Copula and mixture prior variational autoencoders for small sample blasting fragmentation modelling

Abstract

Synthetic tabular data may support blasting research when observations are scarce, but distributional resemblance and predictive transfer answer different questions. This study evaluates an existing fragmentation benchmark containing 262 harmonised records from three literature sources and compares Gaussian, Student-t and Clayton copulas with vanilla, Kullback-Leibler annealed and Gaussian mixture prior tabular variational autoencoders. The reported protocol separates a real hold-out set before generator fitting and combines likelihood summaries, maximum mean discrepancy, an autoencoder embedding distance and train-on-synthetic-test-on-real utility. The mixture prior model attained the highest reported utility, with approximately 0.736 for R² and 1.698 for root mean squared error in fragmentation-index units; corresponding fidelity summaries were approximately 0.160 and 0.436. Annealing improved utility relative to the vanilla model, whereas copula-derived generator inputs generally reduced performance. These observations support multimodal latent modelling as a useful candidate for heterogeneous fragmentation tables. They do not establish an augmentation gain over a matched real-only predictor or transfer to an unseen mine. Interpretation is further limited by a discrepancy between the six-variable utility schema and the eight-dimensional parameter count implied by the copula summary, incomplete seed-level reporting and potentially shared blast records across literature sources. The contribution is a technically qualified comparison and a reproducible evaluation specification that distinguishes synthesis, post-blast inference and prospective engineering prediction.