Efficient Fourier Neural Operators by Group Convolution and Channel Shuffling

Abstract

Fourier neural operators (FNOs) have emerged as data-driven alternatives to conventional numerical simulators for solving partial differential equations (PDEs). However, these models typically require a substantial number of learnable parameters. In this study, we explore parameter-efficient FNO architectures through modifications in their width, depth, and applications of group convolutiopn and channel shuffling. We perform benchmark on different problems on learning the operator of Maxwell's equations and Darcy flow equations. Our approach leads to significant improvement in prediction accuracy for both small and large FNO models. The proposed methods are widely adaptable across various problem types and neural operator architectures, aiming to boost prediction accuracy.