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

TL;DR

This paper introduces an efficient algorithm for epistemic uncertainty quantification in stochastic PDE models, leveraging surrogate modeling, post-processing, and domain decomposition to reduce computational costs.

Contribution

The authors develop a novel offline/online framework that significantly improves the efficiency of EUQ-PDE simulations using coarse stochastic solution adaptation.

Findings

Reduces computational cost of EUQ-PDE models

Enables efficient high-dimensional uncertainty quantification

Demonstrates effectiveness through numerical experiments

Abstract

Partial differential equations (PDEs) are fundamental for theoretically describing numerous physical processes that are based on some input fields in spatial configurations. Understanding the physical process, in general, requires computational modeling of the PDE. Uncertainty in the computational model manifests through lack of precise knowledge of the input field or configuration. Uncertainty quantification (UQ) in the output physical process is typically carried out by modeling the uncertainty using a random field, governed by an appropriate covariance function. This leads to solving high-dimensional stochastic counterparts of the PDE computational models. Such UQ-PDE models require a large number of simulations of the PDE in conjunction with samples in the high-dimensional probability space, with probability distribution associated with the covariance function. Those UQ computational models having explicit knowledge of the covariance function are known as aleatoric UQ (AUQ) models. The lack of such explicit knowledge leads to epistemic UQ (EUQ) models, which typically require solution of a large number of AUQ models. In this article, using a surrogate, post-processing, and domain decomposition framework with coarse stochastic solution adaptation, we develop an offline/online algorithm for efficiently simulating a class of EUQ-PDE models.