Seminar in Numerical Analysis: Mario S. Mommer (Universität Heidelberg)

On the robustification of optimum experimental design problems

Optimum experimental design (OED) is the problem of finding setups for an experiment in such a way that the collected data allows for optimally accurate estimation of the parameters of interest - taking into account an experimental budget. In practice, the parameters are only approximately known as a matter of course, while at the same time, solving an OED problem is in a way equivalent to magnifying the dependence of the system response on these quantities.  As a consequence, designs computed on the basis of a "good guess" of the parameters may underperform dramatically in practice, especially for problems involving nonlinear models.

In this talk, we consider robust formulations for optimum experimental design that work under significant uncertainty. Our focus is on problem settings in which the model is described by differential equations of some type that are solved numerically. Our approach is based on a semi-infinite programming formulation in which we exploit additional problem structure, together with sparse grids, to ensure tractability. The talk includes numerical experiments to illustrate and compare the effectiveness of the approaches.

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