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Factorized Fourier Neural Operators
Alasdair Tran · Alexander Mathews · Lexing Xie · Cheng Soon Ong

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, weight sharing, 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.

Author Information

Alasdair Tran (Australian National University)
Alexander Mathews (Australian National University)
Lexing Xie (Australian National University)
Cheng Soon Ong (Data61 and Australian National University)

Cheng Soon Ong is a principal research scientist at the Machine Learning Research Group, Data61, CSIRO, and is the director of the machine learning and artificial intelligence future science platform at CSIRO. He is also an adjunct associate professor at the Australian National University. He is interested in enabling scientific discovery by extending statistical machine learning methods.

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