I-FENN for thermoelasticity based on physics-informed temporal convolutional network (PI-TCN)

Abstract

We propose an integrated finite element neural network (I-FENN) framework to expedite the solution of coupled multiphysics problems. A physics-informed temporal convolutional network (PI-TCN) is embedded within the finite element framework to leverage the fast inference of neural networks (NNs). The PI-TCN model captures some of the fields in the multiphysics problem, and their derivatives are calculated via automatic differentiation available in most machine learning platforms. The other fields of interest are computed using the finite element method. We introduce I-FENN for the solution of transient thermoelasticity, where the thermo-mechanical fields are fully coupled. We establish a framework that computationally decouples the energy equation from the linear momentum equation. We first develop a PI-TCN model to predict the temperature field based on the energy equation and available strain data. The PI-TCN model is integrated into the finite element framework, where the PI-TCN output (temperature) is used to introduce the temperature effect to the linear momentum equation. The finite element problem is solved using the implicit Euler time discretization scheme, resulting in a computational cost comparable to that of a weakly-coupled thermoelasticity problem but with the ability to solve fully-coupled problems. Finally, we demonstrate the computational efficiency and generalization capability of I-FENN in thermoelasticity through several numerical examples