Physics-Informed Neural Networks

Abstract

Physics-informed neural networks (PINNs) are used for problems where data are scarce. The underlying physics is enforced via the governing differential equation, including the residual in the cost function. PINNs can be used for both solving and discovering differential equations. In this chapter, PINNs are illustrated with three one-dimensional examples. The first example shows how the displacement of a static bar can be computed. The temperature evolution in a one-dimensional spatial domain is determined using the non-linear heat equation, using both a continuous and a discrete approach. Finally, the data-driven identification is illustrated with the static bar, where the cross-sectional stiffness is estimated from the displacement.