Sensor selection for hyper‐parameterized linear Bayesian inverse problems

Abstract

AbstractModels 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.