  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.
