[Objective] Data-driven models for coal mill outlet temperature prediction often have difficulty maintaining high prediction accuracy while also satisfying the physical requirement of energy balance. This study proposes an outlet temperature prediction method that incorporates physical priors of the coal mill, with the aim of improving both the numerical accuracy and the physical consistency of the prediction results. 

[Methods] Operating data from an MPS medium-speed coal mill in a 350 MW coal-fired generating unit were used to construct a Physics-Guided Long Short-Term Memory-Physics-Informed Neural Network (PG-LSTM-PINN). The method introduces the air-coal ratio and hot-air ratio to represent the matching relationship between primary air and coal feed and the mixing state of hot and cold air. Differences between operating conditions are then used to correct the temporal attention mechanism so that historical information is weighted according to its relevance to the current condition. A thermal-inertia decay factor is embedded in the forget gate of the Long Short-Term Memory (LSTM) network to represent the dynamic influence of the mill thermal process on state updating. In addition, a physical loss is constructed from the energy-balance relationship and incorporated into model training. Model comparison, physical-consistency evaluation, ablation experiments, reduced-training-data experiments, and physical-loss-weight sensitivity experiments were conducted to evaluate the contribution and effectiveness of the proposed method. Together, these experiments evaluate prediction accuracy, energy-balance physical consistency, and performance with limited training data. 

[Results] PG-LSTM-PINN achieved a coefficient of determination (R²) of 0.981 1, a root mean square error (δRMSE) of 0.078 2 °C, and a mean absolute error (δMAE) of 0.061 1 °C. Compared with LSTM, its δRMSE and δMAE were reduced by 50.69% and 52.41%, respectively. The physical-residual root mean square error (δRMSE,p) and physical-residual mean absolute error (δMAE,p) were 21.35 kJ/s and 16.23 kJ/s, respectively. In the ablation experiments, removing any physical-guidance module increased both the prediction error and the physical residual, indicating that each module contributed to the overall performance of the complete model. In the reduced-training-data experiments, PG-LSTM-PINN maintained relatively low prediction errors at all tested training proportions. The sensitivity analysis of the physical-loss weight showed that the lowest δRMSE was obtained when η was 1.301 3×10⁻⁹. 

[Conclusion] The proposed PG-LSTM-PINN integrates operating-condition representation, temporal information weighting, thermal-inertia modeling, and energy-balance constraints within a unified prediction framework. The results show that it can improve the accuracy of coal mill outlet temperature prediction, reduce the energy-balance physical residual, and provide better prediction performance when the amount of training data is limited.