  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.
