Accelerating simulation for the multiple-point statistics algorithm using vector quantization

Three-dimensional reconstruction of granular porous media based on deep generative models

Reconstruction of microstructure in granular porous media, which can be viewed as granular assemblies, is crucial for studying their characteristics and physical properties in various fields concerned with the behavior of such media, including petroleum geology and computational materials science. In spite of the fact that many existing studies have investigated grain reconstruction, most of them treat grains as simplified individuals for discrete reconstruction, which cannot replicate the complex geometrical shapes and natural interactions between grains. In this work, a hybrid generative model based on a deep-learning algorithm is proposed for high-quality three-dimensional (3D) microstructure reconstruction of granular porous media from a single two-dimensional (2D) slice image. The method extracts 2D prior information from the given image and generates the grain set as a whole. Both a self-attention module and effective pattern loss are introduced in a bid to enhance the reconstruction ability of the model. Samples with grains of varied geometrical shapes are utilized for the validation of our method, and experimental results demonstrate that our proposed approach can accurately reproduce the complex morphology and spatial distribution of grains without any artificiality. Furthermore, once the model training is complete, rapid end-to-end generation of diverse 3D realizations from a single 2D image can be achieved.

Improved recurrent generative model for reconstructing large-size porous media from two-dimensional images

Modeling the three-dimensional (3D) structure from a given 2D image is of great importance for analyzing and studying the physical properties of porous media. As an intractable inverse problem, many methods have been developed to address this fundamental problems over the past decades. Among many methods, the deep learning-(DL) based methods show great advantages in terms of accuracy, diversity, and efficiency. Usually, the 3D reconstruction from the 2D slice with a larger field-of-view is more conducive to simulate and analyze the physical properties of porous media accurately. However, due to the limitation of reconstruction ability, the reconstruction size of most widely used generative adversarial network-based model is constrained to 64^{3} or 128^{3}. Recently, a 3D porous media recurrent neural network based method (namely, 3D-PMRNN) (namely 3D-PMRNN) has been proposed to improve the reconstruction ability, and thus the reconstruction size is expanded to 256^{3}. Nevertheless, in order to train these models, the existed DL-based methods need to down-sample the original computed tomography (CT) image first so that the convolutional kernel can capture the morphological features of training images. Thus, the detailed information of the original CT image will be lost. Besides, the 3D reconstruction from a optical thin section is not available because of the large size of the cutting slice. In this paper, we proposed an improved recurrent generative model to further enhance the reconstruction ability (512^{3}). Benefiting from the RNN-based architecture, the proposed model requires only one 3D training sample at least and generates the 3D structures layer by layer. There are three more improvements: First, a hybrid receptive field for the kernel of convolutional neural network is adopted. Second, an attention-based module is merged into the proposed model. Finally, a useful section loss is proposed to enhance the continuity along the Z direction. Three experiments are carried out to verify the effectiveness of the proposed model. Experimental results indicate the good reconstruction ability of proposed model in terms of accuracy, diversity, and generalization. And the effectiveness of section loss is also proved from the perspective of visual inspection and statistical comparison.

Three-dimensional reconstruction of porous media using super-dimension-based adjacent block-matching algorithm

As porous media play an essential role in a variety of industrial applications, it is essential to understand their physical properties. Nowadays, the super-dimensional (SD) reconstruction algorithm is used to stochastically reconstruct a three-dimensional (3D) structure of porous media from a given two-dimensional image. This algorithm exhibits superiority in accuracy compared with classical algorithms because it learns information from the real 3D structure. However, owing to the short development time of the SD algorithm, it also has some limitations, such as inexact porosity characterization, long run time, blocking artifacts, and suboptimal accuracy that may be improved. To mitigate these limitations, this study presents the design of a special template that contains two parts of data (i.e., adjacent blocks and a central block); the proposed method matches adjacent blocks during reconstruction and assigns the matched central block to the area to be reconstructed. Furthermore, we design two important mechanisms during reconstruction: one for block matching and the other for porosity control. To verify the effectiveness of the proposed method compared with an existing SD method, both methods were tested on silica particle material and three homogeneous sandstones with different porosities; meanwhile, we compared the proposed method with a multipoint statistics method and a simulated annealing method. The reconstructed results were then compared with the target both visually and quantitatively. The experimental results indicate that the proposed method can overcome the aforementioned limitations and further improve the accuracy of existing methods. This method achieved 4-6 speedup factor compared with the traditional SD method.

Three-dimensional multiscale fusion for porous media on microtomography images of different resolutions

Accurately acquiring the three-dimensional (3D) image of a porous medium is an imperative issue for the prediction of multiple physical properties. Considering the inherent nature of the multiscale pores contained in porous media such as tight sandstones, to completely characterize the pore structure, one needs to scan the microstructure at different resolutions. Specifically, low-resolution (LR) images cover a larger field of view (FOV) of the sample, but are lacking small-scale features, whereas high-resolution (HR) images contain ample information, but sometimes only cover a limited FOV. To address this issue, we propose a method for fusing the spatial information from a two-dimensional (2D) HR image into a 3D LR image, and finally reconstructing an integrated 3D structure with added fine-scale features. In the fusion process, the large-scale structure depicted by the 3D LR image is fixed as background and the 2D image is utilized as training image to reconstruct a small-scale structure based on the background. To assess the performance of our method, we test it on a sandstone scanned with low and high resolutions. Statistical properties between the reconstructed image and the target are quantitatively compared. The comparison indicates that the proposed method enables an accurate fusion of the LR and HR images because the small-scale information is precisely reproduced within the large one.

Reconstruction of porous media from extremely limited information using conditional generative adversarial networks

Porous media are ubiquitous in both nature and engineering applications. Therefore, their modeling and understanding is of vital importance. In contrast to direct acquisition of three-dimensional (3D) images of this type of medium, obtaining its subregion (s) such as 2D images or several small areas can be feasible. Therefore, reconstructing whole images from limited information is a primary technique in these types of cases. Given data in practice cannot generally be determined by users and may be incomplete or only partially informed, thus making existing reconstruction methods inaccurate or even ineffective. To overcome this shortcoming, in this study we propose a deep-learning-based framework for reconstructing full images from their much smaller subareas. In particular, conditional generative adversarial network is utilized to learn the mapping between the input (a partial image) and output (a full image). To ensure the reconstruction accuracy, two simple but effective objective functions are proposed and then coupled with the other two functions to jointly constrain the training procedure. Because of the inherent essence of this ill-posed problem, a Gaussian noise is introduced for producing reconstruction diversity, thus enabling the network to provide multiple candidate outputs. Our method is extensively tested on a variety of porous materials and validated by both visual inspection and quantitative comparison. It is shown to be accurate, stable, and even fast (∼0.08 s for a 128×128 image reconstruction). The proposed approach can be readily extended by, for example, incorporating user-defined conditional data and an arbitrary number of object functions into reconstruction, while being coupled with other reconstruction methods.

Correlation-driven direct sampling method for geostatistical simulation and training image evaluation

Multiple-point geostatistics (MPS) is a competitive algorithm that produces a set of geologically realistic models. Viewing a training image (TI) as a prior model, MPS extracts patterns from the TI and reproduces patterns which are compatible with the hard data (HD). However, two challenges within the MPS framework are the geologically complex simulation and the TI evaluation. With the objective to achieve a high-quality simulation, we explore a way to address these two issues. First, correlation-driven direct sampling (CDS) is proposed to realize geostatistical simulation. We introduce the correlation-driven distance as a measure of similarity between two patterns. The weights in our distance measurement are derived by the concepts of the ellipse, correlation coefficient, Gaussian function, and affine transformation. Second, we fulfill TI evaluation on the basis of the consistency between TI and HD. Inspired by CDS, the minimum correlation-driven distance (MCD) is proposed to improve the evaluation accuracy. We suggest a conditioning pattern extraction history strategy to speed up the evaluation program. Third, the local consistency is presented to address nonstationarity. The program automatically divides the simulation domain into several subareas. A two-dimensional (2D) channelized reservoir image and a three-dimensional (3D) rock image are used to validate our proposed method. In comparison with previous methods, CDS yields better simulation quality. The further applications include a set of 2D TI evaluations and a 3D simulation domain segmentation. MCD exhibits sensible evaluation accuracy, excellent computational efficiency, and the ability to deal with nonstationarity.