A greedy sensor selection algorithm for hyperparameterized linear Bayesian inverse problems with correlated noise models

Journal of Computational Physics, vol. 498, pp. 112599

Abstract

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.

Authors 4

1. Nicole Aretz Aachen Aachen Institute for Advanced Study in Computational Engineering and Science

   RWTH Aachen University · Aachen Institute for Advanced Study in Computational Engineering Science · The University of Texas at Austin

   Affiliation as printed

   Aachen Institute for Advanced Study in Computational Engineering and Science, RWTH Aachen University, Schinkelstr. 2, 52062 Aachen, Germany

   Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, 201 E 24th St, Austin, TX 78712, USA

2. Peng Chen

   The University of Texas at Austin · Georgia Institute of Technology

   Affiliation as printed

   Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, 201 E 24th St, Austin, TX 78712, USA

   School of Computational Science and Engineering, Georgia Institute of Technology, 756 W Peachtree St NW, Atlanta, GA 30308, USA

3. Denise Degen Aachen Computational Geoscience

   RWTH Aachen University

   Affiliation as printed

   Computational Geoscience, Geothermics, and Reservoir Geophysics, RWTH Aachen University, Mathieustr. 30, 52074 Aachen, Germany

4. Karen Veroy corresponding

   Eindhoven University of Technology

   Affiliation as printed

   Center for Analysis, Scientific Computing and Applications, Department of Mathematics and Computer Science, Eindhoven University of Technology, 5612 AZ Eindhoven, the Netherlands