A data-driven model order reduction approach for Stokes flow through random porous media

TL;DR

This paper introduces a probabilistic, data-driven reduced-order model for simulating Stokes flow in random porous media, significantly reducing computational costs while maintaining high accuracy and providing confidence metrics.

Contribution

It develops a Darcy-type model that learns from limited full-scale simulations to predict flow behavior in complex porous structures efficiently.

Findings

Model accelerates uncertainty quantification tasks.

Provides quantitative confidence metrics.

Learns effective diffusivity from few simulations.

Abstract

Direct numerical simulation of Stokes flow through an impermeable, rigid body matrix by finite elements requires meshes fine enough to resolve the pore-size scale and is thus a computationally expensive task. The cost is significantly amplified when randomness in the pore microstructure is present and therefore multiple simulations need to be carried out. It is well known that in the limit of scale-separation, Stokes flow can be accurately approximated by Darcy's law with an effective diffusivity field depending on viscosity and the pore-matrix topology. We propose a fully probabilistic, Darcy-type, reduced-order model which, based on only a few tens of full-order Stokes model runs, is capable of learning a map from the fine-scale topology to the effective diffusivity and is maximally predictive of the fine-scale response. The reduced-order model learned can significantly accelerate uncertainty quantification tasks as well as provide quantitative confidence metrics of the predictive estimates produced.