Physically constrained tabular variational autoencoders for small sample blasting fragmentation data

Small blasting datasets challenge generative models because physical bounds, heterogeneous fragmentation regimes and algebraically related variables must be represented simultaneously. This study examines an existing 62-record fragmentation benchmark in which separate tabular variational autoencoders were fitted within fragmentation-index groups, with a Gaussian copula fallback for subsets smaller than 20 records. Eight engineering variables were generated, and fragmentation index was reconstructed by adding an empirical residual to the logarithm of the in-situ-block-size to fragment-size ratio. The reported workflow attained an overall SDV fidelity score of 0.8568, compared with 0.8261 for a pure TVAE and 0.8023 for Gaussian simulation. Train-on-synthetic-test-on-real regression produced R² = 0.7030 and mean absolute error = 0.0364 m, while the reverse transfer yielded R² = 0.1302. Reported support precision and recall were 0.9247 and 0.9194. These results favour the grouped workflow descriptively, especially for marginal fidelity, but do not isolate the contributions of grouping, reconstruction and rejection constraints. They also do not establish independent predictive validity because split chronology and task-specific predictor lists are incompletely documented. The classification label based on in-situ block size is a threshold proxy, rather than a measured post-blast oversize outcome, and can become circular if its defining variable is retained as an input. The analysis develops the assumptions behind residual reconstruction, interprets transfer asymmetry and specifies the additional validation needed to establish engineering utility without overstating the evidence.