Physics-informed machine learning for grade prediction in froth flotation

In this paper, physics-informed neural network models are developed to predict the concentrate gold grade in froth flotation cells. Accurate prediction of concentrate grades is important for the automatic control and optimization of mineral processing. Both first-principles and data-driven machine learning methods have been used to model the flotation process. The complexity of models based on first-principles restricts their direct use, while purely data-driven models often fail in dynamic industrial environments, leading to poor generalization. To address these limitations, this study integrates classical mathematical models of froth flotation processes with conventional deep learning methods to construct physics-informed neural networks. The models are trained, evaluated, and tested on datasets generated from a digital twin model of flotation cells that merges real-process data with physics-based simulations, with data collected over nearly half a year at a five-minute sampling rate. Compared to the best purely data-driven model, the top-performing physics-informed neural network reduced the mean squared error by 65% and the mean relative error by 34%, demonstrating superior generalization and predictive performance. • Developed PINNs to model the froth flotation process. • Classical mathematical models were used as soft penalties in loss functions. • PINNs showed better generalization and accuracy than purely data-driven models.