用深度学习从二维孔隙图像预测渗透率张量，效率远超传统方法。
Neural Networks for Predicting Permeability Tensors of 2D Porous Media: Comparison of Convolution- and Transformer-based Architectures
- 对比卷积与Transformer模型，基于图像直接预测渗透率。
- ConvNeXt-Small在4000个测试样本上达到0.9946的R²，精度极高。
- 数据增强和更大数据集能提升模型泛化能力，适合地质、油藏等场景。
渗透率是描述流体通过多孔介质宏观行为的核心概念，广泛应用于油气开采与水文地质等领域。传统计算方法依赖流体模拟或实验，耗时且成本高；而基于科岑尼-卡曼方程的解析方法又因过于简化，难以准确反映孔隙尺度特征。本文提出一种基于深度学习的高效替代方案，利用二维二值图像（固体为1，孔隙为0）预测渗透率张量。构建了24,000个合成随机周期性多孔介质样本，控制孔隙率和特征长度，通过格子玻尔兹曼模拟计算渗透率，数值跨度达三个数量级。评估了三类图像模型：ResNet-50/101、ViT-T16/S16和ConvNeXt-Tiny/Small。采用权重衰减、学习率调度和数据增强提升泛化能力。结果表明，数据增强与更大数据集可显著提高预测精度；ConvNeXt与ResNet收敛更快，而ViT易过拟合。ConvNeXt-Small在4,000个未见测试样本上取得最高R²为0.99460，证明图像驱动神经网络可高精度预测渗透率张量。
原文摘要 · Abstract (English)
Permeability is a central concept in the macroscopic description of flow through porous media, with applications spanning from oil recovery to hydrology. Traditional methods for determining the permeability tensor involving flow simulations or experiments can be time consuming and resource-intensive, while analytical methods, e.g., based on the Kozeny-Carman equation, may be too simplistic for accurate prediction based on pore-scale features. In this work, we explore deep learning as a more efficient alternative for predicting the permeability tensor based on two-dimensional binary images of porous media, segmented into solid ($1$) and void ($0$) regions. We generate a dataset of 24,000 synthetic random periodic porous media samples with specified porosity and characteristic length scale. Using Lattice-Boltzmann simulations, we compute the permeability tensor for flow through these samples with values spanning three orders of magnitude. We evaluate three families of image-based deep learning models: ResNet (ResNet-$50$ and ResNet-$101$), Vision Transformers (ViT-T$16$ and ViT-S$16$) and ConvNeXt (Tiny and Small). To improve model generalisation, we employ techniques such as weight decay, learning rate scheduling, and data augmentation. The effect of data augmentation and dataset size on model performance is studied, and we find that they generally increase the accuracy of permeability predictions. We also show that ConvNeXt and ResNet converge faster than ViT and degrade in performance if trained for too long. ConvNeXt-Small achieved the highest $R^2$ score of $0.99460$ on $4,000$ unseen test samples. These findings underscore the potential to use image-based neural networks to predict permeability tensors accurately.
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