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

This study introduces PCP-GAN, a multi-conditional Generative Adversarial Network that generates representative, property-constrained pore-scale images from RGB thin sections to overcome data scarcity and spatial heterogeneity, achieving significantly higher fidelity in porosity, mineralogy, and morphological characteristics compared to randomly extracted real sub-images.

Original authors: Ali Sadeghkhani, Brandon Bennett, Masoud Babaei, Arash Rabbani

Published 2026-06-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ali Sadeghkhani, Brandon Bennett, Masoud Babaei, Arash Rabbani

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to understand the inside of a giant, hidden sponge that holds oil, water, or gas deep underground. To do this, scientists usually take a physical core sample (a cylinder of rock) and slice it into thin pieces to look at under a microscope. These slices show the tiny holes (pores) where fluids flow.

However, there are two big problems with this method:

The "Missing Piece" Problem: You can't drill a hole everywhere. You only have samples from a few specific spots. If you want to know what the rock looks like halfway between two drill sites, you're stuck guessing.
The "Bad Snapshot" Problem: Even when you do have a sample, the tiny slice you look at might not represent the whole rock. It might be a lucky slice with huge holes or an unlucky one with almost none. It's like trying to guess the average height of a forest by measuring just one tree; you might pick a giant oak or a tiny sapling and get the wrong idea.

The Solution: A "Digital Rock Chef" (PCP-GAN)

This paper introduces a new computer program called PCP-GAN. Think of it as a highly skilled "Digital Rock Chef" that can cook up brand-new, realistic images of rock pores from scratch. But this chef is special because it follows a strict recipe based on two specific ingredients: Porosity (how many holes the rock has) and Depth (where in the ground the rock is).

Here is how it works, broken down into simple concepts:

1. The Training: Learning from Real Rock

The computer was fed thousands of real, colorful microscope images of rock slices from four different depths in a carbonate rock formation.

The Color Trick: Most rock images are black and white, which loses important details. This program learned from color images (RGB). In these images, the rock minerals are different colors (like white anhydrite vs. gray dolomite), and the holes are dyed blue. This helps the computer understand not just where the holes are, but what kind of rock surrounds them.
The "Porosity" Lesson: The computer learned that rock at Depth A looks different from rock at Depth B, even if they have the same number of holes. It learned the unique "personality" of the rock at each depth.

2. The Magic: Cooking Up New Images

Once trained, you can ask the computer: "Make me a picture of rock from Depth 1 that has exactly 15% holes."

The computer doesn't just copy-paste a picture. It generates a brand new, unique image that has never existed before.
It ensures the new image looks geologically real (with the right grain shapes and mineral colors) and hits the exact "hole count" (porosity) you asked for.

3. Why This is Better Than Random Sampling

The researchers tested their "Digital Rock Chef" against the old method of just cutting random slices from real rocks.

The Old Way (Random Slices): If you grab a random slice from a real rock core, the "hole count" and fluid flow properties might be way off from the average of the whole rock. The error was huge (sometimes off by 700%!).
The New Way (PCP-GAN): The computer-generated images were much more accurate. They matched the real rock's average properties with very small errors (mostly under 12%).
The Analogy: Imagine trying to guess the average temperature of a city.
- Random Sampling: You stand on a hot sidewalk and a cold park bench and guess. You might be way off.
- PCP-GAN: You use a smart model that knows the city's layout and the time of day to generate a perfect "average temperature" reading every time.

4. The "Taste Test" (Validation)

How do we know the fake rocks look real? The researchers ran them through a series of rigorous tests:

The "Shape" Test: They checked if the size of the holes, the surface area, and the "tortuosity" (how twisty the paths are) matched real rocks. They did.
The "Connectivity" Test: They checked if the holes were connected in a natural way, like a real maze, rather than just being scattered dots. The computer got this right too.
The "Resolution" Test: They tested the computer with different levels of zoom (magnification). It worked perfectly at all levels, proving it learned the rules of rock, not just the pictures.

5. What It Can't Do (Limitations)

The paper is honest about what this tool cannot do yet:

It only works on the specific type of rock (carbonate) and depth range it was trained on. It can't magically predict what a sandstone rock looks like if you haven't shown it sandstone yet.
It generates 2D images (slices). While it predicts 3D properties, it doesn't create a full 3D movie of the rock yet.
It relies on a formula to guess "permeability" (how fast fluid flows), which is an estimate, not a direct measurement.

The Bottom Line

This paper presents a tool that solves the "missing data" problem in geology. Instead of hoping to find a perfect rock sample, scientists can now use this AI to generate the perfect rock sample they need for their simulations. It creates geologically authentic images that are statistically more reliable than random slices from real rocks, helping engineers better understand how fluids move underground for things like carbon storage or groundwater management.

Technical Summary: PCP-GAN

Problem Statement
Subsurface characterization faces a fundamental challenge in obtaining pore-scale images that accurately match bulk formation properties. Natural spatial heterogeneity causes extracted sub-images from core samples to deviate significantly from measured values, while data scarcity limits physical sampling to sparse well locations. Existing deep learning approaches for pore-scale reconstruction often rely on unconditional generation or lack specific constraints on crucial attributes like porosity and depth. Furthermore, previous methods typically utilize grayscale or binary representations, which discard critical petrographic information (e.g., mineralogical differentiation between anhydrite and dolomite, grain boundaries, and distinct porosity systems) essential for accurate geological modeling. Current conditional GANs have not successfully integrated simultaneous control of porosity with depth-specific geological characteristics within a unified architecture, nor have they demonstrated the preservation of complex color-encoded mineralogical relationships.

Methodology
The study introduces PCP-GAN, a multi-conditional Generative Adversarial Network (cGAN) framework designed to generate representative pore-scale images with precisely controlled properties.

Data Preparation: The model was trained on RGB thin-section images from four depths (1879.50 m to 1943.50 m) of a carbonate formation. Images were processed using an enhanced U-Net architecture (incorporating attention gates and deep supervision) to automatically quantify porosity and generate binary masks. To address class imbalance, a data balancing strategy was employed, creating uniform datasets of 1,600 images per sample by augmenting underrepresented porosity classes.
Architecture: The framework utilizes a unified generator and discriminator.
- Generator: Takes a 100-dimensional latent noise vector, continuous porosity values ( $\phi$ ), and discrete depth labels (one-hot encoded) as inputs. It processes these through a dense layer and a series of transposed convolutional layers to output 480 $\times$ 480 $\times$ 3 RGB images.
- Discriminator: Evaluates the authenticity of images by concatenating the input (real or generated) with the corresponding porosity and depth condition vectors, processing them through convolutional layers with downsampling and dropout.
Training: The model was trained on a unified dataset combining all four depths, simultaneously conditioning on porosity and depth parameters. The training utilized a dual-constraint approach where the generator learns to produce images that satisfy specific porosity targets while adhering to the geological characteristics of the specified depth.

Key Contributions

Unified Multi-Conditional Framework: Development of the first GAN architecture that simultaneously learns porosity-depth-pore network relationships across multiple geological formations without requiring separate models for each formation type.
RGB Thin-Section Utilization: Demonstration that using RGB images preserves critical mineralogical and textural information (anhydrite-dolomite differentiation, grain boundaries, interparticle vs. intraparticle porosity) lost in grayscale approaches, enabling the generation of geologically authentic images.
Dual-Constraint Validation: Introduction of a validation framework that quantifies not only morphological preservation but also demonstrates that synthetically generated images can better match bulk formation properties (porosity and permeability) than randomly extracted real sub-images.
Comprehensive Validation: Validation across diverse carbonate fabrics (from grainstones to crystalline formations with anhydrite inclusions) and imaging resolutions (1.8–3.0 $\mu$ m/pixel), confirming geological authenticity through morphological analysis, spatial continuity ( $S_2$ ) analysis, and robustness testing.

Results

Porosity Control: The model achieved strong porosity control across all formations with an $R^2$ of 0.95 and Mean Absolute Errors (MAE) ranging from 0.0099 to 0.0197.
Morphological Preservation: Statistical analysis (Kolmogorov-Smirnov tests, t-tests, Cohen's d) confirmed the preservation of critical pore network characteristics, including average pore radius, specific surface area, and tortuosity. The model successfully captured the inverse relationship between porosity and tortuosity.
Spatial Continuity: Two-point correlation ( $S_2$ ) analysis demonstrated that generated images preserve the spatial continuity and characteristic length scales of natural pore networks, rather than reproducing porosity in a spatially incoherent manner.
Property Fidelity: When validated against core sample properties, generated images showed significantly higher fidelity than random sub-images. Dual-constraint errors (combined porosity-permeability deviations) for generated images ranged from 1.9% to 12.4%, compared to 37.5% to 713.4% for randomly extracted real sub-images.
Architecture Necessity: Comparative analysis with reduced-parameter baseline models (24% and 50% parameter reduction) confirmed that the original 50M-parameter architecture is necessary; reduced models exhibited repetitive pattern generation or complete failure in geological feature reconstruction.
Resolution Robustness: The framework maintained consistent porosity control and reconstruction accuracy across tested resolutions (1.8, 2.25, and 3.0 $\mu$ m/pixel).

Significance
The paper claims that PCP-GAN provides practical tools for subsurface characterization by addressing the long-standing limitation of obtaining pore-scale images that match bulk formation properties. By generating geologically authentic images with precisely controlled properties, the framework offers a solution for modeling processes in carbon storage, geothermal energy, and groundwater management where digital rock physics relies on knowing the characteristic morphology of the pore space. The study asserts that the framework learns fundamental pore geometry-petrophysical property relationships rather than merely replicating visual patterns, thereby enhancing formation analysis and fluid flow simulation accuracy in scenarios where natural heterogeneity compromises sample representativeness.