Physics-informed neural networks for solving partial differential equations

Sharma, Prakhar; Tindall, Michelle; Nithiarasu, Perumal

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Physics-informed neural networks for solving partial differential equations

Prakhar Sharma

, Michelle Tindall, Perumal Nithiarasu

Artificial Intelligence in Heat Transfer: Advances in Numerical Heat Transfer Volume 6, Volume: 6

Swansea University Authors: Prakhar Sharma , Michelle Tindall, Perumal Nithiarasu

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Abstract

In recent years, Physics-Informed Neural Networks (PINNs) have gained popularity, across differentengineering disciplines, as an alternative to conventional numerical techniques for solving partialdifferential equations (PDEs). PINNs are physics-based deep learning frameworks that seamlesslyintegrat...

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Published in:	Artificial Intelligence in Heat Transfer: Advances in Numerical Heat Transfer Volume 6
Published:	CRC Press, Taylor and Francis Group LLC
URI:	https://cronfa.swan.ac.uk/Record/cronfa66597

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last_indexed	2024-11-25T14:18:29Z
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spelling	2024-07-24T15:43:41.0181452 v2 66597 2024-06-05 Physics-informed neural networks for solving partial differential equations c940112620a47fad0bab66de278a47b5 0000-0002-7635-1857 Prakhar Sharma Prakhar Sharma true false 9111447ad90bfa112e53275aa499f67c Michelle Tindall Michelle Tindall true false 3b28bf59358fc2b9bd9a46897dbfc92d 0000-0002-4901-2980 Perumal Nithiarasu Perumal Nithiarasu true false 2024-06-05 In recent years, Physics-Informed Neural Networks (PINNs) have gained popularity, across differentengineering disciplines, as an alternative to conventional numerical techniques for solving partialdifferential equations (PDEs). PINNs are physics-based deep learning frameworks that seamlesslyintegrate the measurements and the PDE in a multitask loss function. In forward problems,these measurements are initial (IC) and boundary conditions (BCs), whereas in the inverse problemsthey are sparse measurements such as temperature recorded by thermocouples. The scope ofPDEs applicable in PINNs could include integer-order PDEs, integro-differential equations, fractionalPDEs or even stochastic PDEs. This chapter presents a brief state-of-the-art overview ofPINNs for solving PDEs. Our discussion primarily focuses on solution to parametric problems,approaches to tackle stiff-PDEs and problems involving complex geometries. The advantages anddisadvantages of several PINNs frameworks are also discussed. Book chapter Artificial Intelligence in Heat Transfer: Advances in Numerical Heat Transfer Volume 6 6 CRC Press, Taylor and Francis Group LLC 0 0 0 0001-01-01 COLLEGE NANME COLLEGE CODE 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 Accelerate AI projects, which is part-funded by the European Regional Development Fund (ERDF) via the Welsh Government for giving us access to NVIDIA A100 40GB GPUs for batch training. We also acknowledge the support of NVIDIA academic hardware grant for donating us NVIDIA RTX A5000 24GB for local testing. 2024-07-24T15:43:41.0181452 2024-06-05T10:04:28.4763036 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering Prakhar Sharma 0000-0002-7635-1857 1 Michelle Tindall 2 Perumal Nithiarasu 0000-0002-4901-2980 3 66597__30542__e2ef8546b6b343699d57cee76865a730.pdf 66597.pdf 2024-06-05T10:09:35.6503591 Output 1097752 application/pdf Accepted Manuscript true Author accepted manuscript document released under the terms of a Creative Commons CC-BY licence using the Swansea University Research Publications Policy (rights retention). true eng https://creativecommons.org/licenses/by/4.0/deed.en
title	Physics-informed neural networks for solving partial differential equations
spellingShingle	Physics-informed neural networks for solving partial differential equations Prakhar Sharma Michelle Tindall Perumal Nithiarasu
title_short	Physics-informed neural networks for solving partial differential equations
title_full	Physics-informed neural networks for solving partial differential equations
title_fullStr	Physics-informed neural networks for solving partial differential equations
title_full_unstemmed	Physics-informed neural networks for solving partial differential equations
title_sort	Physics-informed neural networks for solving partial differential equations
author_id_str_mv	c940112620a47fad0bab66de278a47b5 9111447ad90bfa112e53275aa499f67c 3b28bf59358fc2b9bd9a46897dbfc92d
author_id_fullname_str_mv	c940112620a47fad0bab66de278a47b5_*_Prakhar Sharma 9111447ad90bfa112e53275aa499f67c__Michelle Tindall 3b28bf59358fc2b9bd9a46897dbfc92d_**_Perumal Nithiarasu
author	Prakhar Sharma Michelle Tindall Perumal Nithiarasu
author2	Prakhar Sharma Michelle Tindall Perumal Nithiarasu
format	Book chapter
container_title	Artificial Intelligence in Heat Transfer: Advances in Numerical Heat Transfer Volume 6
container_volume	6
institution	Swansea University
publisher	CRC Press, Taylor and Francis Group LLC
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hierarchy_parent_title	Faculty of Science and Engineering
department_str	School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering
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description	In recent years, Physics-Informed Neural Networks (PINNs) have gained popularity, across differentengineering disciplines, as an alternative to conventional numerical techniques for solving partialdifferential equations (PDEs). PINNs are physics-based deep learning frameworks that seamlesslyintegrate the measurements and the PDE in a multitask loss function. In forward problems,these measurements are initial (IC) and boundary conditions (BCs), whereas in the inverse problemsthey are sparse measurements such as temperature recorded by thermocouples. The scope ofPDEs applicable in PINNs could include integer-order PDEs, integro-differential equations, fractionalPDEs or even stochastic PDEs. This chapter presents a brief state-of-the-art overview ofPINNs for solving PDEs. Our discussion primarily focuses on solution to parametric problems,approaches to tackle stiff-PDEs and problems involving complex geometries. The advantages anddisadvantages of several PINNs frameworks are also discussed.
published_date	0001-01-01T20:31:22Z
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Physics-informed neural networks for solving partial differential equations

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