A velocity vector field attention-based flow matching model for industrial soft sensing with limited data

Abstract

In industrial soft sensor modeling, data scarcity severely limits the accuracy of data-driven approaches. Data augmentation can mitigate this limitation by generating virtual samples. To this end, we propose a novel velocity vector field attention-based flow matching (VAFM) model for soft sensor development. The proposed model constructs a probability path from a prior distribution to the real data distribution, enabling high-quality data generation. The path is optimized by learning a velocity vector field that guides samples along the path through continuous evolution. Furthermore, the model employs an attention mechanism to deeply mine the intrinsic structural features of the velocity vector field. This designed velocity vector field attention mechanism allows precise correction of generation direction deviations in traditional flow matching, significantly enhancing the reliability and distribution authenticity of the generated data. Experimental results on both wastewater treatment and steelmaking datasets demonstrate that VAFM consistently improves predictive performance. Specifically, in data-scarce scenarios, the VAFM-based data augmentation yields relative improvements in R2 of 21.07% and 8.35% over the baseline deep neural networks.