Li, M., Wang, H. and Jimack, P. orcid.org/0000-0001-9463-7595 (2024) Generative modeling of Sparse Approximate Inverse Preconditioners. In: Computational Science – ICCS 2024: 24th International Conference, Malaga, Spain, July 2–4, 2024, Proceedings, Part III. International Conference on Computational Science (ICCS), 02-04 Jul 2024, Málaga. Springer , Berlin, Heidelberg , pp. 378-392. ISBN 978-3-031-63758-2
Abstract
We present a new deep learning paradigm for the generation of sparse approximate inverse (SPAI) preconditioners for matrix systems arising from the mesh-based discretization of elliptic differential operators. Our approach is based upon the observation that matrices generated in this manner are not arbitrary, but inherit properties from differential operators that they discretize. Consequently, we seek to represent a learnable distribution of high-performance preconditioners from a low-dimensional subspace through a carefully-designed autoencoder, which is able to generate SPAI preconditioners for these systems. The concept has been implemented on a variety of finite element discretizations of second- and fourth-order elliptic partial differential equations with highly promising results.
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_40 |
Keywords: | Deep learning, Sparse matrices, Preconditioning, Elliptic partial differential equations, Finite element methods |
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 10:13 |
Last Modified: | 26 Jul 2024 14:57 |
Published Version: | https://dl.acm.org/doi/10.1007/978-3-031-63759-9_4... |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/978-3-031-63759-9_40 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:211956 |
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