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

Autor:	Riffaud, Sébastien, Fernández, Miguel Angel, Lombardi, Damiano
Přispěvatelé:	COmputational Mathematics for bio-MEDIcal Applications (COMMEDIA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), ANR-18-CE46-0001,ADAPT,Méthodes tensorielles parallèles dynamiques et adaptatives(2018)
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	Tensor methods Parameter estimation Low-rank approximation Tensor methods Parameter estimation Uncertainty quantification Contents Low-rank approximation Uncertainty quantification Contents [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=od_______165::d4c7c98ff9c0967d7186baf3eb57c717 https://inria.hal.science/hal-03908682/file/main.pdf Zobrazit plný text záznamu