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

We consider optimal sensor placement for hyper-parameterized linear Bayesian\ninverse problems, where the hyper-parameter characterizes nonlinear\nflexibilities in the forward model, and is considered for a range of possible\nvalues. This model variability needs to be taken into account for the\nexperimental design to guarantee that the Bayesian inverse solution is\nuniformly informative. In this work we link the numerical stability of the\nmaximum a posterior point and A-optimal experimental design to an observability\ncoefficient that directly describes the influence of the chosen sensors. We\npropose an algorithm that iteratively chooses the sensor locations to improve\nthis coefficient and thereby decrease the eigenvalues of the posterior\ncovariance matrix. This algorithm exploits the structure of the solution\nmanifold in the hyper-parameter domain via a reduced basis surrogate solution\nfor computational efficiency. We illustrate our results with a steady-state\nthermal conduction problem.\n