Structure exploiting methods for fast uncertainty quantification in multiphase flow through heterogeneous media

TL;DR

This paper introduces a computational framework that combines dimension reduction and surrogate modeling techniques to efficiently perform uncertainty quantification in complex multiphase flow models within heterogeneous porous media, relevant for radioactive waste storage.

Contribution

It develops a novel approach that integrates global sensitivity measures, active subspace ideas, and polynomial chaos expansions for fast uncertainty quantification without requiring gradient computations.

Findings

Effective surrogate models for high-dimensional, function-valued outputs.

Significant acceleration in uncertainty quantification tasks.

Validated approach with comprehensive numerical experiments.

Abstract

We present a computational framework for dimension reduction and surrogate modeling to accelerate uncertainty quantification in computationally intensive models with high-dimensional inputs and function-valued outputs. Our driving application is multiphase flow in saturated-unsaturated porous media in the context of radioactive waste storage. For fast input dimension reduction, we utilize an approximate global sensitivity measure, for function-value outputs, motivated by ideas from the active subspace methods. The proposed approach does not require expensive gradient computations. We generate an efficient surrogate model by combining a truncated Karhunen-Lo\'{e}ve (KL) expansion of the output with polynomial chaos expansions, for the output KL modes, constructed in the reduced parameter space. We demonstrate the effectiveness of the proposed surrogate modeling approach with a comprehensive set of numerical experiments, where we consider a number of function-valued (temporally or spatially distributed) QoIs.