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Direct numerical simulation of Stokes flow through a random, impermeable rigid body matrix by finite elements requires meshes fine enough to resolve the pore‐size scale and is thus a computationally expensive task. It is well known that on a larger scale, Stokes flow can accurately be approximated by Darcy's law [1] with an effective diffusivity field depending on viscosity and the matrix phase topology. We propose a fully probabilistic Darcy type reduced‐order model which, based on only a few tens of full‐order model runs, is capable to learn a fine‐scale topology to effective diffusion map which is maximally predictive for fine‐scale response. After training, the model provides sharp predictive distributions based on repeated evaluation of the much cheaper Darcy equation only.

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