Physics-informed deep learning for three-dimensional transient heat transfer analysis of functionally graded materials

authored by: Hongwei Guo, Xiaoying Zhuang, Xiaolong Fu, Yunzheng Zhu, Timon Rabczuk
Abstract: We present a physics-informed deep learning model for the transient heat transfer analysis of three-dimensional functionally graded materials (FGMs) employing a Runge–Kutta discrete time scheme. Firstly, the governing equation, associated boundary conditions and the initial condition for transient heat transfer analysis of FGMs with exponential material variations are presented. Then, the deep collocation method with the Runge–Kutta integration scheme for transient analysis is introduced. The prior physics that helps to generalize the physics-informed deep learning model is introduced by constraining the temperature variable with discrete time schemes and initial/boundary conditions. Further the fitted activation functions suitable for dynamic analysis are presented. Finally, we validate our approach through several numerical examples on FGMs with irregular shapes and a variety of boundary conditions. From numerical experiments, the predicted results with PIDL demonstrate well agreement with analytical solutions and other numerical methods in predicting of both temperature and flux distributions and can be adaptive to transient analysis of FGMs with different shapes, which can be the promising surrogate model in transient dynamic analysis.
Organisation(s): Institute of Photonics
External Organisation(s): Tongji University
Xi'an Modern Chemistry Research Institute
University of California (UCLA)
Bauhaus-Universität Weimar
Type: Article
Journal: Computational mechanics
Volume: 72
Pages: 513-524
No. of pages: 12
ISSN: 0178-7675
Publication date: 09.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-023-02287-x (Access: Open)
https://doi.org/10.1007/s00466-023-02350-7 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{b028741f6b4e45c89a88f179af19dced,
title = "Physics-informed deep learning for three-dimensional transient heat transfer analysis of functionally graded materials",
abstract = "We present a physics-informed deep learning model for the transient heat transfer analysis of three-dimensional functionally graded materials (FGMs) employing a Runge–Kutta discrete time scheme. Firstly, the governing equation, associated boundary conditions and the initial condition for transient heat transfer analysis of FGMs with exponential material variations are presented. Then, the deep collocation method with the Runge–Kutta integration scheme for transient analysis is introduced. The prior physics that helps to generalize the physics-informed deep learning model is introduced by constraining the temperature variable with discrete time schemes and initial/boundary conditions. Further the fitted activation functions suitable for dynamic analysis are presented. Finally, we validate our approach through several numerical examples on FGMs with irregular shapes and a variety of boundary conditions. From numerical experiments, the predicted results with PIDL demonstrate well agreement with analytical solutions and other numerical methods in predicting of both temperature and flux distributions and can be adaptive to transient analysis of FGMs with different shapes, which can be the promising surrogate model in transient dynamic analysis.",
keywords = "Activation function, Deep learning, Discontinuous time scheme, Functionally graded materials, Heat transfer, Physics-informed",
author = "Hongwei Guo and Xiaoying Zhuang and Xiaolong Fu and Yunzheng Zhu and Timon Rabczuk",
note = "Funding Information: The authors extend their appreciation to the Distinguished Scientist Fellowship Program (DSFP) at King Saudi University for funding this work. ",
year = "2023",
month = sep,
doi = "10.1007/s00466-023-02287-x",
language = "English",
volume = "72",
pages = "513--524",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "3",
}

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