Factorized Fourier Neural Operators
Abstract
We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the performance gap between pure machine learning approaches to that of the best numerical or hybrid solvers. This is achieved with new representations - separable spectral layers and improved residual connections - and a combination of training strategies such as the Markov assumption, Gaussian noise, and cosine learning rate decay. On several challenging benchmark PDEs on regular grids, structured meshes, and point clouds, the F-FNO can scale to deeper networks and outperform both the FNO and the geo-FNO, reducing the error by 83% on the Navier-Stokes problem, 31% on the elasticity problem, 57% on the airfoil flow problem, and 60% on the plastic forging problem. Compared to the state-of-the-art pseudo-spectral method, the F-FNO can take a step size that is an order of magnitude larger in time and achieve an order of magnitude speedup to produce the same solution quality.
Cite
@article{arxiv.2111.13802,
title = {Factorized Fourier Neural Operators},
author = {Alasdair Tran and Alexander Mathews and Lexing Xie and Cheng Soon Ong},
journal= {arXiv preprint arXiv:2111.13802},
year = {2023}
}
Comments
Published in The Eleventh International Conference on Learning Representations (2023). Code is available at https://github.com/alasdairtran/fourierflow