A Fully Data-Driven Solver for Combined Field Integral Equations of 3-D Conducting Bodies Based on Graph Neural Networks

In this article, we present a fully data-driven solver for solving combined field integral equations (CFIEs) of 3-D conducting bodies based on graph neural networks (GNNs). Rao-Wilton-Glisson (RWG) basis functions are employed to discretely and accurately represent the geometry of 3-D conducting bodies. A concise and informative graph representation is then constructed by treating each RWG function as a node in the graph, enabling the flow of current between nodes. With the transformed graphs, GraphSolver is developed to directly predict real and imaginary parts of the x, y, and z components of the surface current densities at each node (RWG function). Numerical results demonstrate the efficacy of GraphSolver in solving CFIEs for 3-D conducting bodies with varying levels of geometric complexity, including basic 3-D targets, nose-cone-shaped targets, and airplane-shaped targets.