@article{WalterSchmidtKoerkel, author = {Walter, Sebastian F. and Schmidt, Andreas and K{\"o}rkel, Stefan}, title = {Adjoint-based optimization of experimental designs with many control variables}, series = {Journal of Process Control}, volume = {24}, journal = {Journal of Process Control}, number = {10}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0959-1524}, doi = {10.1016/j.jprocont.2014.06.019}, pages = {1504 -- 1515}, abstract = {We propose a method for an efficient optimization of experimental designs, using a combination of discrete adjoint computations, Taylor arithmetic and matrix calculus. Compared to the state of the art of using finite differences or the forward mode of automatic differentiation, our proposed approach leads to a reduction of the relative temporal complexity from linear to constant time in the number of control variables and measurement weights. We demonstrate that the advantageous complexity results are not only of theoretical nature, but lead to significant speedups in practice as well. With our implementation we are very close to the theoretical bound of the cheap gradient principle. We present one academic (spatially discretized heat equation) and two industrial application examples (biochemical process/Diesel-oxidation catalysis process) where we achieve speedups that range between 10 and 100. In addition to our core results, we also describe an efficient adjoint approach for the treatment of differential algebraic equations and present adjoint formulas for constrained least-squares problems.}, language = {de} } @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} }