A convolutional neural network surrogate for hierarchical homogenization: fast elastic moduli prediction of digital rocks

Abstract

Digital rock physics (DRP) aims to estimate effective rock properties (e.g., elastic moduli) directly from 3D micro-CT images. However, direct numerical simulations (DNS) on high-resolution large 3D scans are often computationally prohibitive and severely limit the application of DRP. To address this bottleneck, we combine a lightweight 3D convolutional neural network (CNN) with hierarchical homogenization (HHM) and apply it to determine effective elastic moduli. In this scheme, a large rock image is divided into subcubes. The CNN replaces costly DNS by directly predicting subcube elastic moduli, while HHM upscales subcube-level predictions to the full rock. Using a shared convolutional backbone, we systematically compare three training targets: (i) full anisotropic $6\times6$ stiffness tensors, (ii) isotropic bulk and shear moduli $(K, G)$, and (iii) Hashin--Shtrikman (HS)-normalized factors. Across multiple rock types, all three models agree well with DNS results while substantially reducing the computational cost. Moreover, training from scratch on each rock type is fast enough that transfer learning is unnecessary. Across all three targets, the accuracy is comparable. In our comparative study, the HS-normalized factor offers the best overall speed--accuracy trade-off while guaranteeing physical consistency, making it a convenient default. The isotropic $(K, G)$ target is a slightly more accurate alternative.