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

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.

Figures (19)

• Figure 1: Schematic of coupled free-flow and porous-medium systems with a transition region $\Omega_{\mathrm{tr}}$ (left) and a complex interface $\Gamma$ (right)
• Figure 2: Probability density functions (PDF) and histograms of the uncertain parameters.
• Figure 3: Schematic setting (left) and velocity (right) for filtration problem.
• Figure 4: Schematic setting (left) and velocity (right) for splitting flow problem.
• Figure 5: Mean, standard deviation and log-variance of the horizontal and vertical velocities $(u,v)$ computed from 50,000 MC samples.