A Complex-Valued Neural Operator for Solving 2-D Wave Equations Based on Graph Neural Networks

In this work, we propose a complex-valued neural operator (CV-NeuralOp) based on graph neural networks (GNNs) to solve 2-D wave equations. Inspired by Green’s function method for solving partial differential equations, CV-NeuralOp applies an iterative algorithmic framework to approximate the integral operator with Green’s function theory. Inherited from Green’s function method and GNNs, CV-NeuralOp demonstrates its proficiency in accommodating diverse domain shapes and grid densities. The efficacy of CV-NeuralOp is verified by solving 2-D wave equations defined in both square and cruciform domains. Its generalization ability is further assessed in terms of various scatterer shapes and different grid densities. Numerical results substantiate that CV-NeuralOp attains commendable computational precision, accompanied by a reduction in computing time when compared to the method of moments (MoM). This work presents a deep learning-based approach to approximate an integral operator for accelerating EM simulation.