Computational Mathematics and Scientific Computing Seminar

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We present a Bayesian optimal experimental design (OED) framework for sensor placement in large-scale, PDE-constrained inverse problems, extending our recent work on real-time Bayesian inversion for linear time-invariant dynamical systems. Given a set of candidate sensor locations, we formulate sensor selection as a D-optimal design problem and solve it with a greedy algorithm that iteratively selects sensors to maximize expected information gain. The same greedy procedure accommodates two objectives: a standard formulation that reduces uncertainty across the full parameter posterior, and a goal-oriented formulation that instead targets uncertainty in a specified quantity of interest. Evaluating either objective conventionally requires repeated evaluations of the log-determinant of the high-dimensional posterior covariance; we instead reformulate the problem in the lower-dimensional data space, exploiting the linear time-invariant structure of the underlying dynamics to make this evaluation tractable, and develop a scalable multi-GPU implementation to solve the resulting OED problem for a billion-parameter inverse problem. We apply this framework to a digital twin for tsunami early warning in the Cascadia Subduction Zone, where seafloor pressure sensors inform an inversion for earthquake-induced seafloor motion and enable real-time tsunami forecasts. We present sensor configurations obtained under both the standard and goal-oriented objectives and compare their effects on inversion and forecast accuracy.

Joint work with Sreeram Venkat and Omar Ghattas (https://doi.org/10.48550/arXiv.2604.08812).