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Abstract
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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 complete 3 × 3 permeability tensor, including off-diagonal components, from compact directional correlation functions. The dataset comprised 998 synthetic binary porous-media images of voxels, generated over porosity values of 0.10–0.25 and blobness values of 1.0–3.0. Four structural descriptors, the two-point , lineal-path , cluster , and surface–surface correlation functions, were calculated along the , , and 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.
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