Mineral resource estimation using spatial copulas and machine learning optimized with metaheuristics in a copper deposit

This study aimed to estimate mineral resources using spatial copula models (Gaussian, t-Student, Frank, Clayton, and Gumbel) and machine learning algorithms, including Random Forest (RF), Support Vector Regression (SVR), XGBoost, Decision Tree (DT), K-Nearest Neighbors (KNN), and Artificial Neural Networks (ANN), optimized through metaheuristics such as Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), and Genetic Algorithms (GA) in a copper deposit in Peru. The dataset consisted of 185 diamond drill holes, from which 5,654 15-meter composites were generated. Model validation was performed using leave-one-out cross-validation (LOO) and grade–tonnage curve analysis on a block model containing 381,774 units. Results show that copulas outperformed ordinary kriging (OK) in terms of estimation accuracy and their ability to capture spatial variability. The Frank copula achieved R ²  = 0.78 and MAE = 0.09, while the Clayton copula reached R ²  = 0.72 with a total estimated resource of 2,426.42 Mt of copper, compared to 2,202.57 Mt estimated by OK (R ²  = 0.69, MAE = 0.10). Among the machine learning models, the best performance was achieved by KNN + GA, with R ²  = 0.82, RMSE = 0.12, a mean grade of 0.3278%, and a total resource of 2,302.68 Mt. Other models such as RF + PSO and XGBoost + ACO also delivered strong results, with resources exceeding 2,050 Mt and R ² values of 0.63. In conclusion, copulas and machine learning are robust alternatives to OK. Rather than being exclusive, they can be combined based on deposit type and project context to improve the reliability and quality of resource estimation.