Physics Embedded Iterative Neural Network for Solving Integral Equations

The integral equations describing forward scattering problems are generally solved numerically by iterative methods. In this work, we apply iterative deep neural network to solve both surface integral equation (SIE) and volume integral equation (VIE). The Green’s function describing wave physics is involved in both training and prediction stage. The trained neural network can predict either the surface current density on conducting targets from SIE, or the total electromagnetic (EM) field in dielectric volume from VIE. We validate this method with two numerical examples, one for SIE and the other for VIE. This work may provide us a new perspective of incorporating wave physics into neural networks for fast EM computation.