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

Alen Alexanderian, Noemi Petra, Georg Stadler, Isaac Sunseri

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)163-184
Number of pages22
JournalSIAM-ASA Journal on Uncertainty Quantification
Volume9
Issue number1
DOIs
StatePublished - 2021

Keywords

  • Bayesian inference
  • Inverse problems
  • Model uncertainty
  • Optimal experimental design
  • Sensor placement
  • Sparsified designs

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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