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Physics-informed neural networks for solving partial differential equations

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

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

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

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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spelling 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. 2024-06-05T10:09:45.4030841 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
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
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 - Mechanical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering
document_store_str 0
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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 0001-01-01T10:09:45Z
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