In many branches of earth sciences, the problem of rock study on the micro-level arises. However, a significant number of representative samples is not always feasible. Thus the problem of the generation of samples with similar properties becomes actual. In this paper, we propose a novel deep learning architecture for three-dimensional porous media reconstruction from two-dimensional slices. We fit a distribution on all possible three-dimensional structures of a specific type based on the given dataset of samples. Then, given partial information (central slices), we recover the three-dimensional structure around such slices as the most probable one according to that constructed distribution. Technically, we implement this in the form of a deep neural network with encoder, generator and discriminator modules. Numerical experiments show that this method provides a good reconstruction in terms of Minkowski functionals.

翻译：在地球科学的许多分支中,在微观层面的岩石研究问题出现,然而,大量具有代表性的样品并不总是可行的,因此,产生具有类似特性的样品的问题就成为实际问题。在本文件中,我们提议从二维片段重建三维多孔媒体的新深层次学习结构。我们根据给定的样品数据集,将所有可能的三维特定类型的结构进行分布。然后,根据部分信息(中央切片),我们根据所建的分布,将这种切片周围的三维结构恢复为最可能的结构。技术上,我们以一个带有编码器、生成器和导体模块的深神经网络的形式实施这一结构。数字实验表明,这种方法在Minkowski功能方面提供了良好的重建。