A derivative-fidelity failure mode in physics-informed neural networks: strengthened benchmark evidence from function-value training
Not provided in the abstract
Abstract
This paper investigates the failure mode of derivative fidelity in physics-informed neural networks (PINNs) and demonstrates that good function value approximation does not guarantee accurate derivatives.
Reality Card
The study establishes that visually accurate function approximations can have significantly larger second-derivative errors, particularly in high-curvature regions.
The experiments reveal substantial second-derivative errors, especially near boundary regions, despite accurate function value approximations.
The main limitation is the reliance on automatic differentiation, which may not generalize well across different types of functions or neural network architectures.
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