Session: CIE-23/24: AMS/SEIKM

Paper Number: 117766

117766 - Physics Informed Neural Networks for Estimation of Temperature Field and Thermal Conductivity 

   Heat conduction is one of the common heat transfer modes by transferring thermal energy within a medium or between materials in contact. This phenomenon is common in life and valuable in various engineering and scientific applications. Heat conduction problems described by partial differential equations (PDEs) have been fully developed to investigate temperature distribution in the temporal and spatial domains. With known thermal properties and boundary conditions, the temperature distribution can be obtained by forward modeling. 

   Generally, the forward modeling of temperature distribution is performed by solving PDEs. For many high-dimension models and complex scenarios, it is hard to obtain analytical solutions. Thus, numerical methods, such as finite difference method (FDM) and finite element method (FEM), are widely used in most problems and then the results are validated by experiments. However, numerical simulations cannot be directly used to inversely estimate the thermal properties of materials. The experimental measurement and optimization methods are the most common approaches for the estimation of thermal properties. With the high dependency between the thermal properties and temperature distribution, there is a pressing need to develop an efficient and accurate approach to inversely estimate the thermal properties with some available temperature readings.

   Recently, physics-informed neural networks (PINNs) were proposed to investigate heat transfer problems. Based on the automatic differentiation algorithm, the physical knowledge can be embedded into deep neural networks to solve the well-posed PDEs or ODEs. Previous studies have reported that PINNs not only have the ability to predict temperature fields but also to inversely estimate unknown parameters in PDEs. However, the PINNs are limited by the low accuracy and high computational cost when the automatic differentiation algorithm is used, especially for a long back propagation chain in the deep neural network. In this paper, a novel PINNs framework combined with numerical differentiation is proposed to estimate the temperature field and thermal conductivity simultaneously. Both the accuracy and efficiency of PINNs are also improved with the proposed numerical differentiation approach.

   The proposed framework consists of two coupled neural networks to train the temperature at each spatial-temporal point and identify the thermal conductivity respectively. The training process of both networks is carried out simultaneously. The obtained outputs are substituted into the discretized equations instead of taking automatic differentiation with respect to input data. The discretization of PDEs is based on traditional numerical methods. Specifically, the first-order forward difference is used to approximate the partial derivative term in the time domain, and the second-order central difference is used to approximate the partial derivative term in the spatial domain. The total loss function is composed of the mean squared error (MSE) between the predicted temperature and the measurements at the boundary, and the MSE of the discretized equation. By iteratively minimizing the loss function, the physical law will be embedded into the neural networks. The network for thermal property estimation is also tuned so that the relationship between the changing variables and the thermal property is explored.

 

Presenting Author: Yanglong Lu Hong Kong University of Science and Technology

Presenting Author Biography: Dr. Yanglong Lu is an assistant professor of Mechanical and Aerospace Engineering at the Hong Kong University of Science and Technology. He received his Ph.D. and B.S. degrees both in Department of Mechanical Engineering from Georgia Institute of Technology. Before joining the Hong Kong University of Science and Technology, he worked as a postdoctoral research fellow at University of Michigan. His research focuses on process monitoring of additive manufacturing processes, multi-physics modeling and simulation, and machine learning for smart manufacturing. His research interest also includes the investigation of physics-informed data driven approaches with applications in diagnosis and prognosis of medical diseases. He received ASME Computers and Information in Engineering Division (CIE) Best Ph.D. Dissertation Award in 2021.

Authors:

Yanglong Lu Hong Kong University of Science and Technology
Tong Zhu Hong Kong University of Science and Technology
Qiye Zheng Hong Kong University of Science and Technology