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Partial differential equations (PDEs) are fundamental for theoreticallydescribing numerous physical processes that are based on some input fields inspatial configurations. Understanding the physical process, in general,requires computational modeling of the PDE. Uncertainty in the computationalmodel manifests through lack of precise knowledge of the input field orconfiguration. Uncertainty quantification (UQ) in the output physical processis typically carried out by modeling the uncertainty using a random field,governed by an appropriate covariance function. This leads to solvinghigh-dimensional stochastic counterparts of the PDE computational models. SuchUQ-PDE models require a large number of simulations of the PDE in conjunctionwith samples in the high-dimensional probability space, with probabilitydistribution associated with the covariance function. Those UQ computationalmodels having explicit knowledge of the covariance function are known asaleatoric UQ (AUQ) models. The lack of such explicit knowledge leads toepistemic UQ (EUQ) models, which typically require solution of a large numberof AUQ models. In this article, using a surrogate, post-processing, and domaindecomposition framework with coarse stochastic solution adaptation, we developan offline/online algorithm for efficiently simulating a class of EUQ-PDEmodels.

An efficient epistemic uncertainty quantification algorithm for a class of stochastic models: A post-processing and domain decomposition framework