Models of physical processes often depend on parameters, such as material properties or source terms, that are only known with some uncertainty. Measurement data can be used to estimate these parameters and thereby improve the model's credibility. When measurements become expensive, it is important to choose the most informative data. This task becomes even more challenging when the model configurations vary and the data noise is correlated. In this poster we summarize our results in [1] and present an observability coefficient that describes the influence of the sensors on the inverse solution. It can guide optimal sensor selection towards a uniformly good parameter estimate over all admissible model configurations. We propose a sensor selection algorithm that iteratively improves the observability coefficient, and present numerical results for a steady‐state heat conduction problem with correlated noise.

We consider optimal sensor placement for a family of linear Bayesian inverse problems characterized by a deterministic hyper-parameter. The hyper-parameter describes distinct configurations in which measurements can be taken of the observed physical system. To optimally reduce the uncertainty in the system's model with a single set of sensors, the initial sensor placement needs to account for the non-linear state changes of all admissible configurations. We address this requirement through an observability coefficient which links the posteriors' uncertainties directly to the choice of sensors. We propose a greedy sensor selection algorithm to iteratively improve the observability coefficient for all configurations through orthogonal matching pursuit. The algorithm allows explicitly correlated noise models even for large sets of candidate sensors, and remains computationally efficient for high-dimensional forward models through model order reduction. We demonstrate our approach on a large-scale geophysical model of the Perth Basin, and provide numerical studies regarding optimality and scalability with regard to classic optimal experimental design utility functions.

Früher waren sie aus dem Vorlesungsalltag nicht wegzudenken: Die wächsernen Modelle aus dem Hause Ziegler in Freiburg. Ganz gleich, wo auf der Welt man in der ersten Hälfte des 20. Jahrhunderts Biologie studierte, Zieglers Modelle zur Entwicklung des Hühnerembryos oder die achtteilige Serie zu Wirbeltiergehirnen, aus dem weichen Naturmaterial gegossen und handbemalt, waren treue Gefährten.