Deep learning for diffusion in porous media

We adopt convolutional neural networks (CNN) to predict the basic properties of the porous media. Two different media types are considered: one mimics the sandstone, 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 system's geometry and 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. The models predict with reasonable accuracy but only within the data type, they are trained on. For instance, the model trained on sandstone-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. Moreover, the network trained on one data type works well for the other. For instance, the model trained on sandstone-like samples works perfectly on biological-like samples.

Predicting Porosity, Permeability, and Tortuosity of Porous Media from Images by Deep Learning

Convolutional neural networks (CNN) are utilized to encode the relation between initial configurations of obstacles and three fundamental quantities in porous media: porosity ($\varphi$), permeability $k$, and tortuosity ($T$). The two-dimensional systems with obstacles are considered. The fluid flow through a porous medium is simulated with the lattice Boltzmann method. It is demonstrated that the CNNs are able to predict the porosity, permeability, and tortuosity with good accuracy. With the usage of the CNN models, the relation between $T$ and $\varphi$ has been reproduced and compared with the empirical estimate. The analysis has been performed for the systems with $\varphi \in (0.37,0.99)$ which covers five orders of magnitude span for permeability $k \in (0.78, 2.1\times 10^5)$ and tortuosity $T \in (1.03,2.74)$.