Li, Mou;
Wang, He;
Jimack, Peter K;
(2024)
Generative Modeling of Sparse Approximate Inverse Preconditioners.
In: Franco, L and DeMulatier, C and Paszynski, M and Krzhizhanovskaya, VV and Dongarra, JJ and Sloot, PMA, (eds.)
Computational Science – ICCS 2024. 24th International Conference, Malaga, Spain, July 2–4, 2024, Proceedings, Part III.
(pp. 378-392).
Springer: Cham, Switzerland.
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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.
| Type: | Book chapter |
|---|---|
| Title: | Generative Modeling of Sparse Approximate Inverse Preconditioners |
| ISBN-13: | 978-3-031-63758-2 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/978-3-031-63759-9_40 |
| Publisher version: | https://doi.org/10.1007/978-3-031-63759-9_40 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10215214 |
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