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

TL;DR

This paper advances physics-informed neural networks (PINNs) for modeling 3D electromagnetic problems with material discontinuities, improving convergence and handling static and transient regimes without explicit interface conditions.

Contribution

It introduces a domain decomposition approach and analyzes Maxwell's equations formulations, enhancing PINN performance for discontinuous media.

Findings

PINNs effectively model electromagnetic problems with discontinuities.

Using the first-order Maxwell's equations improves interface problem handling.

Domain decomposition enhances convergence rates of PINNs.

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.