Fast Solver of 2D Maxwell’s Equations Based on Fourier Neural Operator

The finite difference time domain (FDTD) is a general numerical method to directly obtain the electric and magnetic fields of space for EM scattering and radiation problems. The numerical dispersion and the stability conditions put forward the limitation of time and space steps for FDTD, resulting in a very long simulation time, especially for the open domain scattering problem. Nowadays, Neural networks have been used to solve partial differential equations (PDEs) because it can learn the mappings between finite-dimensional Euclidean spaces. Fourier neural operator (FNO) is proposed to learn mappings between infinite-dimensional spaces of functions. And the Fourier transform makes FNO superior to the general neural operators in time complexity. In this paper, FNO is applied to solve Maxwell’s equations of a 2D scattering problem. Through three experiments, we verify the generalization ability of the FNO for source at different locations, different source type and different object shape. Because of the generalization ability, it is several hundred times faster than FDTD to solve Maxwell’s equations of a 2D scattering problem.