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arXiv Machine Learning By Xilai Liang, Zhao Zhang

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

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The study compares two methods for computing spatial derivatives in physics‑informed neural networks (PINNs): automatic differentiation (AD) and Fourier spectral differentiation. Using identical neural architectures, training schedules, and data sampling, the authors evaluate both approaches on periodic PINNs for the Allen–Cahn, Korteweg–de Vries, and Kuramoto–Sivashinsky equations. Fourier spectral differentiation achieves significant speedups (2.90×–18.52×) and reduces GPU memory usage by 68.7%–94.1% while maintaining comparable solution accuracy.

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