Physics-informed machine learning surrogate models: Enhancing data-driven forecasting for digital twins in mineral processing

• Physics-based constraints were integrated into data-driven surrogate models to create physics-informed ML models. • All physics-informed machine learning surrogate models outperformed their data-driven counterparts. • Adding physics-based constraints to ML models can improve their accuracy and robustness but must be considered case by case. In mineral processing, optimal operation and process control are essential. Accurate forecasting models are needed, and while data-driven models for multistep forecasting have shown promise, the potential for incorporating physics-based information to enhance accuracy was investigated in this paper. The objective was to determine accuracy improvement by adding physics information to the baseline data-driven models. Three purely data-driven multivariate multistep forecasting models (CNN, GRU, LSTM) from previous research were selected and their architectures recreated for comparison. Pre-processing and feature engineering methods were harmonised to form baseline models, which were validated on the same physical flotation process. Physics information was added using two different physics-guided loss functions that utilised mass balance, resulting in surrogate models based on multivariate multistep forecasting and physics-informed machine learning (PIML). These models were trained and tested on the same dataset to compare performance with baseline models and among different algorithms. Key findings indicated that all the PIML models outperformed their data-driven counterparts. The largest improvements in the NRMSE and NMAE were observed in the LSTM models, while the CNN models showed the lowest improvement. Error distributions across the forecasting horizons improved for all the models, and a loss function utilising a mean absolute error performed better than a mean-squared error across all models. In conclusion, incorporating physics information into multivariate multistep forecasting surrogates generally enhanced forecasting accuracy. However, the extent of improvement varied, and the decision to integrate physics should be made on a case-by-case basis, considering the need for domain knowledge and the increased time and resource requirements for PIML model development.