Derivative-extended POD reduced-order modeling 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 inf...
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| Hauptverfasser: | , , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
December 3, 2013
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| In: |
SIAM journal on scientific computing
Year: 2013, Jahrgang: 35, Heft: 6, Pages: A2696-A2717 |
| ISSN: | 1095-7197 |
| DOI: | 10.1137/120896694 |
| Online-Zugang: | Verlag, Volltext: http://dx.doi.org/10.1137/120896694 Verlag, Volltext: http://epubs.siam.org/doi/abs/10.1137/120896694 
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| Verfasserangaben: | A. Schmidt, A. Potschka, S. Körkel, and H. Bock |
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| 520 | |a 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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