Surrogate-assisted global sensitivity analysis of a hybrid-dimensional Stokes--Brinkman--Darcy model

TL;DR

This paper develops a surrogate-assisted global sensitivity analysis method for a complex hybrid-dimensional fluid flow model, comparing polynomial chaos techniques to efficiently quantify parameter influence.

Contribution

It introduces a surrogate-based sensitivity analysis framework for the Stokes--Brinkman--Darcy model, evaluating different polynomial chaos methods for high-dimensional parameter spaces.

Findings

Multi-resolution polynomial chaos provides the most accurate Sobol' index estimates.

Surrogate models significantly reduce computational costs in sensitivity analysis.

The approach effectively identifies influential parameters in fluid flow models.

Abstract

Development of new multiscale mathematical models often entails considerable complexity and multiple undetermined parameters, typically arising from closure relations. To enable reliable simulations, one must quantify how uncertain physical parameters influence model predictions. We propose surrogate-assisted global sensitivity analysis that combines computational efficiency with a rigorous assessment of parameter influence. In this work, we analyze the recently proposed hybrid-dimensional Stokes--Brinkman--Darcy model, which describes fluid flows in coupled free-flow and porous-medium systems with arbitrary flow directions at the fluid--porous interface. The model results from vertical averaging and contains several unknown parameters. We perform surrogate-assisted global sensitivity analysis using Sobol' indices to investigate the sensitivity of the model to variations of physical parameters for two test cases: filtration and splitting flows. However, constructing surrogates for higher-dimensional random fields requires either many training runs or sophisticated sampling strategies. To address this, we compare polynomial chaos surrogates, including sparse and multi-resolution representations, for their efficiency in global sensitivity analysis, using a predefined Sobol' sequence of training samples. Across the tested cases, multi-resolution approach delivers the most accurate estimation of Sobol' indices.