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 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.