A greedy sensor selection algorithm for hyperparameterized linear Bayesian inverse problems with correlated noise models. (English) Zbl 07797623
Summary: 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.
MSC:
| 65Nxx | Numerical methods for partial differential equations, boundary value problems |
| 35Qxx | Partial differential equations of mathematical physics and other areas of application |
| 65Cxx | Probabilistic methods, stochastic differential equations |
Keywords:
optimal sensor placement; Bayesian inverse problems; correlated noise; model order reduction; greedy algorithm; orthogonal matching pursuitReferences:
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