Accelerating PDE-Constrained Optimization by Model Order Reduction with Error Control

Design optimization problems are often formulated as PDE-constrained 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 our previous work, we embedded model order reduction and parametric model order reduction in the damped BFGS method. In this talk, 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, ETR and EP, to t 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.status: publishe