PoreDiT: A Scalable Generative Model for Large-Scale Digital Rock Reconstruction

Yizhuo Huang; Baoquan Sun; Haibo Huang

cs.AIApr 11, 2026

PoreDiT: A Scalable Generative Model for Large-Scale Digital Rock Reconstruction

Authors: Yizhuo Huang, Baoquan Sun, Haibo Huang

Organizations: College of Intelligent Robotics and Advanced Manufacturing, FuDan University, Shanghai, China · State Key Laboratory of Shale Oil and Gas Enrichment Mechanisms and Efficient Development, Dongying, Shandong, China · Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, Hefei, Anhui, China

Abstract

This manuscript presents PoreDiT, a novel generative model designed for high-efficiency digital rock reconstruction at gigavoxel scales. Addressing the significant challenges in digital rock physics (DRP), particularly the trade-off between resolution and field-of-view (FOV), and the computational bottlenecks associated with traditional deep learning architectures, PoreDiT leverages a three-dimensional (3D) Swin Transformer to break through these limitations. By directly predicting the binary probability field of pore spaces instead of grayscale intensities, the model preserves key topological features critical for pore-scale fluid flow and transport simulations. This approach enhances computational efficiency, enabling the generation of ultra-large-scale ( $1024^3$ voxels) digital rock samples on consumer-grade hardware. Furthermore, PoreDiT achieves physical fidelity comparable to previous state-of-the-art methods, including accurate porosity, pore-scale permeability, and Euler characteristics. The model's ability to scale efficiently opens new avenues for large-domain hydrodynamic simulations and provides practical solutions for researchers in pore-scale fluid mechanics, reservoir characterization, and carbon sequestration.

Figures & tables

Figure 1: Overview of the PoreDiT framework and inference mechanism. The diagram illustrates the complete workflow from microscopic training to large-scale generation. (A) Probability Field Learning: The model predicts the conditional probability of pore phase existence, quantifying aleatoric uncertainty. (B) 3D Patch Embedding: Input volumes are partitioned into patch sequences to optimize memory efficiency while capturing global topology via Swin Transformers. (C) Large-scale Inference: A Gaussian-weighted overlap-tile strategy enables seamless gigavoxel reconstruction.

Figure 2: Schematic of the Forward Diffusion Process and Multi-modal Embedding Framework.

Figure 4: Schematic diagram of the reverse denoising inference process of the PoreDiT model.

Figure 5: Schematic diagram of the reverse denoising inference process of the PoreDiT model.

Panel of Figure 6 — Figure 6: Visual comparison of microscopic structures. The left column displays 2D cross-sections ( $256\times 256$ pixels) extracted from the ground truth volumes, and the right column shows the corresponding synthetic slices generated by our model. The rows correspond to samples with high (a, b), average (c, d), and low (e, f) porosity levels, respectively.

Panel of Figure 7 — Figure 7: Comparison of 3D pore network structures. (a) Isosurface rendering of a real sandstone sub-volume ( $128^{3}$ voxels) randomly extracted from the training set. (b) A synthetic sub-volume ( $128^{3}$ voxels) generated by the PoreDiT model. Gray solid regions represent the pore space, illustrating the effective reconstruction of topological connectivity.

Figure 8: Comparison of the two-point correlation function $S_{2}(r)$ between the ground truth and generated samples.

Figure 9: Comparison of Minkowski Functionals (MFs) distributions between original training samples and synthetic samples. The panels display the statistical distributions of (a) Porosity $\phi$ (corresponding to $M_{0}$ ), (b) Specific Surface Area $S_{V}$ (corresponding to $M_{1}$ ), and (c) Euler Characteristic Density $\chi_{V}$ (corresponding to $M_{2}$ ). The boxes represent the interquartile range (IQR), the central dashed lines indicate the median, whiskers extend to the full data range (excluding outliers), and ’+’ symbols denote outliers.

Figure 10: Permeability comparison via LBM simulations. The left panel shows the porosity-permeability relationship, indicating that the generated samples fall within the valid physical range of the ground truth. The right panel displays the probability density of permeability; despite a slight leftward shift in the peak ( $\sim 0.8$ Darcy offset), the generated distribution (red) shows high structural similarity to the ground truth (black) and lies within its statistical support.

Figure 11: Generative Novelty Analysis. Histogram of the Distance to Nearest Neighbor ( $D_{min}$ ) for generated samples. The X-axis represents the pixel-wise distance ( $\epsilon_{pixel}$ ) to the nearest neighbor in the training set. The red dashed line ( $x=0$ ) indicates the theoretical position for ”exact data copying.” The solid teal line represents the Kernel Density Estimation (KDE) curve, and the dotted line indicates the mean distance of the samples.

Figure 12: Visual inspection of the most similar pair (Data-Copying Check). (Left) The generated sample with the minimum distance metric. (Middle) The nearest neighbor sample identified from the training set. (Right) The pixel-wise difference map between the two. High-intensity red regions indicate significant pixel residuals ( $D_{min}\approx 0.33$ ), confirming structural distinctness.

Figure 13: Ablation Study: Impact of physical guidance on morphological consistency ( $S_{2}(r)$ ). The green dotted line represents the Unconditional Baseline, the red solid points with error bars represent the Porosity-Guided model (Ours), and the black dashed line represents the Ground Truth (GT).

Panel of Figure 14 — Figure 14: Ablation Study: Controllability Analysis of Physical Properties. (a) Probability Density Function (PDF) of absolute permeability $K$ . The grey shaded area, red curve, and black dashed line represent the Unconditional Baseline, Porosity-Guided model, and Ground Truth, respectively. (b) Joint distribution of porosity $\phi$ and permeability $K$ . Grey triangles, red crosses, and blue circles correspond to the Unconditional, Porosity-Guided, and Ground Truth samples, respectively.

Sample Name	Dimensions (Voxels)	Porosity ( $\phi$ )	Connectivity (Largest Cluster %)
Ground Truth	$1000^{3}$	0.2672	99.43%
Gen_512	$512^{3}$	0.2701	99.15%
Gen_1024	$1024^{3}$	0.2725	99.49%

Table 1: Comparison of physical properties across different reconstruction scales. Note that permeability is analyzed separately in Figure 18 via sub-volume partitioning.

Figure 15: Three-dimensional visualization of the pore network structure within the generated large-scale sample ( $512^{3}$ voxels, since $1024^{3}$ is difficult to visualize).The grey isosurface represents the pore space, illustrating global connectivity without visible stitching artifacts.

Figure 16: A representative orthogonal cross-section (Slice No. 0257) extracted from the $1024^{3}$ generated volume. Black regions denote pore space, and white regions denote the solid matrix. The image demonstrates seamless texture transition and long-range structural coherence.

Panel of Figure 17 — Figure 17: Statistical comparison between the Ground Truth (black dashed line) and the generated large-scale sample (red solid line). (a) The overlapping $S_{2}^{*}(r)$ curves indicate high statistical isomorphism in skeletal structure. (b) The parallel descent of the $L(r)$ curves suggests a consistent pore size distribution, despite a slight porosity offset.

Figure 18: Porosity-Permeability Relationship Analysis of Large-scale Generation. The gray circles and dashed line represent the ground truth experimental data and its exponential fit trend. The red diamonds and blue triangles represent the sub-volumes sliced from the generated $512^{3}$ (8 sub-volumes) and $1024^{3}$ (64 sub-volumes) samples, respectively. The tight clustering around the GT trend line confirms physical consistency and stationarity across scales.

Panel of Figure 19 — Figure 19: Generalization verification on Ketton Limestone. (a) Comparison of the Two-point Correlation Function $S_{2}(r)$ . The generated samples (red) exhibit high morphological consistency with the ground truth (black), accurately reproducing the characteristic correlation length ( $l_{c}$ ) and specific surface area. (b) Joint porosity-permeability distribution. The generated samples (red crosses) tightly cluster around the trend of the ground truth data (black circles), demonstrating that the model preserves the physical transport properties of the carbonate rock.

Part I: Methodology and Physical Fidelity
Method	Paradigm	S 2 Mismatch	Permeability ( $K$ )	Connectivity
Stochastic (SA)	Optimization (SA)	Very Low	—	Poor ( $S_{2}$ only) / Good (Hybrid)
DCGAN	Adversarial Training	Good Agreement	Good Match	Good (Euler Characteristic)
WGAN-GP	Deep Learning	Good Agreement	—	Qualitatively Good (No Metric)
PG-GAN	Deep Learning	—	—	Good (Pore Network Matched)
RockGPT	DL (Autoregressive)	Good Agreement	Good (Dist. Match)	Good (Euler Characteristic)

Table 2: Comparative analysis of PoreDiT against established reconstruction paradigms. The comparison is divided into two parts for clarity. Part I focuses on methodology and physical fidelity metrics (

S_{2}

K

, Connectivity), while Part II details scalability and computational efficiency metrics. Values for PoreDiT are experimentally derived from the Bentheimer sandstone dataset (

1024^{3}

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Hyperparameter	Value
Input Resolution	$256\times 256\times 256$
Patch Size	$16\times 16\times 16$
Embedding Dimension ( $C$ )	768
Depth ( $L$ )	16
Number of Heads	12
Window Size	$4\times 4\times 4$

Appendix

Table 3: Hyperparameter Settings of PoreDiT

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