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Hyperparameter selection for physics-informed neural networks (PINNs) – Application to discontinuous heat conduction problems

Prakhar Sharma Orcid Logo, Llion Evans Orcid Logo, Michelle Tindall Orcid Logo, Perumal Nithiarasu Orcid Logo

Numerical Heat Transfer, Part B: Fundamentals, Pages: 1 - 15

Swansea University Authors: Prakhar Sharma Orcid Logo, Llion Evans Orcid Logo, Perumal Nithiarasu Orcid Logo

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DOI (Published version): 10.1080/10407790.2023.2264489

Abstract

In recent years, physics-informed neural networks (PINNs) have emerged as an alternative to conventional numerical techniques to solve forward and inverse problems involving partial differential equations (PDEs). Despite its success in problems with smooth solutions, implementing PINNs for problems...

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Published in: Numerical Heat Transfer, Part B: Fundamentals
ISSN: 1040-7790 1521-0626
Published: Informa UK Limited 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa64585
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spelling v2 64585 2023-09-21 Hyperparameter selection for physics-informed neural networks (PINNs) – Application to discontinuous heat conduction problems c940112620a47fad0bab66de278a47b5 0000-0002-7635-1857 Prakhar Sharma Prakhar Sharma true false 74dc5084c47484922a6e0135ebcb9402 0000-0002-4964-4187 Llion Evans Llion Evans true false 3b28bf59358fc2b9bd9a46897dbfc92d 0000-0002-4901-2980 Perumal Nithiarasu Perumal Nithiarasu true false 2023-09-21 FGSEN In recent years, physics-informed neural networks (PINNs) have emerged as an alternative to conventional numerical techniques to solve forward and inverse problems involving partial differential equations (PDEs). Despite its success in problems with smooth solutions, implementing PINNs for problems with discontinuous boundary conditions (BCs) or discontinuous PDE coefficients is a challenge. The accuracy of the predicted solution is contingent upon the selection of appropriate hyperparameters. In this work, we performed hyperparameter optimization of PINNs to find the optimal neural network architecture, number of hidden layers, learning rate, and activation function for heat conduction problems with a discontinuous solution. Our aim was to obtain all the settings that achieve a relative L2 error of 10% or less across all the test cases. Results from five different heat conduction problems show that the optimized hyperparameters produce a mean relative L2 error of 5.60%. Journal Article Numerical Heat Transfer, Part B: Fundamentals 1 15 Informa UK Limited 1040-7790 1521-0626 Discontinuous boundaries conditions, heat conduction, hyperparameter tuning, physics-informed neural networks, stiff partial differential equation 9 10 2023 2023-10-09 10.1080/10407790.2023.2264489 http://dx.doi.org/10.1080/10407790.2023.2264489 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University This work is part-funded by the United Kingdom Atomic Energy Authority (UKAEA) and the Engineering and Physical Sciences Research Council (EPSRC) under the Grant Agreement Numbers EP/W006839/1, EP/T517987/1, and EP/R012091/1. We acknowledge the support of Supercomputing Wales and AccelerateAI projects, which is part-funded by the European Regional Development Fund (ERDF) via the Welsh Government for giving us access to NVIDIA A100 40 GB GPUs for batch training. We also acknowledge the support of NVIDIA academic hardware grant for donating us NVIDIA RTX A5000 24 GB for local testing. 2023-10-18T15:20:21.6492024 2023-09-21T12:04:10.8672869 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Prakhar Sharma 0000-0002-7635-1857 1 Llion Evans 0000-0002-4964-4187 2 Michelle Tindall 0000-0003-3034-9636 3 Perumal Nithiarasu 0000-0002-4901-2980 4 64585__28821__73d8e6a8fee142ffa9d46ed411907eab.pdf 64585.VOR.pdf 2023-10-18T15:18:26.2710390 Output 1981229 application/pdf Version of Record true © 2023 The Author(s). Published with license by Taylor & Francis Group, LLC. Distributed under the terms of a Creative Commons Attribution 4.0 License (CC BY 4.0). true eng https://creativecommons.org/licenses/by/4.0/
title Hyperparameter selection for physics-informed neural networks (PINNs) – Application to discontinuous heat conduction problems
spellingShingle Hyperparameter selection for physics-informed neural networks (PINNs) – Application to discontinuous heat conduction problems
Prakhar Sharma
Llion Evans
Perumal Nithiarasu
title_short Hyperparameter selection for physics-informed neural networks (PINNs) – Application to discontinuous heat conduction problems
title_full Hyperparameter selection for physics-informed neural networks (PINNs) – Application to discontinuous heat conduction problems
title_fullStr Hyperparameter selection for physics-informed neural networks (PINNs) – Application to discontinuous heat conduction problems
title_full_unstemmed Hyperparameter selection for physics-informed neural networks (PINNs) – Application to discontinuous heat conduction problems
title_sort Hyperparameter selection for physics-informed neural networks (PINNs) – Application to discontinuous heat conduction problems
author_id_str_mv c940112620a47fad0bab66de278a47b5
74dc5084c47484922a6e0135ebcb9402
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author_id_fullname_str_mv c940112620a47fad0bab66de278a47b5_***_Prakhar Sharma
74dc5084c47484922a6e0135ebcb9402_***_Llion Evans
3b28bf59358fc2b9bd9a46897dbfc92d_***_Perumal Nithiarasu
author Prakhar Sharma
Llion Evans
Perumal Nithiarasu
author2 Prakhar Sharma
Llion Evans
Michelle Tindall
Perumal Nithiarasu
format Journal article
container_title Numerical Heat Transfer, Part B: Fundamentals
container_start_page 1
publishDate 2023
institution Swansea University
issn 1040-7790
1521-0626
doi_str_mv 10.1080/10407790.2023.2264489
publisher Informa UK Limited
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
url http://dx.doi.org/10.1080/10407790.2023.2264489
document_store_str 1
active_str 0
description In recent years, physics-informed neural networks (PINNs) have emerged as an alternative to conventional numerical techniques to solve forward and inverse problems involving partial differential equations (PDEs). Despite its success in problems with smooth solutions, implementing PINNs for problems with discontinuous boundary conditions (BCs) or discontinuous PDE coefficients is a challenge. The accuracy of the predicted solution is contingent upon the selection of appropriate hyperparameters. In this work, we performed hyperparameter optimization of PINNs to find the optimal neural network architecture, number of hidden layers, learning rate, and activation function for heat conduction problems with a discontinuous solution. Our aim was to obtain all the settings that achieve a relative L2 error of 10% or less across all the test cases. Results from five different heat conduction problems show that the optimized hyperparameters produce a mean relative L2 error of 5.60%.
published_date 2023-10-09T15:20:23Z
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