Factorized Fourier Neural Operators
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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 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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