用图神经网络加速三维导体电磁场计算，提升求解效率。
Study on a Fast Solver for Combined Field Integral Equations of 3D Conducting Bodies Based on Graph Neural Networks
- 将矩量法基函数建模为图节点，用图神经网络直接预测电流分布。
- 在复杂几何目标上实现快速求解，计算速度显著优于传统方法。
- 适合需要高效电磁仿真的人工智能与天线设计领域研究者。
本文提出一种基于图神经网络（GNN）的快速求解器（GraphSolver），用于求解三维导体物体的混合场积分方程（CFIE）。采用瑞-威尔顿-格利森（RWG）基函数对三维导体几何进行离散化表示，精确刻画表面结构。通过将每个RWG函数视为图中的节点，构建简洁且信息丰富的图结构，实现节点间电流流动的建模。在此基础上，GraphSolver被设计用于直接预测每个节点处表面电流密度的x、y、z分量的实部和虚部。数值结果表明，该方法在不同几何复杂度的目标上均表现优异，包括基本三维目标、导弹形目标和飞机形目标，具备良好的泛化能力与求解效率。
原文摘要 · Abstract (English)
In this paper, we present a graph neural networks (GNNs)-based fast solver (GraphSolver) for solving combined field integral equations (CFIEs) of 3D conducting bodies. Rao-Wilton-Glisson (RWG) basis functions are employed to discretely and accurately represent the geometry of 3D 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 3D conducting bodies with varying levels of geometric complexity, including basic 3D targets, missile-shaped targets, and airplane-shaped targets.
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