A low-rank solver for parameter estimation and uncertainty quantification in linear time dependent systems of Partial Differential Equations

In this work we propose a low-rank solver in view of performing parameter estimation and uncertainty quantification in linear systems of Partial Differential Equations. The solution approximation is look for in a space-parameter separated form. The discretisation in the parameter direction is made e...

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Bibliographic Details
Published in:Journal of scientific computing 2024, Vol.99 (2)
Main Authors: Riffaud, Sébastien, Fernández, Miguel Angel, Lombardi, Damiano
Format: Article
Language:English
Subjects:
Mathematics
Numerical Analysis
Online Access:Get full text
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Summary:In this work we propose a low-rank solver in view of performing parameter estimation and uncertainty quantification in linear systems of Partial Differential Equations. The solution approximation is look for in a space-parameter separated form. The discretisation in the parameter direction is made evolve in time through a Markov Chain Monte Carlo method. The resulting method is a Bayesian sequential estimation of the parameters. The computational burden is mitigated by the introduction of an efficient interpolator, based on a reduced-basis built by exploiting the low-rank solves. The method is tested on three different applications.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-024-02488-3