Spatial-Temporal Electromagnetic Field Simulation Based on Fourier Neural Operator

In the study of electromagnetic (EM) applications, solving Maxwell’s equations to obtain spatial-temporal field evolution is a critical step. The deep learning (DL) is a new promising way to solve partial differential equations (PDEs), by training various neural networks to identify the mapping between inputs and solutions. These approaches are much faster than traditional computational electromagnetic methods after the networks are trained. Previous works focuses on predicting low dimensional results, while the spatial-temporal field evolution of a realistic EM simulation using four-dimensional (4D) datasets is rarely studied. In this work, we employ an innovative deep learning framework, the Fourier neural operator (FNO), to solve Maxwell's equations. FNO leverages the Fourier transform to learn mappings between high-dimensional function spaces, efficiently capturing global information and significantly improving computational efficiency and accuracy. Compared to traditional numerical algorithms, FNO achieves a two-order-of-magnitude speedup and supports super-resolution capabilities, greatly enhancing simulation efficiency. Furthermore, FNO successfully addresses the challenges of three-dimensional (3D) EM simulations, providing a new framework for solving complex EM problems.