  Most currently available methods for modeling multiphysics, including
thermoelasticity, using machine learning approaches, are focused on solving
complete multiphysics problems using data-driven or physics-informed
multi-layer perceptron (MLP) networks. Such models rely on incremental
step-wise training of the MLPs, and lead to elevated computational expense;
they also lack the rigor of existing numerical methods like the finite element
method. We propose an integrated finite element neural network (I-FENN)
framework to expedite the solution of coupled transient thermoelasticity. A
novel physics-informed temporal convolutional network (PI-TCN) is developed and
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; then, the network output is used to compute the other
fields of interest using the finite element method. 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 spatiotemporal
evolution of the temperature field across the simulation time based on the
energy equation and 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 I-FENN's computational efficiency and generalization
capability in thermoelasticity through several numerical examples.
