Stochastic reconstruction of 2D volcanic rock pore structure using Growing Neural Cellular Automata

Characterizing rock pore structure is crucial for geothermal energy extraction, hydrocarbon assessment, and carbon capture and storage. The pore structure is conventionally estimated from core samples and well-log data. However, 2D images derived from drill cuttings offer an abundant and cost-effective alternative to complement lab and log analysis. Digital Rock Physics, combined with Artificial Intelligence, has the potential to provide robust tools to generate representative digital rock models directly from these 2D images. Specifically, Growing Neural Cellular Automata (GNCA) offer a distinct advantage; they follow simple learned local update rules and are efficient for emulating complex systems and natural phenomena, such as the regeneration of biological patterns and self-organizing textures. Moreover, they demonstrate training stability and low computational resource demands. Therefore, we propose training GNCA on 2D images to stochastically reconstruct the pore structure of selected volcanic rock samples to demonstrate the feasibility of the method. 

GNCA treat reconstruction as an evolving morphogenetic process, growing the pore structure iteratively from a seed state. Their lightweight architecture enables efficient training on consumer-grade hardware by utilizing gradient accumulation to handle input resolutions useful for pore-scale analysis (≥320² px). A key contribution of our work is the physically-informed hybrid loss function, L_total, designed to bridge the gap between perceptual texture and physical topology:

L_total = W_vgg L_vgg + λ (W_tpcf L_tpcf + W_vt L_vt + W_α L_α + W_por L_por),

where: L_vgg captures local perceptual texture, while the physical constraints include L_tpcf for spatial statistics via the two-point correlation function, L_vt to regulate specific surface area via Total Variation, L_α to constrain global pore aspect ratio using the Global Inertia Tensor, and L_por for porosity compliance. The weights W_i balance individual loss contributions, while λ modulates the trade-off between perceptual quality and physical fidelity. 

This model was trained using micro-CT slices from distinct volcanic samples from the Los Humeros Geothermal Field, Mexico. For validation, we compare the stochastic reconstructions against randomly selected reference slices. We also evaluate the standard two-point correlation function S₂(r) and the two-point cluster function C₂(r) to assess the pore spatial distribution and topological connectivity, respectively. In addition, the morphological fidelity is assessed via non-cumulative Pore Size Distribution and Aspect Ratio Distribution histograms, ensuring that the model captures the shape diversity of volcanic vesiculation. Furthermore, we implement a spectral analysis using the indicator function's Fourier transform, χ_V(k), which demonstrates that GNCA reproduce power spectral density across spatial frequencies, from macro-structures to fine details. Finally, the trained model successfully generates complete stochastic slices that are statistically equivalent to the original images at a 95% confidence level. This demonstrates that GNCA are efficient for reconstructing the studied volcanic samples.

In conclusion, the proposed GNCA framework, constrained by a physically-informed hybrid loss function, constitutes a viable alternative for the stochastic reconstruction of complex pore topologies in 2D images, yielding high-fidelity results on the analyzed volcanic rock samples.