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We consider optimal design of infinite-dimensional Bayesian linear inverseproblems governed by partial differential equations that contain secondaryreducible model uncertainties, in addition to the uncertainty in the inversionparameters. By reducible uncertainties we refer to parametric uncertaintiesthat can be reduced through parameter inference. We seek experimental designsthat minimize the posterior uncertainty in the primary parameters, whileaccounting for the uncertainty in secondary parameters. We accomplish this byderiving a marginalized A-optimality criterion and developing an efficientcomputational approach for its optimization. We illustrate our approach forestimating an uncertain time-dependent source in a contaminant transport modelwith an uncertain initial state as secondary uncertainty. Our results indicatethat accounting for additional model uncertainty in the experimental designprocess is crucial.

Optimal design of large-scale Bayesian linear inverse problems under reducible model uncertainty: good to know what you don't know