Physics-Informed Supervised Residual Learning for Electromagnetic Modeling

TL;DR

This paper introduces a physics-informed deep learning framework called PhiSRL for 2D electromagnetic modeling, leveraging residual networks and fixed-point iteration concepts to accurately solve integral equations with high precision.

Contribution

The paper presents a novel physics-informed residual learning approach that combines fixed-point iteration theory with CNNs for electromagnetic modeling, improving accuracy and generalization.

Findings

Achieved mean squared errors of ~10^{-4} and ~10^{-7} for different models.

Validated the effectiveness on lossless and lossy scatterers.

Demonstrated strong generalization capabilities.

Abstract

In this study, physics-informed supervised residual learning (PhiSRL) is proposed to enable an effective, robust, and general deep learning framework for 2D electromagnetic (EM) modeling. Based on the mathematical connection between the fixed-point iteration method and the residual neural network (ResNet), PhiSRL aims to solve a system of linear matrix equations. It applies convolutional neural networks (CNNs) to learn updates of the solution with respect to the residuals. Inspired by the stationary and non-stationary iterative scheme of the fixed-point iteration method, stationary and non-stationary iterative physics-informed ResNets (SiPhiResNet and NiPhiResNet) are designed to solve the volume integral equation (VIE) of EM scattering. The effectiveness and universality of PhiSRL are validated by solving VIE of lossless and lossy scatterers with the mean squared errors (MSEs) converging to $\sim 10^{-4}$ (SiPhiResNet) and $\sim 10^{-7}$ (NiPhiResNet). Numerical results further verify the generalization ability of PhiSRL.