Robust Information Divergences for Model-Form Uncertainty Arising from Sparse Data in Random PDE

Eric Joseph Hall, Markos A. Katsoulakis

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We develop a novel application of hybrid information divergences to analyze uncertainty in steady-state subsurface flow problems. These hybrid information divergences are nonintrusive, goal-oriented uncertainty quantification tools that enable robust, data-informed predictions in support of critical decision tasks such as regulatory assessment and risk management. We study the propagation of model-form or epistemic uncertainty with numerical experiments that demonstrate uncertainty quantification bounds for (i) parametric sensitivity analysis and (ii) model misspecification due to sparse data. Further, we make connections between the hybrid information divergences and certain concentration inequalities that can be leveraged for efficient computing and account for any available data through suitable statistical quantities.
Original languageEnglish
Pages (from-to)1364–1394
Number of pages31
JournalSIAM/ASA Journal on Uncertainty Quantification
Volume6
Issue number4
Early online date9 Oct 2018
DOIs
Publication statusPublished - 2018

Keywords

  • Uncertainty Quantification
  • Data
  • Data-driven analysis
  • Information Theory
  • Concentration inequalities
  • Sensitivity analysis
  • Model misspecification
  • Random PDE
  • Steady-state flow

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