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arXiv Machine Learning By Brandon Zhao, Yixuan Wang, Jonathan T. Barron, Katherine L. Bouman, Dor Verbin, Pratul P. Srinivasan

Fourier Feature Pyramids for Physics-Informed Neural Networks

Read the original on arXiv Machine Learning →

The paper introduces beignet, a neural field architecture that replaces the random Fourier feature embedding in physics-informed neural networks with a trainable multi‑resolution Fourier feature pyramid. By using Fourier interpolation and spectral derivatives, beignet efficiently computes spatial derivatives and scales accuracy through the feature pyramid rather than the neural network size. Experiments show that beignet achieves more accurate PDE solutions with fewer parameters than existing PINN methods and can reach machine‑precision residuals on the inviscid Burgers blowup problem using the Adam optimizer.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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