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

arXiv: https://arxiv.org/abs/2608.25327 · HTML: https://mlsanity.com/paper/2608.25327/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 20 references that are in the map.
- First posted on arXiv 26 Aug 2026.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Improving Reproducibility in Machine Learning Research (A Report from the NeurIPS 2019 Reproducibility Program)](https://mlsanity.com/paper/2003.12206/) (2020)
- [Challenges in Training PINNs: A Loss Landscape Perspective](https://mlsanity.com/paper/2402.01868/) (2024)
- [PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs](https://mlsanity.com/paper/2306.08827/) (2023)
- [PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks](https://mlsanity.com/paper/2307.11833/) (2023)
- [FP64 is All You Need: Rethinking Failure Modes in Physics-Informed Neural Networks](https://mlsanity.com/paper/2505.10949/) (2025)
- [Sub-Sequential Physics-Informed Learning with State Space Model](https://mlsanity.com/paper/2502.00318/) (2025)
- [Unveiling Multi-regime Patterns in SciML: Distinct Failure Modes and Regime-specific Optimization](https://mlsanity.com/paper/2605.29153/) (2026)

## Abstract (arXiv)

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 ℓ2 error below 0.05. The two remedies act on disjoint regime-and-seed slices: neither substitutes for the other. On hard convection (β=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.