Seminar in Numerical Analysis: Bernard Haasdonk (Universität Stuttgart)

Reduced Basis Surrogate Models for Parameter Optimization of Evolution Problems

In this presentation we introduce a method for rapid and certified parameter optimization of problems with PDE constraints given by evolution equations. We make use of an RB-formulation for a general class of evolution problems covering standard iterative time-stepping schemes. The reduced spaces for such problems are beneficially constructed by the POD-Greedy procedure, for which we recently provided theoretical foundation by convergence rate proofs. Extensions of this procedure involve parameter- and time-partitioning approaches. We will demonstrate, how these ingredients can be used in iterative direct parameter optimization problems. In addition to approximate surrogate optimization results, we provide rigorous a-posteriori error bounds for solutions, outputs, sensitivities and optimal parameters.

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