Scalable variational Gaussian process framework for implicit geological modelling and compositional grade interpolation

Abstract

Geological modelling and estimation of polymetallic ore grades require methods that simultaneously honour spatial heterogeneity, compositional constraints, and predictive uncertainty. We present a scalable probabilistic workflow that integrates centered log-ratio (CLR) compositional data analysis with sparse variational Gaussian processes (VGP) for joint implicit geological modelling and multi-element grade interpolation. Drillhole assays ( ) from the Thalanga volcanic-hosted massive sulfide (VHMS) deposit, Queensland (Australia), are transformed using the CLR mapping and rotated via principal component analysis to obtain decorrelated features in Euclidean space. Spatial prediction is performed using a sparse VGP architecture initialised with = 1,500 inducing points, selected by K-means clustering and organised into 10 local experts (≈150 inducing points each), enabling scalable non-stationary modelling while preserving local geological detail. This formulation reduces computational complexity from to and supports full-grid inference over voxels (before filtering) voxels, with probabilistic ore volumes of 1.23 × 10 6 cells extracted at a 50% ore-probability threshold, all computed in under 10 hours on a single 8 GB GPU. Posterior samples are back-transformed to compositional space, enforcing closure and yielding voxel-wise uncertainty estimates for Cu–Pb–Zn. Compared with ordinary kriging, which attenuates extreme values, and inverse distance weighting, which exaggerates them, the VGP model preserves heavy-tailed grade distributions while providing empirically assessed calibration. Implicit geological modelling via probabilistic classification and threshold-based surface extraction produce stratiform lenses, and zones of elevated predictive variance that highlight priority targets for infill drilling. The proposed compositional VGP framework unifies categorical and continuous modelling within a single Bayesian workflow, accommodates non-stationarity, and delivers grade prediction and risk assessment concurrently. Although demonstrated at Thalanga, the approach is broadly applicable to multi-element mineral systems and provides a robust foundation for data-driven resource estimation, mine planning and exploration targeting. • First integration of compositional transforms with sparse VGP for 3D implicit geological modelling • Scalable VGP reduces training complexity from to , enabling million-voxel inference in <10 h • Joint Cu-Pb-Zn interpolation preserves heavy-tailed grade distributions and delivers voxel-level uncertainty • Implicit ore volumes extracted directly via probabilistic classification without manual wireframing