Mathematics

Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems for partial differential equations. We provide an overview of currently available mathematical guarantees for PINNs and related models that constitute the backbone of physics-informed machine learning. A detailed review of available results on approximation, generalization and training errors and their behaviour with respect to the type of the PDE and the dimension of the underlying domain is presented.