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Factorized Fourier Neural Operators

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arxiv 2111.13802 v4 pith:BYFQ5FRQ submitted 2021-11-27 cs.LG cs.CE

Alasdair Tran , Alexander Mathews , Lexing Xie , Cheng Soon Ong This is my paper · ORCID
classification cs.LGcs.CE
keywords f-fnoproblemfourierfactorizedflowlearningmagnitudeneural
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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.

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Cited by 16 Pith papers

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  3. Adaptive Mamba Neural Operators

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    ELECTRAFI predicts periodic electron densities by analytically Fourier-transforming a Gaussian mixture, reaching near-SOTA accuracy with up to 633× faster inference and ~20% end-to-end DFT speedups.

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    Adding NFM-style bi-interaction layers to PINNs and DeepONets improves accuracy on several high-dimensional smooth PDEs and shock-dominated conservation laws, but not on low-dimensional smooth problems.

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  15. A Neural Operator based on Dynamic Mode Decomposition

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