QUANTIFYING UNCERTAINTY OF PHYSICS-INFORMED NEURAL NETWORKS FOR CONTINUUM MECHANICS APPLICATIONS

Physics-informed neural networks (PINNs) are a relatively new technique that has gained significant attention in recent years as a versatile and robust way to solve a wide range of physical problems, including continuum mechanics. One of the main advantages of using PINNs is that they can directly incorporate physical laws and constraints into the learning process, allowing them to accurately capture the underlying behavior of a system without the need for large amounts of labeled training data. Nevertheless, as they result from a stochastic optimization process, quantifying the model uncertainty is a crucial step before considering real-world applications. In this paper, we study the uncertainty related to the optimization process on PINNs applied to continuum mechanics. We introduce two possible implementations of PINNs to solve boundary value problems (direct and parallel). To be able to quantify the accuracy of the approximations, we address a linear elasticity problem that has an analytical solution. The