Factorized Fourier Neural Operators

• URL: http://arxiv.org/abs/2111.13802v2
• Date: Tue, 30 Nov 2021 02:04:46 GMT
• Title: Factorized Fourier Neural Operators
• Authors: Alasdair Tran, Alexander Mathews, Lexing Xie, Cheng Soon Ong
• Abstract summary: The Factorized Fourier Neural Operator (F-FNO) is a learning-based method for simulating partial differential equations. We show that our model maintains an error rate of 2% while still running an order of magnitude faster than a numerical solver.
• Score: 77.47313102926017
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Fourier Neural Operator (FNO) is a learning-based method for efficiently simulating partial differential equations. We propose the Factorized Fourier Neural Operator (F-FNO) that allows much better generalization with deeper networks. With a careful combination of the Fourier factorization, a shared kernel integral operator across all layers, the Markov property, and residual connections, F-FNOs achieve a six-fold reduction in error on the most turbulent setting of the Navier-Stokes benchmark dataset. We show that our model maintains an error rate of 2% while still running an order of magnitude faster than a numerical solver, even when the problem setting is extended to include additional contexts such as viscosity and time-varying forces. This enables the same pretrained neural network to model vastly different conditions.

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