Learning to solve related linear systems
Learning to solve related linear systems
Solving multiple parametrised related systems is an essential component of many numerical tasks, and learning from the already solved systems will make this process faster. In this work, we propose a novel probabilistic linear solver over the parameter space. This leverages information from the solved linear systems in a regression setting to provide an efficient posterior mean and covariance. We advocate using this as companion regression model for the preconditioned conjugate gradient method, and discuss the favourable properties of the posterior mean and covariance as the initial guess and preconditioner. We also provide several design choices for this companion solver. Numerical experiments showcase the benefits of using our novel solver in a hyperparameter optimisation problem.
stat.ML, cs.LG, cs.NA, math.NA
103-121
Hegde, Disha
5e7d8e1b-5b2a-4828-9e49-42e9e94c9725
Cockayne, Jon
da87c8b2-fafb-4856-938d-50be8f0e4a5b
1 September 2025
Hegde, Disha
5e7d8e1b-5b2a-4828-9e49-42e9e94c9725
Cockayne, Jon
da87c8b2-fafb-4856-938d-50be8f0e4a5b
Hegde, Disha and Cockayne, Jon
(2025)
Learning to solve related linear systems.
Proceedings of Machine Learning Research, 271, .
Abstract
Solving multiple parametrised related systems is an essential component of many numerical tasks, and learning from the already solved systems will make this process faster. In this work, we propose a novel probabilistic linear solver over the parameter space. This leverages information from the solved linear systems in a regression setting to provide an efficient posterior mean and covariance. We advocate using this as companion regression model for the preconditioned conjugate gradient method, and discuss the favourable properties of the posterior mean and covariance as the initial guess and preconditioner. We also provide several design choices for this companion solver. Numerical experiments showcase the benefits of using our novel solver in a hyperparameter optimisation problem.
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2503.17265v1
- Author's Original
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2503.17265v2
- Accepted Manuscript
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hegde25a
- Version of Record
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Accepted/In Press date: 20 August 2025
Published date: 1 September 2025
Keywords:
stat.ML, cs.LG, cs.NA, math.NA
Identifiers
Local EPrints ID: 506082
URI: http://eprints.soton.ac.uk/id/eprint/506082
ISSN: 2640-3498
PURE UUID: c7043909-eaa4-47bd-84af-45a0734cfda4
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Date deposited: 28 Oct 2025 17:58
Last modified: 09 Dec 2025 03:05
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Author:
Disha Hegde
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