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

TL;DR

This work introduces I-FENN, an integrated finite element neural network framework that accelerates transient thermoelasticity by embedding a physics-informed temporal convolutional network (PI-TCN) to surrogate the energy equation. The PI-TCN is trained offline and integrated into FE calculations, effectively decoupling energy from momentum while preserving fully coupled thermoelastic responses through the neural surrogate. Compared with PINNs and data-driven TCNs, PI-TCN within I-FENN achieves higher accuracy and substantial computational savings, demonstrated across 1D, 2D, and 3D examples and across mesh transfers. The approach enables scalable, efficient multiphysics simulations and suggests avenues for extending physics-informed ML surrogates to broader thermo-electro-mechanical and other coupled problems.

Abstract

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.

Figures (35)

• Figure 1: Schematic representation of a body with prescribed displacement, temperature, traction, and flux boundary conditions.
• Figure 2: Physics-informed neural network based on MLP neural networks.
• Figure 3: Illustration for the TCN architecture: (a) A stack of dilated convolutions with dilation factors $d = 1,2,4$ and a filter size $k_{size} = 3$. The pink elements in the sequences are the ones whose information was propagated to a specific pink element in the output sequence. For example, the last element in the output sequence can access information from all the elements from the input sequence and other pink elements in the hidden layers.
• Figure 4: Proposed physics-informed temporal convolutional network (PI-TCN).
• Figure 5: Illustration of the I-FENN framework for thermoelasticity. The pre-trained NN is embedded inside the weak form of the balance of linear momentum of the thermoelasticity problem.