Approximating electromagnetic fields in discontinuous media using a single physics-informed neural network

Abstract

Physics-Informed Neural Networks (PINNs) are a new family of numerical methods, based on deep learning, for modeling boundary value problems. They offer an advantage over traditional numerical methods for high-dimensional, parametric, and data-driven problems. However, they perform poorly on problems where the solution exhibits high frequencies, such as discontinuities or sharp gradients. In this work, we develop a PINN-based solver for modeling three-dimensional, transient and static, parametric electromagnetic problems in discontinuous media. We use the first-order Maxwell's equations to train the neural network. We use a level-set function to represent the interface with a continuous function, and to enrich the network's inputs with high-frequencies and interface information. Finally, we validate the proposed methodology on multiple 3D, parametric, static, and transient problems.