| Abstract: |
| Experimental design determines the quality of available data and often has a strong effect on the well- or ill-posedness of an inverse problem. The classical optimal experimental design methodology rephrases the task of finding a design that yields informative data as an optimization problem that minimizes uncertainty of the reconstruction. In this talk, we want to extend this methodology to what we call qualitative experimental design. By relaxing the optimality to a sufficiency equirement, we concentrate on finding suitable designs that yield data which is sensitive w.r.t. the unknown parameter and thus allows its inference - at least locally. This opens a new methodological toolbox, and we lay out two strategies:
\begin{itemize}
\item some theoretical well-posedness proofs are constructive and rely on the design of suitable measurements. Possibly after discretization, these constructions can be translated to the practical setting in a relaxation-of-theory.
\item a more generally applicable approach samples designs according to a sensitivity based distribution derived from matrix sketching. This method shall be investigated on an easy toy system, the potential reconstruction problem related to the stationary Schroedinger equation.
\end{itemize}
We shall demonstrate both approaches on an inverse problem from kinetic PDEs related to bacterial chemotaxis. |
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