Complex-valued Neural Operator for Solving 2D Wave Equation Based on Graph Neural Network

In this work, we propose a complex-valued neural operator (CV-NeuralOp) based on graph neural networks (GNN) to solve 2D wave equation. Inspired by the 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 the Green’s function method and GNN, CV-NeuralOp demonstrates its proficiency in accommodating diverse domain shapes and grid densities. The efficacy of CV-NeuralOp is verified by solving 2D 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.