This work describes connections between optimal experiment design (OED) for PDE-based Bayesian linear inverse problems and the column subset selection problem (CSSP) in matrix approximation. We derive bounds, both lower and upper, for the D-optimality criterion via CSSP for the independent and colored noise cases. Additionally, we describe ways to interpolate “left-out” sensor data using the “selected” sensors along with the errors in the data completion process. We develop and analyze randomized algorithms which achieve these bounds. Finally, we experimentally verify these results on a model advection-diffusion problem.
Bio: Srinivas Eswar
Srinivas Eswar is the Wilkinson Fellow in the Mathematical and Computer Science division at Argonne National Laboratory. He received his Ph.D. from Georgia Tech in 2022. His research interests are in scalable data mining via numerical methods. In particular, he works on matrix and tensor approximation techniques.
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