Goal-Oriented OED for Large Scale Bayesian Inverse Problems Governed by Autonomous Dynamical Systems
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We present a goal-oriented algorithm for optimal experimental design (OED) that extends our recent work on real-time, extreme-scale Bayesian inversion for linear autonomous dynamical systems. That work utilized a predetermined set of observation points (sensors) to perform real-time parameter inference and predict quantities of interest (QoI). Sensor deployment is often constrained by a budget, making the strategic placement of a limited number of sensors a critical design challenge. We address this challenge via a framework for optimal sensor selection. Our approach employs a greedy algorithm that, given a set of candidate locations, incrementally selects sensors to maximize expected information gain from the data. This information gain objective is tailored to be goal-oriented, prioritizing sensor locations that most reduce uncertainty in specific QoI. The tractability of this framework is enabled by the fast, FFT-based forward and adjoint operators from our prior work, while the greedy selection algorithm is readily parallelizable on multi-GPU clusters. This goal-oriented OED framework is applied to a digital twin (DT) for tsunami early warning in the Cascadia subduction zone. This DT assimilates observations from seafloor pressure sensors during an earthquake to inform a billion-parameter inverse problem for the seafloor motion and issue uncertainty-equipped predictions of tsunami wave heights in real time. Sensor locations are optimized to maximize the information gain from the sensor data about tsunami wave height forecasts.
