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

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 satisfy certain given properties, such as porosity. To fill this gap, we propose a new framework, 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 the same model, and the reconstructed samples can successfully meet certain specified porosities. 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.