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：目前大多数利用机器学习方法对多物理场（包括热弹性）进行建模的方法，都集中于使用数据驱动或物理信息的多层感知器（MLP）网络来解决完整的多物理场问题。此类模型依赖于MLP的逐步增量训练，导致计算开销较高；同时，它们也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（I-FENN）框架，以加速耦合瞬态热弹性问题的求解。我们开发了一种新颖的物理信息时间卷积网络（PI-TCN），并将其嵌入有限元框架中，以利用神经网络（NN）的快速推理能力。PI-TCN模型捕获多物理场问题中的部分场；然后，利用有限元方法根据网络输出计算其他感兴趣的场。我们建立了一个从计算上将能量方程与线性动量方程解耦的框架。首先，我们基于能量方程和应变数据开发了一个PI-TCN模型，用于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，其中PI-TCN的输出（温度）用于将温度效应引入线性动量方程。有限元问题采用隐式欧拉时间离散格式求解，其计算成本与弱耦合热弹性问题相当，但能够求解完全耦合问题。最后，我们通过多个数值算例展示了I-FENN在热弹性问题中的计算效率和泛化能力。