Robust information divergences for model-form uncertainty arising from sparse data in random PDE

TL;DR

This paper introduces hybrid information divergences as a robust, goal-oriented method for quantifying model-form uncertainty in steady-state subsurface flow, especially under sparse data conditions, aiding decision-making.

Contribution

It presents a novel, non-intrusive approach to uncertainty quantification that connects divergence measures with concentration inequalities for efficient, data-informed predictions.

Findings

Provides bounds for parametric sensitivity analysis

Addresses model misspecification with sparse data

Links divergences to concentration inequalities

Abstract

We develop a novel application of hybrid information divergences to analyze uncertainty in steady-state subsurface flow problems. These hybrid information divergences are non-intrusive, 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.