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

TL;DR

This paper develops an optimal experimental design framework for large-scale Bayesian linear inverse problems with reducible model uncertainties, emphasizing the importance of accounting for secondary uncertainties to improve parameter estimation.

Contribution

It introduces a marginalized A-optimality criterion and an efficient computational method for experimental design in infinite-dimensional Bayesian inverse problems with secondary uncertainties.

Findings

Accounting for secondary uncertainties improves design effectiveness.

The proposed approach efficiently handles high-dimensional problems.

Including model uncertainty leads to more robust parameter estimates.

Abstract

We consider optimal design of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations that contain secondary reducible model uncertainties, in addition to the uncertainty in the inversion parameters. By reducible uncertainties we refer to parametric uncertainties that can be reduced through parameter inference. 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 estimating an uncertain time-dependent source in a contaminant transport model with an uncertain initial state as secondary uncertainty. Our results indicate that accounting for additional model uncertainty in the experimental design process is crucial.