@article{SchmidtPotschkaKoerkeletal., author = {Schmidt, Andreas and Potschka, Andreas and K{\"o}rkel, Stefan and Bock, Hans Georg}, title = {Derivate-extended pod reduced-order modelling for parameter estimation}, series = {SIAM Journal on Scientific Computing}, volume = {35}, journal = {SIAM Journal on Scientific Computing}, number = {6}, publisher = {SIAM}, address = {Philadelphia, Pa.}, issn = {1095-7197}, doi = {10.1137/120896694}, 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.}, language = {en} } @article{WeilerKoerkel, author = {Weiler, Christoph Karl Felix and K{\"o}rkel, Stefan}, title = {Optimum experimental design for extended Gaussian disorder modeled organic semiconductor devices}, series = {Journal of Applied Physics}, volume = {113}, journal = {Journal of Applied Physics}, number = {9}, publisher = {AIP}, address = {Melville, NY}, doi = {10.1063/1.4794365}, abstract = {We apply optimum experimental design (OED) to organic semiconductors modeled by the extended Gaussian disorder model (EGDM) which was developed by Pasveer et al. [Phys. Rev. Lett. 94, 206601 (2005)]. We present an extended Gummel method to decouple the corresponding system of equations and use automatic differentiation to get derivatives with the required accuracy for OED. We show in two examples, whose parameters are taken from Pasveer et al. [Phys. Rev. Lett. 94, 206601 (2005)] and Mensfoort and Coehoorn [Phys. Rev. B 78, 085207 (2008)] that the linearized confidence regions of the parameters can be reduced significantly by applying OED resulting in new experiments with a different setup.}, language = {en} }