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Prediction of Effective Elastic Moduli of Rocks using Graph Neural Networks

Jaehong Chung, Rasool Ahmad, WaiChing Sun, Wei Cai, Tapan Mukerji

TL;DR

The paper addresses predicting rock effective elastic moduli from microstructure using a Mapper-based graph representation of 3D digital rocks and a Graph Isomorphism Network (GIN) to predict bulk and shear moduli. The approach demonstrates strong generalization to unseen rock types and subcube sizes, outperforming CNN baselines in predicting unseen properties and offering memory-efficiency advantages. By validating graph topological features with a Random Forest and showing near-perfect test accuracy with the GNN, the work highlights the potential of topological graph representations for digital rock analysis. The findings indicate a practical, scalable path for rapid rock-property predictions, though preprocessing the voxel-to-graph transformation remains a bottleneck to be optimized.

Abstract

This study presents a Graph Neural Networks (GNNs)-based approach for predicting the effective elastic moduli of rocks from their digital CT-scan images. We use the Mapper algorithm to transform 3D digital rock images into graph datasets, encapsulating essential geometrical information. These graphs, after training, prove effective in predicting elastic moduli. Our GNN model shows robust predictive capabilities across various graph sizes derived from various subcube dimensions. Not only does it perform well on the test dataset, but it also maintains high prediction accuracy for unseen rocks and unexplored subcube sizes. Comparative analysis with Convolutional Neural Networks (CNNs) reveals the superior performance of GNNs in predicting unseen rock properties. Moreover, the graph representation of microstructures significantly reduces GPU memory requirements (compared to the grid representation for CNNs), enabling greater flexibility in the batch size selection. This work demonstrates the potential of GNN models in enhancing the prediction accuracy of rock properties and boosting the efficiency of digital rock analysis.

Prediction of Effective Elastic Moduli of Rocks using Graph Neural Networks

TL;DR

The paper addresses predicting rock effective elastic moduli from microstructure using a Mapper-based graph representation of 3D digital rocks and a Graph Isomorphism Network (GIN) to predict bulk and shear moduli. The approach demonstrates strong generalization to unseen rock types and subcube sizes, outperforming CNN baselines in predicting unseen properties and offering memory-efficiency advantages. By validating graph topological features with a Random Forest and showing near-perfect test accuracy with the GNN, the work highlights the potential of topological graph representations for digital rock analysis. The findings indicate a practical, scalable path for rapid rock-property predictions, though preprocessing the voxel-to-graph transformation remains a bottleneck to be optimized.

Abstract

This study presents a Graph Neural Networks (GNNs)-based approach for predicting the effective elastic moduli of rocks from their digital CT-scan images. We use the Mapper algorithm to transform 3D digital rock images into graph datasets, encapsulating essential geometrical information. These graphs, after training, prove effective in predicting elastic moduli. Our GNN model shows robust predictive capabilities across various graph sizes derived from various subcube dimensions. Not only does it perform well on the test dataset, but it also maintains high prediction accuracy for unseen rocks and unexplored subcube sizes. Comparative analysis with Convolutional Neural Networks (CNNs) reveals the superior performance of GNNs in predicting unseen rock properties. Moreover, the graph representation of microstructures significantly reduces GPU memory requirements (compared to the grid representation for CNNs), enabling greater flexibility in the batch size selection. This work demonstrates the potential of GNN models in enhancing the prediction accuracy of rock properties and boosting the efficiency of digital rock analysis.
Paper Structure (25 sections, 22 equations, 21 figures, 4 tables)

This paper contains 25 sections, 22 equations, 21 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Digital Rock Dataset and Effective Elastic Moduli Computation
  3. Methods for Machine Learning
  4. Mapper algorithm
  5. Neural network architectures
  6. Graph Neural Networks
  7. Convolutional Neural Networks
  8. Results and Discussions
  9. Verification of Graph's Effectiveness in Property Prediction
  10. Prediction performance of the GNN
  11. Tuning Mapper algorithm and GNN Hyperparameters for Optimal Performance
  12. Assessing Predictive Generalizability on Unseen Rocks
  13. Property Prediction for Unseen Subcube Sizes
  14. Comparative analysis of GNNs and CNNs
  15. Challenges of GNN preprocessing
  16. ...and 10 more sections

Figures (21)

  • Figure 1: Five digital rock images used in the study. Gray represents grain and black represents pore.
  • Figure 2: Workflow: Conversion of a digital rock into a graph via the Mapper algorithm, followed by the utilization of GNN for elastic moduli prediction
  • Figure 3: The process of graph construction using the Mapper algorithm: (a) Original 3D voxel data where gray represents grain and black represents pore, (b) Projection on the $X$-axis using the filter function, (c) Covering procedure dividing the domain into 10 regions, (d) Clustering of pore and solid structures using DFS algorithm, (e) The resulting graph $G(V, E)$
  • Figure 4: CNN architecture for predicting effective elastic stiffness of rocks from 3D segmented images.
  • Figure 5: Two visual representations of the same graph: (Left) one in 3D space with node coordinates and (Right) the other projected in 2D space, underscoring that the graph's inherent properties are defined in a non-Euclidean space.
  • ...and 16 more figures