Jul 24, 2023
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We consider the problem of solving partial differential equations (PDEs) with Fourier neural operators (FNOs), which operate in the frequency domain. Since the laws of physics do not depend on the coordinate system used to describe them, it is desirable to encode such symmetries in the neural operator architecture for better performance and easier learning. While encoding symmetries in the physical domain using group theory has been studied extensively, how to capture symmetries in the frequency domain is under-explored. In this work, by leveraging the equivariance property of Fourier transform, we extend group convolutions to the frequency domain and design Fourier layers that are equivariant to rotations, translations, and reflections. The resulting G-FNO architecture features strong robustness to both symmetries and discretization. Results show that our proposed G-FNO yields consistent and significant performance improvements.We consider the problem of solving partial differential equations (PDEs) with Fourier neural operators (FNOs), which operate in the frequency domain. Since the laws of physics do not depend on the coordinate system used to describe them, it is desirable to encode such symmetries in the neural operator architecture for better performance and easier learning. While encoding symmetries in the physical domain using group theory has been studied extensively, how to capture symmetries in the frequency…
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