Accelerating PDE-constrained optimization by model order reduction with error control

Design optimization problems are often formulated as PDEconstrained optimization problems where the objective is a function of the output of a large-scale parametric dynamical system, obtained from the discretization of a PDE. To reduce its high computational cost, model order reduction techniques can be used. Two-sided Krylov-Padé type methods are very well suited since also the gradient to the design parameters can be computed accurately at a low cost. In Yue and Meerbergen, International J. of Numerical methods in Engineering, 2012, we embedded model reduction and parametric model order reduction in the damped BFGS method. In the current paper, we present a new provable convergent error-based trust region method that allows to better exploit interpolatory reduced models. Then, we propose two practical algorithms to fit in this framework. For our benchmark problems, we use a simple interpolatory model order reduction method based on two-sided Krylov methods for a single interpolatory point. Numerical experiments from civil engineering show that the new methods outperform damped BFGS accelerated by non-interpolatory reduced models.