A Data-Driven Neural Network Applied to Solving Maxwell’s Equations: A novel Fourier neural operator approach.

Abstract

The Fourier Neural Operator (FNO), a recently proposed neural network designed for solving partial differential equations (PDEs), is being explored to accelerate electromagnetic (EM) simulations. FNOs are data-driven models that learn to map material distributions to electromagnetic field solutions based on a full-wave simulation training dataset. Unlike conventional computational electromagnetic solvers that handle individual instances of Maxwell’s equations, FNOs learn an entire family of these equations. The Fourier Neural Operator excels in global feature extraction. When configured with cascaded multilayer Fourier Neural Operators, the network functions similarly to iterative solvers like the Born series expansion used for solving integral equations. In our electrostatic study, we train an FNO to predict electric potential given an arbitrary permittivity distribution in a unit square. In the electrodynamic study, we apply the FNO to an arbitrary-shaped scattering problem involving 2 D TMz coupled Maxwell’s equations. Numerical and electromagnetic benchmarks show that the FNO achieves state-of-the-art accuracy and can be up to three orders of magnitude faster than traditional finite difference method (FDM) solvers.