Quantifying Mineral Resources and Their Uncertainty Using Two Existing Machine Learning Methods

Mineral resources are typically quantified by estimating the grade-tonnage curve for different resource categories. Statutory resource assessment reports (e.g., NI-43-101), however, do not include a measure of uncertainty for the disclosed resources despite the major investments required for mining projects. Although conditional simulation can provide confidence intervals (CIs) for resource estimation, it requires a strong stationarity assumption and depends on the variogram model selected, which is often poorly defined with the available data. In order to avoid these limitations, this research proposes the use and comparison of two machine learning (ML) methods, multiple linear regression and a multilayer neural network, to generate tonnage curves and their CIs directly from the data. The classical variogram modeling step is replaced by the specification of intervals for each parameter of the selected variogram model. The learning is carried out in a perfectly controlled environment using simulations with known variograms. Numerous reference deposits are sampled, and for each one, a series of conditional realizations define the mean tonnage and CI curves. Different statistics computed for the entire data set are used as input to predict the tonnage and CI curves by the ML methods. The results indicate that there are no significant differences between the ML methods. In addition, ML resource predictions outperform those obtained with ordinary kriging, constrained kriging, uniform conditioning and indirect lognormal correction, being surpassed only by the discrete Gaussian model. Nevertheless, these predictors were favored by the use of true variogram models. Moreover, the coverage probabilities of different CIs reach the nominal levels indicating adequate resource uncertainty quantification. Finally, two case studies validate the effectiveness of the proposed approach for tonnage prediction and uncertainty quantification.