Certified PDE-Constrained Parameter Optimization by Reduced Basis Surrogate Models

Bernard Haasdonk* and Markus Dihlmann

PDE-constrained parameter optimization problems with arbitrary output functionals may be quite expensive, when using standard PDE-solvers. Instead we use RB surrogate models for approximately and rapidly solving the optimization problem. Ingredients of our scheme comprise RB-spaces for the solution, its sensitivity derivatives and rigorous a-posteriori error bounds for the solution, derivatives, output functional and the suboptimal parameters. In particular we present two types of a posteriori error estimators for the parameters. Experiments on an instationary convection-diffusion problem demonstrate the benefits of the approach.

Mathematics Subject Classification: 35Q93

Keywords: Reduced Basis Methods, PDE constrained Optimization, a posteriori Error Estimation

Minisymposion: Adaptivity and Model Order Reduction in PDE Constrained Optimization