We consider optimal design of infinite-dimensional Bayesian inverse problems governed by partial differential equations (PDEs) that contain secondary (reducible) model uncertainties, in addition to the uncertainty in the inversion parameters. We seek experimental designs that minimize the posterior uncertainty in the primary parameters while accounting for the uncertainty in secondary parameters. We accomplish this by deriving a marginalized A-optimality criterion and developing an efficient computational approach for its optimization. We illustrate our approach for both linear and nonlinear inverse problems. Our results indicate that accounting for additional model uncertainty in the experimental design process is crucial.
Optimal Design of Large-scale Bayesian Inverse Problems Under Uncertainty*
Noemi Petra, University of California, MercedAuthors: Alen Alexanderian, Ruanui Nicholson, Noemi Petra, Georg Stadler
2022 AWM Research Symposium
Recent Advancements in Inverse Problems and Imaging