Physics-Informed Neural Networks for Inverse Electromagnetic Problems

PDE-constrained inverse problems are very common in electromagnetism, just like in other engineering fields. Their ill-posedness (in the sense of Hadamard) makes their solution non-trivial, also taking into account that solving PDEs could be computationally intensive. In this context, first, we will introduce three frameworks that concern surrogate models and physics-informed neural networks (PINNs). Second, we will show the capability of a PINN in solving an ill-posed direct problem. In fact, PINNs are designed to be trained to satisfy the given training data as well as the relevant governing equations. This way, a neural network can be guided with training data that do not necessarily need to be complete.