Fourier Neural Operator for Parametric Partial Differential Equations | Zongyi Li's Talk
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Fourier Neural Operator for Parametric Partial Differential Equations | Zongyi Li's Talk

Nov 20, 2020
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The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For partial differential equations (PDEs), neural operators directly learn the mapping from any functional parametric dependence to the solution. Thus, they learn an entire family of PDEs, in contrast to classical methods which solve one instance of the equation. In this work, we formulate a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture. We perform experiments on Burgers' equation, Darcy flow, and Navier-Stokes equation. The Fourier neural operator is the first ML-based method to successfully model turbulent flows with zero-shot super-resolution. It is up to three orders of magnitude faster compared to traditional PDE solvers. Additionally, it achieves superior accuracy compared to previous learning-based solvers under fixed resolution.

1:30 Introduction 8:08 Neural Operator 17:30 Graph-based Operator 28:03 Fourier Neural Operator 32:41 Experiments 40:52 Future Work 42:27 Takeaways 43:31 Questions
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