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We develop a novel application of hybrid information divergences to analyzeuncertainty in steady-state subsurface flow problems. These hybrid informationdivergences are non-intrusive, goal-oriented uncertainty quantification toolsthat enable robust, data-informed predictions in support of critical decisiontasks such as regulatory assessment and risk management. We study thepropagation of model-form or epistemic uncertainty with numerical experimentsthat demonstrate uncertainty quantification bounds for (i) parametricsensitivity analysis and (ii) model misspecification due to sparse data.Further, we make connections between the hybrid information divergences andcertain concentration inequalities that can be leveraged for efficientcomputing and account for any available data through suitable statisticalquantities.

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