[Submitted on 25 Jul 2026]
Title:A derivative-fidelity failure mode in physics-informed neural networks: strengthened benchmark evidence from function-value training
View a PDF of the paper titled A derivative-fidelity failure mode in physics-informed neural networks: strengthened benchmark evidence from function-value training, by Koji Koyamada
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Abstract:Physics-informed neural networks (PINNs) use automatic differentiation to impose differential-equation residuals, but good agreement in function values does not necessarily imply accurate derivatives. This paper formulates derivative fidelity as a failure mode of PINNs and tests it with one-dimensional benchmarks. Multilayer perceptrons are trained only on function values for sin(x) and exp(x), while second derivatives obtained by automatic differentiation are evaluated separately. The hypothesis is strengthened by additional tests over training-point density, activation functions, endpoint-dense evaluation, and both L2 and maximum-error diagnostics. The results show that visually accurate function approximation can coexist with substantially larger second-derivative errors, especially near high-curvature boundary regions. The experiment provides a diagnostic protocol for distinguishing value accuracy from physics-residual reliability.
Subjects:
Machine Learning (cs.LG)
Cite as: arXiv:2609.13171 [cs.LG]
(or arXiv:2609.13171v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.13171
arXiv-issued DOI via DataCite
Submission history
From: Koji Koyamada [view email] [v1] Sat, 25 Jul 2026 13:52:51 UTC (800 KB)
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