A Decade of Generative Adversarial Networks for Porous Material Reconstruction

Ali Sadeghkhani; Brandon Bennett; Masoud Babaei; Arash Rabbani

cs.CVMar 12, 2026

A Decade of Generative Adversarial Networks for Porous Material Reconstruction

Authors: Ali Sadeghkhani, Brandon Bennett, Masoud Babaei, Arash Rabbani

Organizations: School of Computer Science, University of Leeds, Leeds, UK. · School of Chemical Engineering, The University of Manchester, Manchester, UK.

Abstract

Digital reconstruction of porous materials has become increasingly critical for applications ranging from geological reservoir characterization to tissue engineering and electrochemical device design. While traditional methods such as micro-computed tomography and statistical reconstruction approaches have established foundations in this field, the emergence of deep learning techniques, particularly Generative Adversarial Networks (GANs), has revolutionized porous media reconstruction capabilities. This review systematically analyzes 96 peer-reviewed articles published from 2017 to early 2026, examining the evolution and applications of GAN-based approaches for porous material image reconstruction. We categorize GAN architectures into six distinct classes, namely Vanilla GANs, Multi-Scale GANs, Conditional GANs, Attention-Enhanced GANs, Style-based GANs, and Hybrid Architecture GANs. Our analysis reveals substantial progress including improvements in porosity accuracy (within 1% of original samples), permeability prediction (up to 79% reduction in mean relative errors), and achievable reconstruction volumes (from initial $64^3$ to current $2{,}200^3$ voxels). Despite these advances, persistent challenges remain in computational efficiency, memory constraints for large-scale reconstruction, and maintaining structural continuity in 2D-to-3D transformations. This systematic analysis provides a comprehensive framework for selecting appropriate GAN architectures based on specific application requirements.

Figures & tables

Figure 1: Word cloud visualization generated from titles and abstracts of reviewed publications in GAN-based porous media reconstruction. Font size corresponds to term frequency, revealing key research themes and methodological approaches.

Figure 2: Overview of GAN architectures for porous media reconstruction. The classification encompasses six distinct architectural paradigms: (1) Vanilla GAN establishing foundational capabilities for 3D reconstruction and multi-phase generation, (2) Multi-Scale GAN enabling hierarchical feature capture and large volume generation through progressive or concurrent training, (3) Conditional GAN providing precise property-controlled generation and manufacturing process optimization, (4) Attention-Enhanced GAN preserving long-range dependencies and structural connectivity through selective feature weighting, (5) Style-based GAN offering hierarchical control from coarse-to-fine features with high-fidelity generation, and (6) Hybrid Architecture GAN combining multiple paradigms to address training stability, data scarcity, and architectural limitations.

Figure 3: Generative adversarial nets training process. Blue dashed line represents the discriminative distribution (D), black dotted line shows the data generating distribution, and green solid line indicates the generative distribution (G). The four stages illustrate progression from (a) initial partially-trained networks through (b,c) alternating discriminator and generator updates to (d) Nash equilibrium where $p_{g}=p_{data}$ . (Figure adapted from Goodfellow et al. ( Goodfellow et al., 2014 ) )

Figure 4: Examples of samples generated by GAN model. (a) MNIST digit samples generated by GAN, with the yellow-highlighted column showing the closest training example to demonstrate the model isn’t simply memorizing the training data. (b) Face samples generated from the Toronto Face Database (TFD), with the yellow-highlighted column again showing the nearest training examples. These examples demonstrate the GAN’s ability to generate realistic synthetic data across different domains. (Figure adapted from Goodfellow et al. ( Goodfellow et al., 2014 ) )

Figure 5: Schematic representation of the GAN architecture for 3D porous media reconstruction. The generator network (left) transforms random noise z into synthetic 3D structures through sequential transpose convolution layers, while the discriminator network (right) evaluates whether samples are real or generated through volumetric convolution layers. (Figure adapted from Mosser et al. ( Mosser et al., 2017 ) )

Figure 6: Comparison of original (top) and GAN-generated (bottom) 3D porous media samples: (a,d) Beadpack showing uniform spherical particles, (b,e) Berea sandstone displaying complex intergranular pore structures, (c,f) Ketton limestone exhibiting intricate pore networks. The generated samples demonstrate visual similarity to the training data while maintaining key morphological and statistical properties. (Figure adapted from Mosser et al. ( Mosser et al., 2017 ) )

Figure 7: Schematic of three-dimensional porous media image generation using a DCGAN algorithm. The framework consists of three main components: (1) Training data preparation where a 1000 3 voxel image is divided into 64 3 subvolumes, (2) A generator network (G1-G5) that processes data with an incremental factor $\alpha$ to enable upscaling, and (3) A discriminator network (D1-D6) that evaluates image quality through multiple stages. The network parameters $\theta_{g}$ and $\theta_{d}$ are updated iteratively using a Hinge Loss function to optimize generation quality. (Figure adapted from Zhang et al. ( Zhang et al., 2025a ) )

Figure 8: Representative results from SliceGAN showing microstructure generation across different material systems. From top to bottom: (A) synthetic polycrystalline grains, (B) anisotropic battery separator material, (C) polycrystalline steel with orientation coloring, and (D) NMC battery cathode. For each row: training image (left), generated 3D volume, parallel 2D slices showing consistency with training data, and 45° angle slices demonstrating 3D structural coherence. (Figure adapted from Kench et al. ( Kench and Cooper, 2021 ) )

Figure 9: Comparison between training and generated microstructures for lithium-ion battery cathode (left) and solid oxide fuel cell (SOFC) anode (right). Top row: Original training set images obtained from experimental data. Bottom row: Synthetic microstructures generated by GAN model. The generated structures demonstrate visual similarity to the training data while maintaining distinct features for each material system. (Figure adapted from Gayon-Lombardo et al. Gayon-Lombardo et al. (2020) )

Figure 10: Schematic overview of the ScaffoldGAN framework showing the generator network G that takes random noise z as input, discriminator network D, and the combined loss functions ( $L_{adv}$ , $L_{g}$ , $L_{s}$ ) used for training. The framework generates synthesized 3D scaffold structures while maintaining spatial coherence through structural and gram losses. (Figure adapted from Zhang et al. ( Zhang et al., 2021b ) , with permission)

Figure 11: Schematic illustration of the progressive growing training strategy for GANs. The methodology initiates with low-resolution networks (4×4 spatial resolution) for both generator (G) and discriminator (D), with subsequent incremental addition of convolutional layers to increase spatial resolution during training. All network layers remain trainable throughout the progressive growth process, enabling stable high-resolution synthesis. The right panel demonstrates representative outputs generated at 1024×1024 resolution, showcasing the framework’s capability for high-quality image synthesis. (Figure adapted from Karras et al. ( Karras et al., 2017 ) ).

Figure 12: Representative carbonate microstructure samples generated by the progressive growing GAN framework. Top row displays three independently synthesized 2D cross-sections at 1024×1024 resolution, with red dashed boxes indicating regions of interest. Bottom row presents magnified views of the corresponding marked regions, revealing the method’s capability to preserve fine-scale pore structure details and phase boundary characteristics. The generated microstructures exhibit visual fidelity comparable to experimental carbonate images, demonstrating diverse micro-scale structural features without resolution degradation. (Figure adapted from You et al. ( You et al., 2021 ) ).

Figure 13: The progressive growing architecture of MS-GAN for multi-scale porous media reconstruction. The network grows from 4×4×4 to 128×128×128 resolution through six stages, with generator (G) and discriminator (D) networks expanding via upsampling (Us) and downsampling (Ds) operations respectively. Random noise inputs (z) are processed through increasingly complex network paths across stages. (Figue adapted from Xia et al. ( Xia et al., 2022 ) ).

Figure 14: Multi-scale feature extraction process using a fixed receptive field (11×11×11 voxels) across different scales. The input image sizes vary from 64×64×64 at the finest scale (scale 0) to 16×16×16 at the coarsest scale (scale 4), with the same receptive field used to capture features at each scale. (Figure adapted from Zhang et al. ( Zhang et al., 2023f ) , with permission).

Figure 15: Visual comparison of porous media reconstruction results using different methods: original training image (TI), SNESIM, FILTERSIM, DS, DCGAN, and multi-GAN. Each row shows the exterior view and cross-sectional view (X=32, Y=32, Z=32) of the reconstructed samples. (Figure adapted from Zhang et al. ( Zhang et al., 2023f ) , with permission).

Figure 16: Comparison of pore space characteristics for sandstone samples between ground truth and different reconstructions: (Left) Visual representation of total pore space, connected pore space, and isolated pore space for ground truth and reconstructed samples using SNESIM, SinGAN, ConSinGAN, and SASGAN; (Right) Quantitative comparison through boxplots showing (b.1) total porosity, (b.2) connected porosity, and (b.3) isolated porosity distributions. The horizontal red dotted lines indicate the corresponding porosity values from the ground truth sample, demonstrating SASGAN’s ability to preserve pore space characteristics. (Figure adapted from Zhang et al. ( Zhang et al., 2023b ) ).

Figure 17: Architecture of Kishimoto et al.’s cGAN for three-phase microstructure generation. The generator $G_{\phi}(z,V)$ accepts a latent vector $z$ (random noise) and conditional vector $V$ (target volume fraction) as inputs. Training employs dual optimization, the discriminator $D_{\theta}$ is trained to distinguish real from generated structures via adversarial loss $\mathcal{L}_{\text{adv}}$ , while the generator minimizes both $\mathcal{L}_{\text{adv}}$ and volume fraction loss $\mathcal{L}_{\text{vf}}$ to produce realistic Ni-YSZ anode structures with precise compositional control (Figure adapted from Kishimoto et al. ( Kishimoto et al., 2023b ) , with permission)

Figure 18: Comparison of real and generated Ni-YSZ anode structures with different volume fractions (60:40 and 40:60), demonstrating the model’s ability to generate realistic microstructures for compositions not included in the training data (Figure adopted from Kishimoto et al. ( Kishimoto et al., 2023b ) , with permission)

Figure 19: Framework of the CVAE-GAN architecture for digital rock reconstruction with porosity control. The network combines a conditional variational autoencoder with a GAN structure, incorporating porosity conditions at multiple stages to enable controlled generation. (Figure adapted from Chi et al. ( Chi et al., 2023 ) , with permission)

Figure 20: Physical property validation of the CVAE-GAN reconstructed samples showing formation factor, velocity-P, and velocity-S measurements across different porosity conditions, demonstrating consistency with real sample properties. (Figure adapted from Chi et al. ( Chi et al., 2023 ) , with permission)

Figure 21: Network architecture for conditional reconstruction of porous media from partial images: (a) Generator network architecture showing convolutional layers (blue arrows), transposed convolutional layers (yellow arrows), and skip connections (orange arrows) that processes the partial image input to reconstruct the complete structure. (b) Discriminator architecture that evaluates generated samples against real data by processing both the conditional input and the generated/real output through convolutional layers with LeakyReLU activation and instance normalization (blue arrows), followed by a Sigmoid activation function (purple arrow). (Figure adapted from Feng et al. ( Feng et al., 2019 ) , with permission).

Figure 22: Overview of the ST-CGAN framework for 3D porous media reconstruction: (a) Architecture showing the statistical data generator that extracts information from 2D input data to create conditional data, and the conditional generative adversarial neural network that combines this with random noise to produce 3D reconstructions. (b) Comparison between original/training samples and reconstructed outputs using different methods (ST-CGAN, 3D GAN, and MJQA), demonstrating ST-CGAN’s high ability to preserve structural features (Figure adapted from Shams et al. ( Shams et al., 2021 ) , with permission).

Figure 23: ConvAttentionBlock architecture for hybrid self-attention mechanism. The block processes input through three parallel pathways generating Query (Q), Key ( $K^{T}$ ), and Value (V) representations via Conv3d operations. Attention weights $A^{\prime}$ are computed from Q and $K^{T}$ interactions, then applied to V through element-wise multiplication. The attention-refined features combine with the input via residual connections and element-wise addition before InstanceNorm3d normalization. The architecture shows three repeated attention modules demonstrating the hierarchical processing structure. (Figure adapted from Wang et al. ( Wang et al., 2023 ) ).

Figure 24: Structure of the Convolutional Block Attention Module (CBAM) showing channel and spatial attention pathways. The channel attention module utilizes max and average pooling operations followed by MLP layers, while the spatial attention module employs convolution operations to generate attention maps. Element-wise multiplication and addition operations combine attention-refined features. (Figure adapted from Zhang et al. ( Zhang et al., 2023c ) ).

Figure 25: Architecture of the SMAGAN generator showing progressive feature generation across multiple scales. The network processes input noise $z_{1}$ through $z_{N}$ at each stage, incorporating $(3\times 3\times 3)$ convolutions (purple), $(1\times 1\times 1)$ convolutions (orange), upsampling operations (red), feature blocks (blue), and CBAM modules (green) at each scale level. The generator progressively creates porous media structures ( $\tilde{x}_{1}$ through $\tilde{x}_{N}$ ) at increasing resolutions, with CBAM enhancing feature extraction at finer scales to capture detailed structural characteristics while maintaining computational efficiency. Element-wise addition operations combine features across scales. (Figure adapted from Zhang et al. ( Zhang et al., 2023c ) ).

Figure 26: Overall framework of AttentionGAN for multiscale fusion of tight sandstone digital rocks. The network consists of bidirectional transformations: LR to HR (top) with generators $G_{C}$ and $G_{A}$ producing content and attention masks, and HR to LR (bottom) with generators $F_{C}$ and $F_{A}$ . Both pathways use cycle-consistency loss to maintain feature consistency. The architecture generates HR attention masks and HR content masks that guide the fusion process, enabling integration of micro-CT (LR) and SEM (HR) images while preserving multiscale structural features. (Figure adapted from Chi et al. ( Chi et al., 2024a ) , with permission).

Figure 27: Comparison between (a) micro-CT images (resolution: 8 $\mu$ m), (b) predicted SEM images, and (c) real SEM images (resolution: 0.5 $\mu$ m). Various mineral components are highlighted: kaolinite (orange), K-feldspar (yellow), pores (red), quartz (blue), albite (purple), and chlorite (green), demonstrating the network’s ability to preserve mineral features across scales. The predicted images show strong consistency with real SEM images while maintaining correspondence with micro-CT structural features, validating AttentionGAN’s effectiveness for multiscale fusion. (Figure adapted from Chi et al. ( Chi et al., 2024a ) , with permission).

Figure 28: Style-based GAN architecture. The mapping network transforms input latent code z into intermediate latent space w through 8 fully-connected layers. The synthesis network progressively generates images from 4×4 to higher resolutions, with style information injected at each scale via adaptive instance normalization (AdaIN) operations. Learned affine transformations (A) modulate styles, while per-channel scaling factors (B) apply noise for stochastic variation. This architecture enables hierarchical control over generated features at different scales. (Figure adapted from Karras et al. ( Karras et al., 2018 ) )

Figure 29: Progressive multi-scale reconstruction in StyleGAN showing hierarchical feature control across different resolutions. Coarse scales define background pore distribution, intermediate scales enrich pore structure and boundaries, and fine scales add microscopic details. Porosity values (por.) indicate progressive refinement at each scale. (Figure adapted from Cao et al. ( Cao et al., 2022 ) , with permission).

Figure 30: Visual comparison of obtained results for Alporas aluminum foam: (a) original image of alporas, (b) result of StyleGAN; Berea sandstone: (c) original image, (d) result of StyleGAN+quilting. (Figure adapted from Fokina et al. ( Fokina et al., 2020 ) , with permission).

Figure 31: Architectural overview of StyleGAN2-ADA generator. (a) The generator network starts with a latent vector z mapped through fully-connected layers to intermediate latent space w. The synthesis network begins with a constant input, progressively upsampling through multiple resolution levels (4×4 to 256×256) with modulation, demodulation, and noise injection at each scale. Style injection occurs through learned affine transformations (A), while noise is added with learned per-channel scaling factors (B). Skip, general, and residual connections are indicated by different colored arrows. (b) Discriminator network, employing a symmetric downsampling path from 256×256 to 4×4 resolution with residual connections and concatenation operations. (Figure adapted from Haribabu et al. ( Haribabu et al., 2023 ) , with permission)

Figure 32: Qualitative comparison between original titanium alloy microstructures (top) and synthetic images generated by StyleGAN2-ADA (bottom) at two different resolutions: 256×256 pixels and 512×512 pixels. Images showcase three distinct microstructural morphologies: bimodal (left), lamellar (middle), and acicular (right). The synthetic images demonstrate high fidelity to the original microstructural features across different scales. (Figure adapted from Haribabu et al. ( Haribabu et al., 2023 ) , with permission).

Figure 33: Architecture of the EFPN-StyleGAN framework for 3D porous media reconstruction from 2D images. The encoder extracts multi-scale features (C0 to C4) using an extended feature pyramid network, which are transformed into style codes (w0 to w4) via map2style modules. The generator incorporates these features through CIAR (ConvTrans-InstNorm-AdaIN-ReLU) blocks to progressively construct the 3D structure. Three discriminators (Dzx, Dxy, Dyz) evaluate orthogonal cross-sections (xy, xz, yz planes) to ensure 3D consistency. (Figure adapted from Li et al. ( Li et al., 2024a ) , with permission).

Figure 34: The architecture of CISGAN (Combined InfoGAN and StyleGAN) for porous media reconstruction. The network consists of a mapping network that transforms latent code and prior information into an intermediate latent space w, a synthesis network that progressively generates the 3D structure through AdaIN operations and convolutions, and a discriminator with a classifier Q to ensure porosity constraints. (Figure adapted from Cao et al. ( Cao et al., 2022 ) , with permission).

Architecture Type	Key Features	Style Injection Method	Notable Implementations	Primary Applications
Original StyleGAN	Mapping network (8 layers) Six connected blocks Progressive resolution growth Dual-channel control system	AdaIN operations after each layer Noise injection for local variations Progressive resolution control (8 $\times$ 8 to 128 $\times$ 128)	Fokina et al. (2020)	Microstructure synthesis for porous media
StyleGAN2-ADA	Adaptive discriminator augmentation Dynamic training adjustment Improved training stability Path length regularization	AdaIN with augmentation-aware mixing Multi-resolution style control Style demodulation	Thakre et al. (2023) Haribabu et al. (2023) Huang et al. (2022)	Limited dataset applications (DP steels, titanium alloys)
Hybrid StyleGAN Architectures	InfoGAN + StyleGAN CycleGAN + StyleGAN2 Multi-scale feature fusion	Combined style injection methods Domain-specific style transfer Multi-scale information fusion	Li et al. (2024) Cao et al. (2022) Liu et al. (2022)	Multi-scale reconstruction, unpaired data handling

Table 1: Technical Variations of StyleGAN Architectures in Material Reconstruction

Figure 35: Hybrid GAN-VAE architecture for 2D-to-3D reconstruction. A 2D slice is encoded into latent vector $z_{vae}$ , concatenated with Gaussian noise $z_{noise}$ , and fed to the generator to produce 3D synthetic realizations (128³ voxels). The discriminator distinguishes between real training volumes and generated outputs. This approach combines learned structural features with stochastic sampling for diverse, high-quality 3D reconstructions. (Figure adapted from Zhang et al. ( Zhang et al., 2021a ) , with permission).

Figure 36: EWGAN-GP architecture for 2D-to-3D reconstruction with multi-directional discrimination. The encoder (E) processes a 2D training image into latent code vector $\mathbf{Z}_{E}$ , which is combined with random latent vector $\mathbf{Z}_{N}$ and fed to generator (G) to produce a 3D reconstruction. Three discriminators ( $D_{xy}$ , $D_{yz}$ , $D_{zx}$ ) evaluate orthogonal cross-sections along x, y, and z axes to ensure statistical consistency across all spatial orientations. A porosity loss function ( $L_{Porosity}$ ) constrains global structural properties. This multi-discriminator approach with Wasserstein distance and gradient penalty enables stable training while preserving pore network connectivity. (Figure adapted from Li et al. ( Li et al., 2023a ) , with permission).

Figure 37: Autoencoder architecture for post-processing GAN-generated images. The encoder $f_{\theta}$ compresses GAN-generated images (containing inter-grain pores) through progressively smaller feature layers into a compressed latent code representation $h^{(t)}$ . The decoder $g_{\theta}$ reconstructs the image through progressively larger layers, incorporating fine-scale intra-grain porosity learned from high-resolution SEM training data. This two-stage approach enables multi-scale reconstruction by combining GAN-generated macro-porosity with AE-enhanced micro-porosity features. (Figure adapted from Shams et al. ( Shams et al., 2020 ) , with permission).

Figure 38: The discriminator architecture of 3D-FGAN showing AE-based regularization with random crop operations and multiple decoder blocks for reconstruction. The discriminator processes fake/true images through DownBlockComp modules, applies random cropping, and uses SimpleDecoders to compute reconstruction losses alongside the discriminator loss for enhanced training stability. (Figure adapted from Zhang et al. ( Zhang et al., 2024a ) , with permission).

Figure 39: Architecture of 3D-MSPGAN showing the dual-generator framework. The network combines multi-scale discrimination with scaling transformation to enable single-image training. The first generator (top) creates reconstructions while the second generator (bottom) performs inverse scaling for validation. Skip connections (dotted lines) facilitate information flow between corresponding encoder-decoder layers. The discriminator (right) evaluates features across multiple scales through scaling transformations. (Figure adapted from Zhang et al. ( Zhang et al., 2022c ) , with permission).

GAN Category	Reference	Code Availability
Vanilla GAN	Zhang Y. et al. ( Zhang et al., 2025a )	https://github.com/ImperialCollegeLondon/porescale https://github.com/iPMLab/Multi-physics-Network-Model
	Amiri H. et al. ( Amiri et al., 2024 )	https://github.com/hamediut/True2Dto3Drecon
	Zhang T. et al. ( Zhang et al., 2023d )	https://github.com/Hugsazp/3DRGAN
	Zhang T. et al. ( Zhang et al., 2022d )	https://github.com/vevvve/IWGAN-GP
	Kench S. et al. ( Kench and Cooper, 2021 )	https://github.com/stke9/SliceGAN
	Gayon-Lombardo A. et al. ( Gayon-Lombardo et al., 2020 )	https://github.com/agayonlombardo/pores4thought

Table 2: Code Availability for GAN-based Porous Media Reconstruction Methods

Figure 40: Decision framework for selecting GAN architectures for porous media reconstruction. The flowchart guides practitioners through critical selection criteria: input data characteristics (2D vs 3D, quantity), reconstruction objectives (property control, volume scale), and architectural constraints (training stability, connectivity preservation). Each architecture pathway displays demonstrated capabilities (green boxes) with quantitative performance benchmarks and known limitations (red boxes) from reviewed literature. Dashed arrows indicate fallback pathways when primary methods encounter limitations. Three decision phases progress from data availability assessment through reconstruction goal specification to final architecture selection.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Reference	Year	Loss Function	Training Images		Generated Images		Image Type	Material	Novelty	Evaluation Metrics	Computational Requirements
			Size	Dim	Size	Dim
Zhou Y. et al. [ 57 ]	2025	WGAN	$383^{2}$ and $400^{2}$ pixels	2D	$383^{3}$ voxels	3D	Binary and Multi-phase (3-phase)	Tight carbonate rocks (Ordovician Majiagou Formation) and Berea sandstone	Application of SliceGAN to tight carbonate reconstruction with MAPS and QEMSCAN integration for multi-component mineral identification (dolomite, calcite), addressing complex pore structures and heterogeneity in tight carbonate reservoirs	Auto-correlation function Two-point probability function Minkowski functions Porosity Mineral content Formation factor Permeability (LBM)	Dataset: Berea 9 samples ( $383^{3}$ ), Carbonate 7 MAPS images ( $400^{2}$ ); GPU RTX 4090; CPU Xeon W-2195 @ 2.30 GHz; 136GB RAM; $\sim$ 2 hours; 20–30 epochs
Liu D. et al. [ 58 ]	2025	WGAN-GP	$614^{2}$ pixels	2D	$384^{3}$ voxels	3D	Multi-phase (4-phase)	Shale (Longmaxi Formation, Sichuan Basin)	Novel REV-size digital rock reconstruction workflow integrating high-resolution MAPS with OM watershed classification into three connectivity types based on surface porosity (Type A ¿20%, B 10–20%, C ¡10%), demonstrating Type C OM dominates gas transport at REV scale	Porosity comparison Pore diameter distributions Coordination number distributions Two-point correlation Connectivity analysis Area ratio stability	Dataset: 3 samples, 144 sub-images per sample ( $614^{2}$ ); FIB-SEM validation $1600\times 1600\times 1000$ voxels; GPU RTX 4000 (8GB); CPU Intel i9-10900K; 64GB RAM; $\sim$ 24 hours; 50 epochs
Zhang Y. et al. [ 47 ]	2025	Hinge Loss	$64^{3}$ voxels	3D	$512^{3}$ voxels	3D	Binary	Bentheimer sandstone	DCGAN with $8^{3}$ upscaling combined with PNM for CO2 storage efficiency prediction and quantifying minimum simulations needed	Minkowski functionals Two-point correlation Morphological properties	Dataset: 6000 sub-volumes ( $64^{3}$ ); GPU/training time not reported
Amiri H. et al. [ 56 ]	2024	WGAN-GP	$256^{2}$ pixels	2D	$256^{3}$ voxels	3D	Binary (2-phase)	Berea sandstone	Systematic 3D reconstruction from purely 2D images without 3D training data, enabling diverse reconstructions for uncertainty assessment	Two-point correlation functions Fréchet Inception Distance Pore characteristics distribution Permeability estimates	Dataset: Large 2D images (7.78–15.56mm BSE, 11.95–23mm optical); GPU RTX A6000 (48GB); 24 hours
Chi P. et al. [ 60 ]	2024	WGAN-GP + Reconstruction Loss (MSE)	3D LR: $128^{3}$ (S1), $512^{3}$ (S2) voxels; 2D HR: up to $4096^{2}$ pixels	3D + 2D	Up to $512^{3}$ voxels (4–8 $\times$ upsampling)	3D	Grayscale and Binary	Tight sandstone	Novel 2D-3D fusion framework combining CT and SEM images Lightweight 3D generator with 2D discriminator architecture Direct high-resolution 3D generation with better continuity 4–8 $\times$ super-resolution capability	Porosity Fractal dimension Pore structure parameters Permeability (Lattice Boltzmann) Autocorrelation function Pore connectivity	Dataset: S1 (CT: 4 $\mu$ m HR/16 $\mu$ m LR); S2 (CT 8 $\mu$ m + SEM 2 $\mu$ m); GPU RTX 3060; $\sim$ 20 hours; Batch 16

Appendix

Table 1: Summary of Vanilla GAN Architectures for Digital Porous Material Reconstruction

Reference	Year	Loss Function	Training Images		Generated Images		Image Type	Material	Novelty	Evaluation Metrics	Computational Requirements
			Size	Dim	Size	Dim
Ugolkov E. et al. [ 71 ]	2025	WGAN-GP with MSE Reconstruction	3D LR: $32^{3}$ voxels; 2D HR LSM: 5 stages from $64^{2}$ to $1024^{2}$ pixels	3D + 2D	$512^{3}$ voxels per sub-volume (up to $4096^{3}$ via stitching)	3D	Segmented (4-phase)	Berea sandstone	Memory-efficient octree-based progressive growing DC WGAN-GP achieving 16× super-resolution (7 µm to 0.44 µm/voxel) using Minkowski Engine for sparse convolutions Uses unpaired 3D micro-CT and 2D LSM images for training Corrects segmentation inaccuracies in minerals with similar X-ray attenuation Generates arbitrary-sized images via sub-volume stitching with 50% overlap Addresses cubic memory scaling limitation of standard Conv3D	Volume fraction Relative surface area Two-point correlation function Pore size distribution (PSD) Pore network extraction (PNE)	Dataset: 3D micro-CT volume $1192\times 1266\times 1540$ voxels (7 µm/voxel), 2D HR LSM images (0.44 µm/pixel) GPU: Two NVIDIA A100 80GB RAM: 450 GB Training: 71 hours total (100 epochs per stage, 5 stages) Batch size: 2
Zhao X. et al. [ 78 ]	2025	WGAN-GP	Variable: $200^{2}$ to $800^{2}$ pixels	2D	Variable: $200^{3}$ to $800^{3}$ voxels	3D	Grayscale	Hardened cement paste	Multi-scale learning strategy capturing cement microstructure at various scales Block-wise synthesis for generating large-size 3D images Slicing strategy for cross-dimensional 2D-3D correlation Successfully handles complex multi-phase cement microstructures Single 3D generator with multiple 2D discriminators at different scales	Gray level histogram Phase proportions (pores, hydration products, unreacted clinkers) Pore size distribution (PSD)	Dataset: Single 2D BSE images at various resolutions GPU: NVIDIA A100 Tensor Core CPU: Intel Xeon Silver 4214R Training: 15.8 hours
Zhu L. et al. [ 70 ]	2024	WGAN-LP with Lipschitz Penalty	$64^{3}$ and $128^{3}$ voxels	3D	Up to $2,200^{3}$ voxels	3D	Binary	Sandstone (Berea, Bentheimer, Mt. Simon) and carbonate (Estaillades, Savonnières)	Laplacian pyramid generator with WGAN-LP for multi-scale feature capture and large-scale generation using FSMR-enhanced discriminator	Porosity Absolute permeability Curvature Specific surface area Euler characteristic Two-point correlation functions Pore shape factors	GPU: NVIDIA Quadro RTX 5000 CPU: Dual Intel Xeon Gold 5222 RAM: 64GB Training: 800 iterations max Generation time: 2.47-5.62s ( $300^{3}$ ), 5h ( $2,200^{3}$ )
Zhang T. et al. [ 74 ]	2023	WGAN-GP with L2 Reconstruction	HR: $80^{3}$ voxels, LR: $40^{3}$ voxels (6 scales: $16^{3}$ to $80^{3}$ )	3D	$80^{3}$ voxels	3D	Binary	Sandstone and Shale	Combines CBAM attention mechanisms and residual blocks with SinGAN for 3D super-resolution from single low-resolution training image	Pore space analysis Absolute permeability in X, Y, Z directions Multi-point connectivity curves Autocorrelation functions Pore/throat size distributions and coordination number	GPU: GeForce RTX3080 CPU: AMD R9 3900X 3.8 GHz RAM: 16GB Training time: 3000 epochs per scale, 6 hours for first reconstruction
Li Y. et al. [ 79 ]	2023	WGAN-GP with L2 Reconstruction	Shale: 2 slices from $120^{3}$ voxel, Berea: 2 slices from $100^{3}$ voxel	2D	Shale: $120^{3}$ , Berea: $100^{3}$	3D	Binary (2-phase)	Shale (anisotropic), Berea Sandstone (isotropic)	Combines MCMC with GAN for 3D reconstruction from only 2 training images, addressing connectivity issues in 2D-to-3D methods	Two-point correlation function in x, y, z directions Porosity Minkowski functionals	Hardware: Not specified Training time: Berea sandstone ( $100^{3}$ ): 0.32h; Shale ( $100^{3}$ ): 0.82h

Appendix

Table 2: Summary of Multi-Scale GAN Architectures for Digital Porous Material Reconstruction

Reference	Year	Loss Function	Training Images		Generated Images		Image Type	Material	Novelty	Evaluation Metrics	Computational Requirements
			Size	Dim	Size	Dim
Torben J. et al. [ 85 ]	2025	CCGAN Loss (reformulated empirical cGAN)	$128^{2}$ pixels	2D	$128^{2}$ pixels, $128\times 128\times 901$ voxels	2D/3D	Binary (2-phase)	Porous Asphalt	CCGAN-based framework with continuous porosity regression label, user-defined vertical porosity profile generation, latent space interpolation for cohesive 3D volume synthesis from 2D slices, integrated segmentation via SoftMax and one-hot encoding, optimal interpolation step determination via RMSE minimization	Porosity profile control Mean correlation between slices RMSE between correlation curves Material properties: porosity, surface area, effective diffusivity TauFactor metrics Statistical analysis (50 volumes)	GPU: NVIDIA 3090 RTX Ti Dataset: 32,000 patches from 2000³ voxel CT scan (cropped to $1000\times 1000\times 901$ ) Generation time: 0.7s per volume Training time: Not specified
Sadeghkhani A. et al. [ 89 ]	2025	Binary Cross Entropy Loss	$480^{2}$ pixels	2D	$480^{2}$ pixels	2D	Colour (RGB)	Carbonate formations (Dolomite, Dolomite-Anhydrite)	Multi-conditional GAN with dual constraints (porosity + depth), RGB thin section processing preserving petrographic information, superior representativeness: 1.9-11.3% error vs. 36.4-578% for real sub-images, automated framework with REV analysis and U-Net	Porosity Control, Morphological parameters: pore radius, specific surface area, tortuosity Dual-property performance: 1.9-11.3% vs. 36.4-578% Statistical tests: KS-test, t-test, Cohen’s d Visual quality and architecture comparison	GPU: NVIDIA A2 (15 GB) CPU: AMD EPYC 9354P 32-Core Dataset: $\sim$ 6,400 images (1,600 per sample $\times$ 4 samples) Training time: 200 epochs
Zhou R. et al. [ 88 ]	2023	WGAN-GP with Porosity Feature Loss	$64^{3}$ voxels	3D	$64^{3}$ voxels	3D	Binary (2-phase)	Berea sandstone	Multi-conditional GAN with petrophysical parameters, dynamic penalty feature loss, and switchable conditioning	Two-point correlation function Statistical distribution of petrophysical parameters Porosity Fractal dimension Specific surface area Tortuosity	GPU: NVIDIA GeForce RTX 3080 CPU: Intel Core i9-12900K Dataset: 3,375 samples Training time: 61 hours
Kishimoto M. et al. [ 83 ]	2023	cGAN Adversarial Loss + Volume Fraction Loss (MSE)	$64^{3}$ voxels	3D	$64^{3}$ to $256^{3}$ voxels	3D	Multi-phase (3-phase)	Ni-YSZ anode for SOFC	Volume fraction control via conditional input, fully convolutional for expandable outputs, extrapolation beyond training	Volume fraction control Specific surface area TPB density	GPU: NVIDIA GeForce RTX 3090 Dataset: 3,000 structures per composition Training time: 100 epochs Batch size: 32
Kishimoto M. et al. [ 136 ]	2023	Adversarial Loss + Volume Fraction Loss (MSE)	$64^{3}$ voxels	3D	$64^{3}$ voxels	3D	Multi-phase (3-phase)	SOFC anode (Ni-YSZ)	Conditional vector with volume fraction loss for generating compositions outside training distribution	Volume fraction control Specific surface area TPB density Volume fraction distributions	GPU: NVIDIA GeForce RTX 3090 Dataset: 3,000 structures total Training time: 100 epochs Batch size: 32

Appendix

Table 3: Summary of Conditional GAN Architectures for Digital Porous Material Reconstruction

Reference	Year	Loss Function	Training Images		Generated Images		Image Type	Material	Novelty	Evaluation Metrics	Computational Requirements
			Size	Dim	Size	Dim
Chi P. et al. [ 97 ]	2024	GAN loss + cycle-consistency loss + identity preserving loss	Micro-CT: $64^{2}$ pixels, SEM: $1024^{2}$ pixels	2D	$16000^{2}$ pixels (stacked to 3D)	3D	Grayscale	Tight Sandstone	Integration of attention mechanisms with GAN for multiscale fusion. Combines micro-CT and SEM images. Focus on clay morphology and micropore reconstruction	Two-point correlation functions, Representative volume element analysis, Pore radius distributions, Mineral content analysis, Quantitative segmentation analysis, Permeability measurements	GPU: NVIDIA GeForce RTX 3090 Dataset: 3,776 SEM images (1024×1024) Training time: 12 hours, 40 epochs Learning rate: 0.0002 with decay
Zhang T. et al. [ 74 ]	2023	WGAN-GP + L2 reconstruction loss	HR: $80^{3}$ , LR: $40^{3}$ voxels	3D	$80^{3}$ voxels	3D	Binary	Sandstone and Shale	Combines attention mechanisms (CBAM) and residual blocks with SinGAN framework. Achieves 3D super-resolution from a single LR training image. Validated on both sandstone and shale samples	Total, connected, and isolated porosities, Absolute permeability (X, Y, Z directions), Multi-point connectivity curves, Autocorrelation functions, Pore/throat size distributions, Pore/throat numbers, Coordination number distributions, Diversity metrics (MS-SWD-MDS)	GPU: NVIDIA RTX 3080 (10GB) CPU: AMD Ryzen 9 3900X Dataset: 6 scales (16³ to 80³ voxels) Training time: 6h initial, 1s subsequent Single-image training approach
Wang B. et al. [ 96 ]	2023	WGAN loss	$64^{3}$ voxels	3D	$64^{3}$ voxels	3D	Grayscale	Carbonate (Estaillades carbonate)	Integration of self-attention mechanism for carbonate rock reconstruction. Combines traditional and fully convolutional self-attention mechanisms. Specific focus on carbonate rock features. Enhanced ability to capture heterogeneity in pore distribution	Porosity accuracy, Grayscale value distribution, Mean value comparison	Dataset: 4,000 samples (augmented 4×) Batch size: 48 Learning rate: 2×10 -4
Wang P. et al. [ 98 ]	2023	Standard GAN logarithmic loss	$64^{3}$ voxels	3D	$64^{3}$ voxels evaluated on $400^{3}$ voxel reconstructions	3D	Binary	Shale	Integration of context-aware modules. High-resolution optical flow estimation. Enhanced feature extraction for nano-micron pores	Two-point correlation function, Two-point cluster function, Linear path function, Chord length distribution function, Porosity metrics, Permeability metrics, Pore structure parameters, REV analysis	GPU: GTX 1080Ti RAM: 32GB Dataset: 10,648 hdf5 files Training time: 12 hours, 400 epochs Batch size: 64
He L. et al. [ 95 ]	2023	Wasserstein loss with gradient penalty (WGAN-GP)	$128^{2}$ pixels	2D	$128^{2}$ pixels	2D	Grayscale segmented	Shale	Introduction of residual self-attention block (RSAB). Combination of residual structure and self-attention mechanism. Enhanced feature correlation learning	Fréchet Inception Distance, Kernel Inception Distance, Two-Point Covariance Function, Minkowski Functions, Pore analysis metrics (number, diameter, distribution)	GPU: NVIDIA RTX 3060 (12GB) Dataset: 100,000 samples (augmented 5×) Training: 100,000 iterations Batch size: 128

Appendix

Table 4: Summary of Attention-Enhanced GAN Architectures for Digital Porous Material Reconstruction

Reference	Year	Loss Function	Training Images		Generated Images		Image Type	Material	Novelty	Evaluation Metrics	Computational Requirements
			Size	Dim	Size	Dim
Li J. et al. [ 103 ]	2024	WGAN-GP loss + pattern density loss	$128^{2}$ pixels	2D	$128^{3}$ voxels	3D	Binary (2-phase)	Sandstone, limestone, silica particles	End-to-end 3D reconstruction from single 2D image using EFPN-StyleGAN architecture Multi-scale feature extraction addressing small pore localization Three discriminators for orthogonal evaluation with pattern density constraint Feature fusion architecture handling varying sensitivities at different scales	Connectivity parameters (porosity, effective porosity, connected pore volume ratio) Morphological descriptors (two-point correlation S2, lineal-path function L, two-point cluster C2, local porosity distribution) Microstructure parameters (pore/throat analysis: AP, AT, ASF, ASPR, ASTR, AVP, AVT, ARRSPT, ACN) Effective permeability (EP)	Dataset: 16,000 2D images for each material type Hardware: NVIDIA GeForce RTX 3090Ti (24GB VRAM), Intel Xeon Silver 4114, 128GB RAM Batch size: 16
Thakre S. et al. [ 105 ]	2023	Traditional GAN loss with binary cross-entropy	$256^{2}$ pixels	2D	$256^{2}$ pixels	2D	Binary (2-phase)	Dual Phase (DP) steels	First quantification of similarity and physical awareness of GAN-generated microstructures Implementation of StyleGAN2 with ADA for microstructure generation Novel evaluation framework combining statistical and physical metrics	Image similarity metrics (SSIM, MSE, PSNR, SNR) Two-point correlation analysis Volume fraction analysis Phase volume ratios ROM prediction accuracy (R² scores)	Dataset: 300 images (50 per class, 6 classes) Training time: 6 hours Hardware: Single Tesla T4 (12GB RAM)
Haribabu G. et al. [ 106 ]	2023	WGAN-GP loss	$512^{2}$ , $256^{2}$ , $128^{2}$ pixels	2D	$512^{2}$ , $256^{2}$ , $128^{2}$ pixels	2D	Grayscale	Ti-6Al-4V (titanium alloy)	First demonstration of StyleGAN2-ADA for generating synthetic titanium alloy microstructures using limited dataset (1225 images)	FID (Frechet Inception Distance) KID (Kernel Inception Distance) IS (Inception Score) Phase fraction analysis Grain type distribution Two-point correlation analysis Local boundary thickness measurements	Dataset: 1,225 images Hardware: Not specified Batch size: 64 Training epochs: 1000
Cao D. et al. [ 102 ]	2022	WGAN-GP + InfoGAN mutual information loss	$128^{3}$ voxels	3D	$128^{3}$ voxels	3D	Binary (2-phase)	Berea Sandstone and Tight Carbonate	Combined InfoGAN and StyleGAN architectures Multi-scale information fusion through style transfer Prior information (porosity) guided generation Classifier Q ensures porosity constraint	Two-point cluster function Multi-point connectivity function Chord length distribution Pore-throat analysis Porosity accuracy Permeability measurements	Dataset: 27 samples (26 training, 1 test) Hardware: NVIDIA TESLA V100 (32GB) Optimizer: Adam Batch size: 2 Learning rate: 0.0002
Huang Y. and Xiang Z. (1) [ 109 ]	2022	WGAN-GP + L2 regularization	$64^{3}$ voxels	2D slices (extracted from 3D volumes)	$64^{3}$ voxels (training), $128^{3}$ voxels (evaluation)	3D	Binary (2-phase)	Berea Sandstone and Estaillades Carbonate	First application of StyleGAN to slice-to-voxel porous media reconstruction Integration of 3D generator with 2D discriminator for computational efficiency Achieves or exceeds voxel-to-voxel method quality with spatial continuity preservation	Two-point correlation function with radial averaging Minkowski functionals (volume, surface area, mean breadth, Euler characteristic) Visual comparison of reconstructed samples Comparison with Mosser et al. method	Dataset: 10,647 samples (64³ voxels each) Training time: 12 hours Hardware: Single NVIDIA GeForce RTX 2080Ti Batch size: 128 Progressive growing from 4³

Appendix

Table 5: Summary of Style-based GAN Architectures for Digital Porous Material Reconstruction

Reference	Year	Loss Function	Training Images		Generated Images		Image Type	Material	Novelty	Evaluation Metrics	Computational Requirements
			Size	Dim	Size	Dim
Zhang T. & Zhang W. [ 130 ]	2025	WGAN-GP + Reconstruction loss (L2 norm)	$64^{3}$ voxels (general pores), $128^{3}$ voxels (fractures)	3D	$64^{3}$ voxels (general pores), $128^{3}$ voxels (fractures)	3D	Binary	Shale (with significant fractures and general pores)	Novel STGAN combining StyleGAN and Transformer for 3D digital rock reconstruction. Multi-scale feature extraction using Transformer blocks (coarse, intermediate, fine scales). Porosity distribution sequence as conditional/prior information. Classifier Q to constrain porosity distribution during reconstruction	Porosity statistics Pore network parameters (pore/throat numbers and diameters) Absolute permeability (X, Y, Z directions) Multiple-point connectivity (MPC) curves Minkowski functionals (surface area, mean breadth, Euler characteristic) MS-SWD-MDS for diversity evaluation	Dataset: 729 sub-images ( $64^{3}$ ) for general pores; 301 sub-images ( $128^{3}$ ) for fractures Training Time: 50,077s for $64^{3}$ ; 85,340s for $128^{3}$ (10 reconstructions, 8000 epochs) GPU: NVIDIA Tesla V100 (16GB) CPU: Intel Xeon (2.30 GHz) RAM: 16GB
Zhang Y. et al. [ 131 ]	2025	WGAN-GP + ResNet50: LogCosh loss + VGG16: MSE + L1 ( $\lambda=512$ )	$1024^{2}$ pixels	2D	$1024^{2}$ pixels (2D slices), $1090\times 1024\times 1024$ voxels (3D reconstruction through stacking)	2D $\rightarrow$ 3D	Binary	Mt. Simon sandstone (heterogeneous)	RVION (ResNet-VGG Inversion Optimization Network) for inferring latent codes of real rock images. ADA-PGGAN with adaptive data augmentation mechanism to handle limited/scarce training data. Latent space interpolation (Slerp) for 3D reconstruction generating 10 interpolated slices between each pair of scanned slices. Cost efficiency: Up to 10 $\times$ reduction in imaging costs	Sliced Wasserstein Distance (SWD) Minkowski functionals (Euler values, porosity) Two-point correlation function S 2 (r) Absolute permeability (x, y, z directions) Microstructure parameters (Amount of throats/pores, Average shape factors, Average size of pore radius, Average volume of pore, Average coordination number) Fluid flow simulation/velocity field comparison	Dataset: 500 training slices ( $1024^{2}$ ) for ADA-PGGAN, 700 test slices (20% validation), 80,000 generated images for ResNet50 training Training Time: 98 hours GPU: NVIDIA GeForce RTX 3090
Liu F. et al. [ 132 ]	2025	StyleGAN2-ADA: Adversarial + ADA mechanism; SRCycleGAN: Adversarial + Cycle-consistency+ Identity; SegGAN: Conditional adversarial + Identity	StyleGAN2-ADA: $512^{2}$ pixels; SRCycleGAN: LR $64^{2}$ pixels, HR $512^{2}$ pixels; SegGAN: $512^{2}$ pixels	2D	StyleGAN2-ADA: $512^{2}$ pixels; SRCycleGAN: $512^{2}$ pixels (8 $\times$ upscaling); SegGAN: $512^{2}$ pixels; 3D case: 5.12 $\mu$ m 3	2D (extendable to 3D)	Grayscale (multi-phase segmentation: pores, organic matter, clay minerals, pyrite)	Shale	Three-stage GAN framework: image augmentation (StyleGAN2-ADA), 8× super-resolution without paired training (SRCycleGAN), and multi-mineral auto-segmentation (SegGAN with U-Net). Reconstructs fine-scale pores unresolved in LR images. Slice-by-slice 3D processing reduces memory requirements. Addresses resolution vs field of view trade-off	Two-point correlation function S 2 (r) Linear-path correlation function L(r) Entropy (E) Porosity Organic Matter Proportion (OMP) Pore/throat size distribution Coordination number Permeability PSNR, SSIM, IoU Gray histogram comparison Mean shape factor	Dataset: StyleGAN2-ADA: 100 HR sub-images ( $512^{2}$ ); SRCycleGAN: S1: 14,626 LR sub-images ( $64^{2}$ ), S2: 7,904 LR sub-images ( $64^{2}$ ); SegGAN: Paired images Training Time: Not specified GPU: Single NVIDIA V100 RAM: 32GB
Zhang Y. et al. [ 117 ]	2024	Encoder loss with $\beta$ -KLD + Generator loss + Discriminator loss	$64^{2}$ pixels	2D	$64^{2}$ pixels	2D	Binary	Alloy, Carbonate, Ceramics, Copolymer, Rubber, Sandstone, Composite, Synthetic (10 materials total)	Incorporation of $\beta$ -VAE into hybrid GAN. Custom differentiable data augmentation scheme. Ability to train on extremely small datasets. Controllable smoothness of latent space	Two-point spatial correlation function RMSE of correlation functions Reconstruction error ( $\lambda_{rec}$ ) Generation error ( $\lambda_{gen}$ ) Volume fraction	Dataset: 16 samples GPU: RTX 3080Ti Training: 30 min, 20,000 epochs RAM: 64GB CPU: AMD Ryzen 9 5900X Batch size: 4
Zhang T. et al. [ 116 ]	2024	WGAN-GP with code discriminator (two-part loss)	$64^{3}$ voxels	3D	$64^{3}$ voxels	3D	Binary	Shale and Berea sandstone	Added code discriminator to VAE-GAN to handle distribution error. Uses WGAN-GP loss function for better stability. Two adversarial learning stages in each epoch	Multi-point connectivity curves Absolute permeability simulation Pore space analysis (Total/Connected/Isolated porosity, Pore number, Average radius) Difference degree for MPC curves Fréchet inception distance	Dataset: 124 training samples (each material) GPU: GeForce RTX-3080 Training: 4000-5000 epochs ( 68,000s first training) RAM: 16GB CPU: AMD-R9 3900X

Appendix

Table 6: Summary of Hybrid Architecture GAN for Digital Porous Material Reconstruction

Generative Adversarial Networks

Generative Adversarial Networks (GANs) train competing generators and discriminators to synthesize data, translate images, and model complex distributions.

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Jul 2, 2026

Property-Constrained 3D Porous Media Reconstruction from 2D Images via Conditional Generative Adversarial Networks

This study presents a conditional Generative Adversarial Network (cGAN) framework for generating 3D porous media volumes with controlled porosity, trained exclusively on 2D thin section images. The key innovation lies in combining property-conditioned generation with 2D-to-3D reconstruction, eliminating the need for expensive 3D training data while maintaining control over petrophysical properties. The framework employs a hybrid architecture with a 3D generator and 2D discriminator, where multi-axis slice extraction enables learning 3D-consistent structures from 2D training data. Porosity labels are extracted using an Enhanced U-Net segmentation model. The methodology was demonstrated on two carbonate samples with different lithologies: dolomite-anhydrite and pure dolomite. Results show that the framework successfully generates realistic 3D volumes capturing lithological features such as anhydrite inclusions and fine crystalline textures. Porosity control achieved an

R^2

of 0.93, with mean absolute errors of 0.019 and 0.010 for the heterogeneous and homogeneous samples, respectively.

Ali Sadeghkhani, Brandon Bennett, Arash Rabbani

School of Computer Science, University of Leeds, Leeds, UK

3D Reconstruction Conditional Generative Modeling Conditional Generation Generative Adversarial Networks

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Oct 22, 2025

PCP-GAN: Property-Constrained Pore-scale image reconstruction via conditional Generative Adversarial Networks

Obtaining truly representative pore-scale images that match bulk formation properties remains a fundamental challenge in subsurface characterization, as natural spatial heterogeneity causes extracted sub-images to deviate significantly from core-measured values. This challenge is compounded by data scarcity, where physical samples are only available at sparse well locations. This study presents a multi-conditional Generative Adversarial Network (cGAN) framework that generates representative pore-scale images with precisely controlled properties. The framework was trained on thin section samples from four depths (1879.50-1943.50 m) of a carbonate formation, simultaneously conditioning on porosity and depth within a single model. It processes RGB thin section images that preserve critical mineralogical information (anhydrite-dolomite differentiation, grain boundaries, porosity distinctions) lost in conventional grayscale representations, capturing characteristics from grainstone fabrics to crystalline textures with anhydrite inclusions. The model achieved strong porosity control (R^2 = 0.95) across all formations with mean absolute errors of 0.0099-0.0197. Morphological validation confirmed preservation of average pore radius, specific surface area, and tortuosity within acceptable tolerances. Two-point correlation (S2) analysis confirmed that generated images preserve the spatial continuity and characteristic length scales of natural pore networks, with results consistent across the imaging resolutions tested (1.8-3.0 micron/pixel). Validated against core sample properties, generated images showed higher property fidelity with dual-constraint errors of 1.9-12.4% compared to 37.5-713.6% for randomly extracted real sub-images. This capability provides practical tools for subsurface characterization, particularly valuable for carbon storage, geothermal energy, and groundwater management.

Ali Sadeghkhani, Brandon Bennett, Masoud Babaei +1

School of Computer Science, University of Leeds, Leeds, LS2 9JT, UK. · Department of Chemical Engineering, The University of Manchester,2026 Manchester, M13 9PL, UK.

Conditional Image Generation Image Generation Generative Adversarial Networks

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Jul 27, 2026

Physics-Guided Generative AI for Property-Targeted 3D Porous Media Design

Inverse design of three-dimensional porous media is central to applications in filtration, catalysis, energy storage, fuel cells, thermal management, and biomedical scaffolds, but remains challenging because many distinct pore geometries can share similar porosity or permeability while small structural changes can strongly affect transport behaviour. This paper proposes a physics-guided generative AI framework for property-targeted porous media design, combining a property-aware variational autoencoder, a conditional latent diffusion model, and an independently trained differentiable structure-to-property surrogate. The framework learns a compact, physically informative latent design space, generates porous structures conditioned on target porosity and directional permeability, and refines generated samples using property-level feedback during denoising and decoding. Experiments on procedurally generated structures and real micro-CT porous-media datasets show improved target-property matching, directional permeability control, and property correlation compared with representative property-aware variational-autoencoder and latent-diffusion baselines. The results demonstrate a scalable route towards controllable inverse design of complex porous geometries and establish a foundation for simulation-informed generative AI tools in engineering and advanced materials discovery.

Peng Wang

Centre for Vision, Speech and Signal Processing (CVSSP), University of Surrey, Guildford, UK

Generative Modeling Conditional Generative Modeling 3D Diffusion Models Inverse Design Porous Media Flow

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Abstract

Generative Adversarial Networks

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Property-Constrained 3D Porous Media Reconstruction from 2D Images via Conditional Generative Adversarial Networks

PCP-GAN: Property-Constrained Pore-scale image reconstruction via conditional Generative Adversarial Networks

Physics-Guided Generative AI for Property-Targeted 3D Porous Media Design