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Physics-informed neural networks for solving partial differential equations
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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...
| Published in: | Artificial Intelligence in Heat Transfer: Advances in Numerical Heat Transfer Volume 6 |
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| Published: |
CRC Press, Taylor and Francis Group LLC
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa66597 |
| 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 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. |
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| College: |
Faculty of Science and Engineering |
| Funders: |
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. |