Factorized Fourier Neural Operators
| Autor: | Tran, Alasdair, Mathews, Alexander, Xie, Lexing, Ong, Cheng Soon |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Published in The Eleventh International Conference on Learning Representations (2023). Code is available at https://github.com/alasdairtran/fourierflow |
| Databáze: | arXiv |
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