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.

翻译：当前大多数利用机器学习方法对多物理场（包括热弹性力学）进行建模的可用方法，主要聚焦于通过数据驱动或物理信息的多层感知机网络解决完整的多物理场问题。此类模型依赖对多层感知机进行增量逐步训练，导致计算成本升高；同时缺乏有限元法等现有数值方法的严谨性。我们提出了一种集成有限元神经网络框架，以加速求解耦合瞬态热弹性力学问题。本文开发了一种新型物理信息时间卷积网络，并将其嵌入有限元框架中，以利用神经网络的快速推理能力。PI-TCN模型捕捉多物理场问题中的部分场变量；随后，网络输出结果被用于通过有限元方法计算其他感兴趣的场变量。我们建立了一个在计算上解耦能量方程与线性动量方程的框架。首先开发PI-TCN模型，基于能量方程和应变数据预测整个仿真时间内温度场的时空演化。该PI-TCN模型被集成到有限元框架中，其输出的温度场被用于将温度效应引入线性动量方程。采用隐式欧拉时间离散格式求解有限元问题，所得计算成本与弱耦合热弹性力学问题相当，但具备求解完全耦合问题的能力。最后，通过多个数值算例展示了I-FENN在热弹性力学中的计算效率与泛化能力。