RockGPT: reconstructing three-dimensional digital rocks from single two-dimensional slice with deep learning

Abstract

Random reconstruction of three-dimensional (3D) digital rocks from two-dimensional (2D) slices is crucial for elucidating the microstructure of rocks and its effects on pore-scale flow in terms of numerical modeling, since massive samples are usually required to handle intrinsic uncertainties. Despite remarkable advances achieved by traditional process-based methods, statistical approaches and recently famous deep learning-based models, few works have focused on producing several kinds of rocks with one trained model and allowing the reconstructed samples to approximately satisfy certain given properties, such as porosity. To fill this gap, we propose a new framework with deep learning, named RockGPT, which is composed of VQ-VAE and conditional GPT, to synthesize 3D samples based on a single 2D slice from the perspective of video generation. The VQ-VAE is utilized to compress high-dimensional input video, i.e., the sequence of continuous rock slices, to discrete latent codes and reconstruct them. In order to obtain diverse reconstructions, the discrete latent codes are modeled using conditional GPT in an autoregressive manner, while incorporating conditional information from a given slice, rock type, and porosity. We conduct two experiments on five kinds of rocks, and the results demonstrate that RockGPT can produce different kinds of rocks with a single model, and the porosities of reconstructed samples can distribute around specified targets with a narrow range. In a broader sense, through leveraging the proposed conditioning scheme, RockGPT constitutes an effective way to build a general model to produce multiple kinds of rocks simultaneously that also satisfy user-defined properties.

Minireview on Porous Media and Microstructure Reconstruction Using Machine Learning Techniques: Recent Advances and Outlook

“…Inspired by VideoGPT, which is introduced to generate videos based on initial frames, Zheng et al developed a framework comprising of Vector-Quantized Variational Autoencoder (VQ-VAE) and conditional Generative Pretraining (GPT) to reconstruct a 3D representation of different porous media using 2D slices. A schematic of the proposed architecture is shown in Figure .…”

“…Such properties are calculated through simulations on reconstructed images, which eventually can be compared against the simulation results on the original microstructure to evaluate the reconstruction performance. The desired transport properties can be obtained through flow simulations using different numerical techniques such as the finite difference method, , finite volume method, , lattice Boltzmann method, , or pore network modeling. ,, One such result is depicted in Figure , where there is good agreement between the permeability calculated for the synthetic and real images.…”

“…In a later work, Zhang et al 66 further improved the architecture of the 3D-PMRNN by utilizing attention and CNNs capabilities to capture the macro features of 2D slices better and proposing a new loss function to enhance the continuity along the Z direction. Inspired by VideoGPT, which is introduced to generate videos based on initial frames, Zheng et al 67 developed a framework comprising of Vector-Quantized Variational Autoencoder (VQ-VAE) and conditional Generative Pretraining (GPT) to reconstruct a 3D representation of different porous media using 2D slices. A schematic of the proposed architecture is shown in Figure 18.…”

“…Kench and Cooper 3 Polypropylene battery separator and nickel manganese cobalt oxide (NMC) cathode Feng et al 60 Sandstone, silica particle, and nonstationary medium Recurrent generative models Zhang et al 62 Isotopic and anisotropic sandstones Zhang et al 66 Bentheimer sandstone Zheng et al 67 Berea sandstone, Doddington sandstone, Estaillades carbonate, Ketton carbonate, and Sandy multiscale medium 3D-to-3D GAN Mosser et al 40 Spherical bead pack, Berea sandstone, and oolitic Ketton limestone Mosser et al 41 Oolitic Ketton limestone GAN-VAE Zhang et al 42 Shale samples Spatial GAN Laloy et al 30 Binary channelized aquifer In eq 8, P is the pore space, while K(r⃗ ,L) represents a measurement cell or template of length L centered at lattice vector r⃗ in the porous medium.…”

Transformer-based deep learning models for predicting permeability of porous media

“…Feng et al (2020) realized the mapping of 2D slices to 3D structures by a BicycleGAN framework. Zheng et al (2022) proposed a RockGPT method to reconstruct 3D structures based on a single 2D slice. treated slices of porous structures as spatial series and proposed a 3D porous media recurrent neural network (3D-PMRNN) to generate 3D porous media from a corresponding 2D image.…”