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Goal oriented optimal design of infinite-dimensional Bayesian inverse problems using quadratic approximations by Neuberger, J. Nicholas; Alexanderian, Alen; Waanders, Bart van Bloemen is a scholarly article available to read on EtoBox.

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We consider goal-oriented optimal design of experiments for infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs). Specifically, we seek sensor placements that minimize the posterior variance of a prediction or goal quantity of interest. The goal quantity is assumed to be a nonlinear functional of the inversion parameter. We propose a goal-oriented optimal experimental design (OED) approach that uses a quadratic approximation of the goal-functional to define a goal-oriented design criterion. The proposed criterion, which we call the Gq-optimality criterion, is obtained by integrating the posterior variance of the quadratic approximation over the set of likely data. Under the assumption of Gaussian prior and noise models, we derive a closed-form expression for this criterion. To guide development of discretization invariant computational methods, the derivations are performed in an infinite-dimensional Hilbert space setting. Subsequently, we propose efficient and accurate computational methods for computing the Gq-optimality criterion. A greedy approach is used to obtain Gq-optimal sensor placements. We illustrate the proposed approa

Author

Neuberger, J. Nicholas; Alexanderian, Alen; Waanders, Bart van Bloemen

Published

2024

Language

EN