Graph Neural Networks for 3D Spatial Continuity Analysis: A Comparative Study with Ordinary Kriging in Ore Grade Estimation

Abstract Accurate modelling of three-dimensional spatial continuity is critical for reliable ore grade estimation in geologically complex deposits. This study evaluates a Geological Graph Neural Network (GNN) as an alternative to Ordinary Kriging (OK) for predicting iron (Fe) grades from 632 composited intervals in 43 drillholes within a structurally heterogeneous carbonate-hosted deposit. The GNN used a k-nearest neighbour graph (k = 16), Edge Convolution layers, Euclidean edge features, and Monte Carlo dropout for predictive uncertainty. OK was implemented with a fitted spherical variogram (nugget = 0.381, sill = 1.19, anisotropy 1.00:0.72:0.51) for benchmarking. Five-fold cross-validation showed that the GNN outperformed OK in predictive accuracy and preservation of short-range variability. At sample support, the GNN achieved R² = 0.72, RMSE = 4.59% Fe, and MAE = 2.54% Fe, compared with OK’s R² = 0.67, RMSE = 5.18% Fe, and MAE = 3.34% Fe. Variogram analysis confirmed that the GNN reproduced short- to medium-range continuity more effectively, while OK introduced smoothing and underestimation of high-grade zones. Residual spatial autocorrelation was minimal for the GNN (Moran’s I = 0.02, p = 0.28) but significant for OK (Moran’s I = − 0.04, p < 0.001). A limitation of this study is that lithological boundaries and geological domains were not incorporated, which may affect predictions in structurally controlled zones. Future work should integrate anisotropy and geological domains into the GNN framework to improve geological realism and strengthen support for selective mining.