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 \textit{et 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.

翻译：本文采用卷积神经网络（CNN）预测多孔介质的基本性质。研究考虑两种介质类型：一类模拟砂土堆积体，另一类模拟源自生物组织细胞外空间的系统。采用格子玻尔兹曼方法获取监督学习所需的标注数据。我们区分两项任务：第一项任务基于系统几何结构分析，预测孔隙率和有效扩散系数；第二项任务重建浓度分布图。针对第一项任务，我们提出两种CNN模型：C-Net和U-Net编码器部分。两种网络均通过添加自归一化模块进行改进[Graczyk \textit{等}，Sci Rep 12, 10583 (2022)]。模型仅在其训练的数据类型内具有合理精度：例如，基于砂土堆积样本训练的模型，应用于生物样本时会出现预测值偏高或偏低的现象。对于第二项任务，我们提出采用U-Net架构，该模型能准确重建浓度场。与第一项任务不同的是，基于单一数据类型训练的U-Net网络可有效迁移至其他类型：例如，基于砂土堆积样本训练的模型，对生物样本仍能完美工作。最终，针对两种数据类型，我们拟合Archie定律中的指数以计算迂曲度，该参数用于描述有效扩散系数与孔隙率的依存关系。