Physics-Informed Neural networks for Advanced modeling

Abstract

Artificial Intelligence (AI) strategies are massively emerging in several fields of academia and industrial research Wang & Liao (2004) due to the growing disposal of data, as well as the great improvement in computational resources. In the area of applied mathematics and simulations, AI strategies are being used to solve problems where classical methods fail (Cuomo et al., 2022). However, the amount of data required to analyze complex systems is often insufficient to make AI predictions reliable and robust. Physics-informed neural networks (PINNs) have been formulated (Raissi et al., 2019) to overcome the issues of missing data, by incorporating the physical knowledge into the neural network training. Thus, PINNs aim to approximate any differential equation by solving a minimization problem in an unsupervised learning setting, learning the unknown field in order to preserve the imposed constraints (boundaries and physical residuals). Formally, we consider the general form of a differential equation, which typically presents the most challenging issues from a numerical point of view.