Reduced Order Modeling for Optimization of Large Scale Dynamical Systems
Master of Arts
This thesis compares different techniques for applying reduced order modeling to PDE constrained optimization and develops a new method based on recent work by Dihlmann and Haasdonk. Model reduction techniques have been used to significantly reduce computation time for solving PDEs. But naive application of model reduction in the optimization context may lead to incorrect results. To overcome this, Dihlmann and Haasdonk recently proposed a method applicable to problems with a small number of optimization parameters. I develop an approach that extends this idea to accommodate problems with a larger number of optimization parameters and, under certain assumptions, satisfies an a posteriori error estimate. I show that the proposed scheme achieves an accurate approximation with as much as a 70 fold decrease in computation time compared to solving the full model. I also show my method compares favorably with an approach proposed by Kunisch and Volkwein.
Dynamical systems; Optimal control; Model reduction; Proper orthogonal decomposition