Physics-informed neural network for modeling dynamic linear elasticity

In this work, we present the physics-informed neural network (PINN) modelapplied particularly to dynamic problems in solid mechanics. We focus onforward and inverse problems. Particularly, we show how a PINN model can beused efficiently for material identification in a dynamic setting. In thiswork, we assume linear continuum elasticity. We show results fortwo-dimensional (2D) plane strain problem and then we proceed to apply the sametechniques for a three-dimensional (3D) problem. As for the training data weuse the solution based on the finite element method. We rigorously show thatPINN models are accurate, robust and computationally efficient, especially as asurrogate model for material identification problems. Also, we employstate-of-the-art techniques from the PINN literature which are an improvementto the vanilla implementation of PINN. Based on our results, we believe thatthe framework we have developed can be readily adapted to computationalplatforms for solving multiple dynamic problems in solid mechanics.