Geometry-Informed Neural Operator with Learnable Activation Functions for Electric Field Integral Equations of 3-D PEC Targets

In this article, a geometry-informed neural operator with learnable activation functions is proposed. It incorporates a data-driven approach for solving the electric field integral equation for three-dimensional (3-D) perfect electric conductor (PEC) targets. The geometry-informed Kolmogorov-Arnold neural operator (GI-KANO) consists of Fourier neural operators (FNO), graph neural operators (GNO), and Kolmogorov-Arnold networks (KAN). FNO can learn the function mappings of query points regularly distributed in space, and GNO can map query points to the surface points of a target as the decoder. Moreover, the kernel functions of the GNO are represented by KAN. The activation functions of KAN are learnable. GI-KANO can solve the electric field integral equation (EFIE) in 3-D space. The purpose of solving the EFIE is to determine the surface current distribution of a target. The shape of the 3-D PEC targets is represented by point clouds. Each point represents the center of each discrete mesh element. Each mesh element needs to solve its corresponding value of the surface current density through EFIE. An electromagnetic scattering simulation dataset is built by the method of moments (MoM), including spheroids, quadrangular prisms and cone frustums as 3-D targets. The experimental results show that GI-KANO can achieve good results in solving electric field integral equations with different targets at different angles of plane wave incidence and reduce the computation time. Owing to the super-resolution capabilities of neural operators, models trained on coarse point clouds can achieve comparable results on dense point clouds during testing.