  In this paper, we propose the physics-informed supervised residual learning
(PISRL) which is a general framework for electromagnetic forward modeling based
on deep learning. PISRL is designed to solve a system of linear matrix
equations and not limited to a specific electromagnetic problem. Stationary and
non-stationary iterative PISRL neural networks (SIPISRLNN and NSIPISRLNN) are
designed based on the mathematical connection between residual neural network
(ResNet)[1] and stationary or non-stationary iterative methods. With
convolutional neural network mapping residuals and modifications, SIPISRLNN and
NSIPISRLNN can improve the approximated solutions via iterative process, which
mimics the procedure of solving linear equations by stationary and
non-stationary iterative methods. The generalities of SIPISRLNN and NSIPISRLNN
are validated by solving different types of volume integral equations (VIEs)
with non-lossy and lossy scatterers. In numerical results of non-lossy
scatterers, the mean squared errors (MSEs) of SIPISRLNN and NSIPISRLNN finally
converge below $3.152 \times 10^{-4}$ and $4.8925 \times 10^{-7}$; in results
of lossy scatterers, the MSEs converge below $1.2775 \times 10^{-4}$ and $1.567
\times 10^{-7}$. The generalization abilities of SIPISRLNN and NSIPISRLNN are
verified by testing them on the data sets of contrast shapes and different
incident frequencies that are unseen during the training process.
