Derivative-extended POD reduced-order modeling for parameter estimation

• Verfasst von: Schmidt, Andreas [VerfasserIn]
• Verfasst von: Potschka, Andreas [VerfasserIn]
• Verfasst von: Körkel, Stefan [VerfasserIn]
• Verfasst von: Bock, Hans Georg [VerfasserIn]
• Titel: Derivative-extended POD reduced-order modeling for parameter estimation
• Verf.angabe: A. Schmidt, A. Potschka, S. Körkel, and H. Bock
• Umfang: 22 S.
• Fussnoten: Gesehen am 29.01.2018
• Titel Quelle: Enthalten in: Society for Industrial and Applied Mathematics: SIAM journal on scientific computing
• Jahr Quelle: 2013
• Band/Heft Quelle: 35(2013), 6, S. A2696-A2717
• ISSN Quelle: 1095-7197
• DOI: doi:10.1137/120896694
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1567757227

Abstract

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.