MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces

TL;DR

This paper introduces MscaleFNO, a multi-scale Fourier neural operator that effectively captures high-frequency oscillations in functions, significantly improving wave scattering predictions in high-frequency regimes.

Contribution

The paper proposes a novel multi-scale Fourier neural operator architecture that reduces spectral bias and enhances learning of oscillatory functions compared to standard FNO.

Findings

MscaleFNO outperforms normal FNO in high-frequency wave scattering tasks.

The method captures various high-frequency components more effectively.

Numerical results show substantial improvement with similar network complexity.

Abstract

In this paper, a multi-scale Fourier neural operator (MscaleFNO) is proposed to reduce the spectral bias of the FNO in learning the mapping between highly oscillatory functions, with application to the nonlinear mapping between the coefficient of the Helmholtz equation and its solution. The MscaleFNO consists of a series of parallel normal FNOs with scaled input of the function and the spatial variable, and their outputs are shown to be able to capture various high-frequency components of the mapping's image. Numerical methods demonstrate the substantial improvement of the MscaleFNO for the problem of wave scattering in the high-frequency regime over the normal FNO with a similar number of network parameters.