High-resolution three-dimensional X-ray microscopy can be used to image the pore space of materials. Machine learning algorithms can generate a statistical ensemble of representative images of arbitrary sizes for rock characterization, modeling, and analysis. However, current methods struggle to capture features at different spatial scales observed in many complex rocks which have a wide range of pore size. We use the Improved Pyramid Wasserstein Generative Adversarial Network (IPWGAN) to automatically reproduce multi-scale features in segmented three-dimensional images of porous materials, enabling the reliable generation of large-scale representations of complex porous media. A Laplacian pyramid generator is introduced, which creates pore-space features across a hierarchy of spatial scales. Feature statistics mixing regularization enhances the discriminator’s ability to distinguish between real and generated images by mixing their feature statistics, thereby indirectly enhancing the generator’s ability to capture and reproduce multi-scale pore-space features, leading to increased diversity and realism in the generated images. The method has been tested on five sandstone and carbonate samples. The generated images, which can be of any size – including cm-scale ten-billion-cell images – demonstrate the power of the approach. These images have two-point correlation functions, porosity, permeability, Euler characteristic, curvature, and specific surface area closer to those of the training datasets than existing machine learning techniques. The generated images accurately capture geometric and flow properties, demonstrating a considerable improvement over previously published studies using generative adversarial networks. For instance, the mean relative error in the calculated absolute permeability between the Berea sandstone images generated by IPWGAN and the corresponding real rock images can be reduced by 79%. The work allows representative models of a wide range of porous media to be generated, offering potential benefits in carbon dioxide sequestration, underground hydrogen storage, and enhanced oil recovery.

中文翻译：

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使用改进的金字塔 Wasserstein 生成对抗网络生成孔隙空间图像


高分辨率三维X射线显微镜可用于对材料的孔隙空间进行成像。机器学习算法可以生成任意大小的代表性图像的统计集合，用于岩石表征、建模和分析。然而，当前的方法很难捕获在许多具有各种孔径的复杂岩石中观察到的不同空间尺度的特征。我们使用改进的金字塔 Wasserstein 生成对抗网络 (IPWGAN) 自动重现多孔材料分段三维图像中的多尺度特征，从而能够可靠地生成复杂多孔介质的大规模表示。引入了拉普拉斯金字塔生成器，它在空间尺度层次结构中创建孔隙空间特征。特征统计混合正则化通过混合特征统计来增强鉴别器区分真实图像和生成图像的能力，从而间接增强生成器捕获和再现多尺度孔隙空间特征的能力，从而增加生成图像的多样性和真实感。该方法已在五个砂岩和碳酸盐样品上进行了测试。生成的图像可以是任何尺寸（包括厘米级的百亿个细胞图像），展示了该方法的强大功能。这些图像的两点相关函数、孔隙度、渗透率、欧拉特征、曲率和比表面积比现有的机器学习技术更接近训练数据集。生成的图像准确地捕捉了几何和流动特性，表明比之前发表的使用生成对抗网络的研究有了相当大的改进。 例如，IPWGAN 生成的伯里亚砂岩图像与相应的真实岩石图像之间计算的绝对渗透率的平均相对误差可以减少 79%。这项工作可以生成各种多孔介质的代表性模型，为二氧化碳封存、地下储氢和提高石油采收率提供潜在的好处。