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

arXiv:2609.02110 · cs.LG · Submitted 2026-09-02 · Read on arXiv

cs.LG

Submitted: 2026-09-02

Updated: 2026-09-02

Comments: 17 pages, 4 figures, 1 table

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Accuracy — 11× in this paper · explained in 1 episode
• Benchmark — 5× in this paper · explained in 2 episodes
• PDE residual — 5× in this paper · explained in 2 episodes
• Adam — 4× in this paper · explained in 2 episodes
• Physics-Informed Neural Networks (PINNs) — 2× in this paper · explained in 6 episodes
• Spectral Informed Neural Network — 2× in this paper
• Higher-order derivatives — 1× in this paper · explained in 2 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes

Sources

• FlashPDE: A Drop-In Fused Triton Operator Library for Neural PDE Solvers
• Neural Spectral Element Methods for stiff multiphysics PDEs with electrochemical transport benchmarks
• Fourier Feature Pyramids for Physics-Informed Neural Networks

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