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

Abstract: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 regime-and-seed slices: neither substitutes for the other. On hard convection ($\beta{=}50$), alignment recovers 2/5 seeds in FP32 and 3/5 in FP64, where the unaligned SSM succeeds on 0/5 seeds at either precision and the vanilla MLP moves only from 0/5 to 1/5 across the precision switch---the recoveries trace to the alignment objective, not the backbone. On reaction the backbone alone already succeeds on 3/5--4/5 seeds, so each remedy covers a regime the other does not. Responses are also seed-specific: the same precision switch flips individual seeds in opposite directions and, on wave, lowers median error with no statistically significant success gain. Tightening the inner L-BFGS tolerance in an independent repeated-step runner likewise lowers median error at a large runtime cost, with success counts unchanged. Precision, stopping, backbone, and alignment must therefore be evaluated jointly and reported per seed.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2608.25327 [cs.LG]

(or arXiv:2608.25327v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.25327 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.