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. Borrowing strength from the solved systems and learning 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
Hegde, Disha
5e7d8e1b-5b2a-4828-9e49-42e9e94c9725
Cockayne, Jon
da87c8b2-fafb-4856-938d-50be8f0e4a5b
21 March 2025
Hegde, Disha
5e7d8e1b-5b2a-4828-9e49-42e9e94c9725
Cockayne, Jon
da87c8b2-fafb-4856-938d-50be8f0e4a5b
[Unknown type: UNSPECIFIED]
Abstract
Solving multiple parametrised related systems is an essential component of many numerical tasks. Borrowing strength from the solved systems and learning 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.
Text
2503.17265v1
- Author's Original
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Accepted/In Press date: 21 March 2025
Published date: 21 March 2025
Keywords:
stat.ML, cs.LG, cs.NA, math.NA
Identifiers
Local EPrints ID: 502369
URI: http://eprints.soton.ac.uk/id/eprint/502369
ISSN: 2331-8422
PURE UUID: 89879998-a2ad-4bc5-ba9e-3f7df36c7838
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Date deposited: 24 Jun 2025 16:40
Last modified: 20 Sep 2025 02:20
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Author:
Disha Hegde
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