Physics-Informed Neural Networks for the Numerical Modeling of Steady-State and Transient Electromagnetic Problems with Discontinuous Media

Abstract: Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize three-dimensional electromagnetic, parametric problems, with material discontinuities, covering both static and transient regimes. By replacing the discontinuous material properties with a continuous approximation, we eliminate the need to directly enforce interface conditions. Using the Neural Tangent Kernel (NTK) analysis, we show that using the first-order formulation of Maxwell's equations is more suitable for interface problems. We introduce a PINN-based decomposition on overlapping domains to enhance the convergence rate of the PINN.