  Optimal experimental design (OED) is a principled framework for maximizing
information gained from limited data in inverse problems. Unfortunately,
conventional methods for OED are prohibitive when applied to expensive models
with high-dimensional parameters, as we target here. We develop a fast and
scalable computational framework for goal-oriented OED of large-scale Bayesian
linear inverse problems that finds sensor locations to maximize the expected
information gain (EIG) for a predicted quantity of interest. By employing
low-rank approximations of appropriate operators, an online-offline
decomposition, and a new swapping greedy algorithm, we are able to maximize EIG
at a cost measured in model solutions that is independent of the problem
dimensions. We demonstrate the efficiency, accuracy, and both data- and
parameter-dimension independence of the proposed algorithm for a contaminant
transport inverse problem with infinite-dimensional parameter field.
