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