arXiv Machine Learning By Adarsh Ganeshram, Valentin Duruisseaux, Haydn Maust, Zongyi Li, Yixuan Wang, Daniel Leibovici, Oscar Bruno, Thomas Hou, Anima Anandkumar

FC-PINO: High Precision Physics-Informed Neural Operators via Fourier Continuation

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arXiv Machine Learning
Oct 8

Fourier Feature Pyramids for Physics-Informed Neural Networks

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.

By Brandon Zhao, Yixuan Wang, Jonathan T. Barron, Katherine L. Bouman, Dor Verbin, Pratul P. Srinivasan
arXiv Machine Learning
Jun 5

On the training of physics-informed neural operators for solving parametric partial differential equations

arXiv:2606. 06164v1 Announce Type: new Abstract: Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data.

By Nanxi Chen, Chuanjie Cui, Airong Chen, Sifan Wang, Rujin Ma
Hugging Face Trending Papers
Jun 4

On the training of physics-informed neural operators for solving parametric partial differential equations

Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data. By incorporating physical constraints into the training objective, PINOs combine the cross-instance generalization of neural operators with the data efficiency of physics-informed learning.