Factorized Fourier Neural Operators

By Alasdair Tran, Alexander Patrick Mathews, Lexing Xie, Cheng Soon Ong. International Conference on Learning Representations, 2021

305 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/50bfb95187503caf0bd0daa6077f6df9de4c7456

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Songming Liu
2. Zijie Li
3. Kazem Meidani
4. Haixu Wu
5. Chengyang Ying
6. Hang Su
7. Jianmin Wang
8. Zhengyi Wang

In Statistical and Nonlinear Physics

1. Songming Liu
2. Zijie Li
3. Kazem Meidani
4. Haixu Wu
5. Chengyang Ying
6. Hang Su
7. Jianmin Wang
8. Zhengyi Wang

Citations in the corpus

• GNOT: A General Neural Operator Transformer for Operator Learning (2023, background): “Some works also propose variants of FNO from other aspects (Gupta et al., 2021; Wen et al., 2022; Tran et al., 2021).”
• Transolver: A Fast Transformer Solver for PDEs on General Geometries (2024, methodology): “F-FNO F-FNO (Tran et al., 2023) enhances model efficiency by employing factorization on the Fourier domain.”
• Transformer for Partial Differential Equations' Operator Learning (2022, background): “Fourier Neural Operator (FNO) (Li et al., 2021a) and its variants (Li et al., 2021b; Guibas et al., 2022; Tran et al., 2021) have shown promising results in various applications (Pathak et al., 2022; Wen et al., 2022).”