Physics-informed neural networks for scientific modeling: uses, implementations, and directions

Physics-informed neural networks (PINNs) are a recently-developed scientific machine learning (SciML) approach useful for predicting behavior of systems governed by differential equations (DEs). Compared to classical methods like finite element method (FEM), PINNs can be easily set up and trained on general DEs and geometries. In this work, we will discuss uses of PINNs in different scientific domains. Our focus will be on the use of pinn-jax, an open-source library we have designed to enable easy development and training of PINNs on varied problems, including forward prediction and inverse estimation. We have designed pinn-jax to be easily extensible while also featuring implementations of some common techniques for enhancing PINNs, and we will demonstrate these on different problems. Particular attention will be paid to evaluating PINNs' performance on problems that vary in behavior across different temporal and spatial scales.