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We consider optimal sensor placement for hyper-parameterized linear Bayesianinverse problems, where the hyper-parameter characterizes nonlinearflexibilities in the forward model, and is considered for a range of possiblevalues. This model variability needs to be taken into account for theexperimental design to guarantee that the Bayesian inverse solution isuniformly informative. In this work we link the numerical stability of themaximum a posterior point and A-optimal experimental design to an observabilitycoefficient that directly describes the influence of the chosen sensors. Wepropose an algorithm that iteratively chooses the sensor locations to improvethis coefficient and thereby decrease the eigenvalues of the posteriorcovariance matrix. This algorithm exploits the structure of the solutionmanifold in the hyper-parameter domain via a reduced basis surrogate solutionfor computational efficiency. We illustrate our results with a steady-statethermal conduction problem.

A sequential sensor selection strategy for hyper-parameterized linear Bayesian inverse problems