# Deep learning for diffusion in porous media

arXiv: https://arxiv.org/abs/2304.02104 · HTML: https://mlsanity.com/paper/2304.02104/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 45 references that are in the map.
- First posted on arXiv 4 Apr 2023.

## Builds on (most cited first, 7 of 7)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Dropout as a Bayesian Approximation: Appendix](https://mlsanity.com/paper/1506.02157/) (2015)
- [Predicting Porosity, Permeability, and Tortuosity of Porous Media from Images by Deep Learning](https://mlsanity.com/paper/2007.02820/) (2020)
- [Predicting Effective Diffusivity of Porous Media from Images by Deep Learning](https://mlsanity.com/paper/1912.05532/) (2019)
- [Self-Normalized Density Map (SNDM) for Counting Microbiological Objects](https://mlsanity.com/paper/2203.09474/) (2022)

## Built on by (most cited first, 1 of 1)

- [Re-optimization of a deep neural network model for electron-carbon scattering using new experimental data](https://mlsanity.com/paper/2508.00996/) (2025)

## Abstract (arXiv)

We adopt convolutional neural networks (CNN) to predict the basic properties of the porous media. Two different media types are considered: one mimics the sand packings, and the other mimics the systems derived from the extracellular space of biological tissues. The Lattice Boltzmann Method is used to obtain the labeled data necessary for performing supervised learning. We distinguish two tasks. In the first, networks based on the analysis of the system's geometry predict porosity and effective diffusion coefficient. In the second, networks reconstruct the concentration map. In the first task, we propose two types of CNN models: the C-Net and the encoder part of the U-Net. Both networks are modified by adding a self-normalization module [Graczyk textitet al., Sci Rep 12, 10583 (2022)]. The models predict with reasonable accuracy but only within the data type, they are trained on. For instance, the model trained on sand packings-like samples overshoots or undershoots for biological-like samples. In the second task, we propose the usage of the U-Net architecture. It accurately reconstructs the concentration fields. In contrast to the first task, the network trained on one data type works well for the other. For instance, the model trained on sand packings-like samples works perfectly on biological-like samples. Eventually, for both types of the data, we fit exponents in the Archie's law to find tortuosity that is used to describe the dependence of the effective diffusion on porosity.