Deep learning for diffusion in porous media

We are pleased to announce a recent publication by a team from the Institute of Theoretical Physics of the Faculty of Physics and Astronomy of the University of Wrocław in the journal Scientifics Reports, a member the Nature group:

K. Graczyk, D. Strzelczyk, M. Matyka, Deep learning for diffusion in porous media, Scientific Reports, 13, 9769 (2023)

The text of the article (Open Access) is available at:

https://www.nature.com/articles/s41598-023-36466-w

The work has been done in its entirety by scientists of our University. The group led by prof. K. Graczyk adopted convolutional neural networks to predict the basic characteristics of the porous media mimicking sand packing and extracellular space of biological tissues. A neural network, taking a picture of a porous medium as input, returns the porosity, diffusion coefficient or concentration distribution.

To teach the network to correctly reconstruct the macroscopic and microscopic features of the medium, several sets containing the geometries under discussion were generated. For each geometry image, the diffusion coefficient and concentration distribution were calculated using the Boltzmann lattice gas method.

Two types of networks were considered: an encoding network – for predicting the diffusion coefficient, and a U-Net (auto-encoder) for predicting concentration distributions. For the former task, the self-normalization module proposed by Prof. Graczyk was also used [Graczyk et al, Sci Rep 12, 10583 (2022)].

This paper is part of the team’s work series and is a follow-up to a previous publication: Graczyk, K. M. and Matyka, M., Predicting Porosity, Permeability, and Tortuosity of Porous Media from Images by Deep Learning, Sci Rep 10, 21488 (2020), which has currently already reached 66 citations according to Google Scholar.

For both types of data, a curvature analysis was successfully carried out and the results of neural network measurement data were matched to the classical Archie’s law of the dependence of effective diffusion on porosity.