Florido, J., Wang, H., Khan, A. et al. (1 more author) (2024) Investigating Guiding Information for Adaptive Collocation Point Sampling in PINNs. In: Computational Science – ICCS 2024: 24th International Conference, Malaga, Spain, July 2–4, 2024, Proceedings, Part III. International Conference on Computational Science (ICCS) 2024: 24th International Conference, 02-04 Jul 2024, Málaga. Springer , Berlin, Heidelberg , pp. 323-337. ISBN 978-3-031-63758-2
Abstract
Physics-informed neural networks (PINNs) provide a means of obtaining approximate solutions of partial differential equations and systems through the minimisation of an objective function which includes the evaluation of a residual function at a set of collocation points within the domain. The quality of a PINNs solution depends upon numerous parameters, including the number and distribution of these collocation points. In this paper we consider a number of strategies for selecting these points and investigate their impact on the overall accuracy of the method. In particular, we suggest that no single approach is likely to be “optimal” but we show how a number of important metrics can have an impact in improving the quality of the results obtained when using a fixed number of residual evaluations. We illustrate these approaches through the use of two benchmark test problems: Burgers’ equation and the Allen-Cahn equation.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Author | ACM 2024. This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in Computational Science – ICCS 2024: 24th International Conference, Malaga, Spain, July 2–4, 2024, Proceedings, Part III, https://doi.org/10.1007/978-3-031-63759-9_36. |
Keywords: | Partial differential equations, Deep learning, Physics-informed neural networks, Adaptivity |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Computation Science & Engineering |
Depositing User: | Symplectic Publications |
Date Deposited: | 29 Apr 2024 09:55 |
Last Modified: | 26 Jul 2024 14:33 |
Published Version: | https://dl.acm.org/doi/abs/10.1007/978-3-031-63759... |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/978-3-031-63759-9_36 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:211954 |
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