A multi-task reconstruction framework for data-efficient soft sensing in flotation

Flotation recovery is a key performance indicator for process optimization and closed-loop control. However, costly and delayed assay labels, substantial sensor noise, and fluctuating operating conditions undermine model reliability when labeled data are limited. This study proposes a multi-task reconstruction-based soft-sensing framework （PM） that combines hierarchical Bayesian denoising with a Transformer enhanced by physical priors. The framework jointly optimizes supervised regression and masked feature reconstruction to learn the relationship between process variables and flotation recovery, while a bounded activation function constrains predictions to 0, 100. Experiments on a mineral flotation dataset yield an RMSE of 2.437, and an R² of 0.9603. Compared with TabTransformer, the best-performing baseline, PM reduces RMSE, MAE, and MAPE by approximately 12.8 %, 15.7 %, and 13.2 %, respectively. The results indicate that the framework improves prediction accuracy, stability, and noise robustness on the current dataset, providing a reference modeling framework for small-sample soft sensing of recovery in complex flotation processes.