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Article Dans Une Revue Journal of Scientific Computing Année : 2024

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

Résumé

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.
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Dates et versions

hal-03908682 , version 1 (20-12-2022)
hal-03908682 , version 2 (04-02-2024)

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Sébastien Riffaud, Miguel Angel Fernández, Damiano Lombardi. A low-rank solver for parameter estimation and uncertainty quantification in linear time dependent systems of Partial Differential Equations. Journal of Scientific Computing, 2024, 99 (2), pp.34. ⟨10.1007/s10915-024-02488-3⟩. ⟨hal-03908682v2⟩
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