Solving Combined Field Integral Equations With Physics-Informed Graph Residual Learning for EM Scattering of 3-D PEC Targets

In this study, physics-informed graph residual learning (PhiGRL) is proposed as an effective and robust deep learning (DL)-based approach for 3-D electromagnetic (EM) modeling. Extended from physics-informed supervised residual learning (PhiSRL), PhiGRL emulates the computation of a fixed-point iteration method to iteratively modify a candidate solution until convergence by applying graph neural networks (GNNs) to predict modifications. The application of GNNs enables PhiGRL to adaptively deal with unstructured data and varying unknown numbers in 3-D EM modeling, where most off-the-shelf DL techniques are inapplicable. PhiGRL is first applied to solve the combined-field integral equations (CFIEs) of basic 3-D perfect electric conductor (PEC) targets, including spheroids, conical frustums, and hexahedrons, in both supervised and unsupervised learning manners. Its generalization abilities on different incident frequencies and target shapes are then verified separately. Numerical results show that PhiGRL can achieve good numerical precision with a significant reduction in computation time (online prediction). PhiGRL is further migrated to simulate more complicated 3-D PEC targets through transfer learning, including missilehead- and airplane-shaped targets. This study explores the possibility of applying DL together with EM physics for 3-D EM modeling.