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A Computational Comparison of Fourier Spectral Differentiation and Spatial Automatic Differentiation in Periodic Physics-Informed Neural Networks

arXiv · AI, language, vision and robotics · article · Sep 2, 2026 · UTC

Physics-informed neural networks (PINNs) commonly evaluate the spatial derivatives appearing in partial differential equation residuals using automatic differentiation (AD), whose computational and memory costs can become substantial when multiple or high-order derivatives are required. We perform a controlled comparison of spatial AD and Fourier spectral differentiation in periodic physical-space PINNs. Within each paired experiment, the neural representation, temporal differentiation, optimizer, sampling procedure, and training schedule are held fixed, so that the two cases differ only in th

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