Physics-informed deep learning for melting heat transfer analysis with model-based transfer learning

authored by: Hongwei Guo, Xiaoying Zhuang, Naif Alajlan, Timon Rabczuk
Abstract: We present an adaptive deep collocation method (DCM) based on physics-informed deep learning for the melting heat transfer analysis of a non-Newtonian (Sisko) fluid over a moving surface with nonlinear thermal radiation. Fitted neural network search (NAS) and model based transfer learning (TL) are developed to improve model computational efficiency and accuracy. The governing equations for this boundary-layer flow problem are derived using Buongiorno's and a nonlinear thermal radiation model. Next, similarity transformations are introduced to reduce the governing equations into coupled nonlinear ordinary differential equations (ODEs) subjected to asymptotic infinity boundary conditions. By incorporating physics constraints into the neural networks, we employ the proposed deep learning model to solve the coupled ODEs. The imposition of infinity boundary conditions is carried out by adding an inequality constraint to the loss function, with infinity added to the hyper-parameters of the neural network, which is updated dynamically in the optimization process. The effects of various dimensionless parameters on three profiles (velocity, temperature, concentration) are investigated. Finally, we demonstrate the performance and accuracy of the adaptive DCM with transfer learning through several numerical examples, which can be the promising surrogate model to solve boundary layer problems.
Organisation(s): Institute of Photonics
External Organisation(s): Tongji University
King Saud University
Bauhaus-Universität Weimar
Type: Article
Journal: Computers and Mathematics with Applications
Volume: 143
Pages: 303-317
No. of pages: 15
ISSN: 0898-1221
Publication date: 01.08.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Modelling and Simulation, Computational Theory and Mathematics, Computational Mathematics
Electronic version(s): https://doi.org/10.1016/j.camwa.2023.05.014 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{6559138a8bcb432d8b5eb336b33b8288,
title = "Physics-informed deep learning for melting heat transfer analysis with model-based transfer learning",
abstract = "We present an adaptive deep collocation method (DCM) based on physics-informed deep learning for the melting heat transfer analysis of a non-Newtonian (Sisko) fluid over a moving surface with nonlinear thermal radiation. Fitted neural network search (NAS) and model based transfer learning (TL) are developed to improve model computational efficiency and accuracy. The governing equations for this boundary-layer flow problem are derived using Buongiorno's and a nonlinear thermal radiation model. Next, similarity transformations are introduced to reduce the governing equations into coupled nonlinear ordinary differential equations (ODEs) subjected to asymptotic infinity boundary conditions. By incorporating physics constraints into the neural networks, we employ the proposed deep learning model to solve the coupled ODEs. The imposition of infinity boundary conditions is carried out by adding an inequality constraint to the loss function, with infinity added to the hyper-parameters of the neural network, which is updated dynamically in the optimization process. The effects of various dimensionless parameters on three profiles (velocity, temperature, concentration) are investigated. Finally, we demonstrate the performance and accuracy of the adaptive DCM with transfer learning through several numerical examples, which can be the promising surrogate model to solve boundary layer problems.",
keywords = "Boundary layer flow, Deep learning, Hyper-parameter optimization, Melting heat transfer, Physics-informed neural networks, Sensitivity analysis, Sisko fluid, Transfer learning",
author = "Hongwei Guo and Xiaoying Zhuang and Naif Alajlan and Timon Rabczuk",
year = "2023",
month = aug,
day = "1",
doi = "10.1016/j.camwa.2023.05.014",
language = "English",
volume = "143",
pages = "303--317",
journal = "Computers and Mathematics with Applications",
issn = "0898-1221",
publisher = "Pergamon Press",
}

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