Predicting porous media permeability tensors with machine learning using correlation functions as structural descriptors

Accurate prediction of permeability tensors is essential for describing flow in anisotropic porous media, yet most machine-learning studies predict only scalar permeability or rely on computationally intensive processing of full three-dimensional images. Here, we present a supervised learning framework for predicting the full 3 × 3 permeability tensor, including off-diagonal components, from compact directional correlation functions. The dataset comprised 998 synthetic binary porous-media images of 30 0 3 voxels, generated over porosity values of 0.10–0.25 and blobness values of 1.0–3.0. Four structural descriptors, the two-point S 2 , lineal-path L 2 , cluster C 2 , and surface–surface F s s correlation functions, were calculated along the x , y , and z directions. Full permeability tensors were obtained using a GPU-based Stokes solver. The correlation-function features were ranked using Random Forest importance and compressed to 250 principal components before training a fully connected deep neural network. The model achieved a test MAE of 0.056, RMSE of 0.09, MAPE of 16.6%, and SMAPE of 15.2% on normalized permeability values. These results demonstrate that directional correlation functions retain sufficient orientation-sensitive structural information for full-tensor prediction while providing a substantially more compact and physically interpretable input representation than raw voxel images. The study therefore fills a gap between conventional scalar feature-based regression and computationally expensive image-based learning, and establishes a proof of concept for rapid tensorial permeability estimation without direct flow simulation at inference time.