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Derivate-extended pod reduced-order modelling for parameter estimation

  • In this article we consider model reduction via proper orthogonal decomposition (POD) and its application to parameter estimation problems constrained by parabolic PDEs. We use a first discretize then optimize approach to solve the parameter estimation problem and show that the use of derivative information in the reduced-order model is important. We include directional derivatives directly in the POD snapshot matrix and show that, equivalently to the stationary case, this extension yields a more robust model with respect to changes in the parameters. Moreover, we propose an algorithm that uses derivative-extended POD models together with a Gauss--Newton method. We give an a posteriori error estimate that indicates how far a suboptimal solution obtained with the reduced problem deviates from the solution of the high dimensional problem. Finally we present numerical examples that showcase the efficiency of the proposed approach.

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Metadaten
Author:Andreas Schmidt, Andreas Potschka, Stefan KörkelGND, Hans Georg Bock
DOI:https://doi.org/10.1137/120896694
ISSN:1095-7197
ISSN:1064-8275
Parent Title (English):SIAM Journal on Scientific Computing
Publisher:SIAM
Place of publication:Philadelphia, Pa.
Document Type:Article
Language:English
Year of first Publication:2013
Release Date:2022/12/08
Tag:error estimates; parameter estimation; proper orthogonal decomposition
Volume:35
Issue:6
Institutes:Fakultät Informatik und Mathematik
Publication:Externe Publikationen
research focus:Lebenswissenschaften und Ethik
Licence (German):Keine Lizenz - Es gilt das deutsche Urheberrecht: § 53 UrhG