Prediction of runoff in the upper reaches of the Hei River based on the LSTM model guided by physical mechanisms

The upper reaches of the Hei River. To improve the accuracy, interpretability and physical consistency of LSTM models for predicting streamflow, we have constructed a physically dominant loss function in the LSTM model based on the monotonic physical mechanism of rainfall-runoff in the water balance. The new model (physics-guided LSTM model, PG-LSTM) was applied to predict streamflow in the upper reaches of the Hei River, and its accuracy and physical consistency in streamflow prediction were analyzed. The PG-LSTM model was successfully applied to the upper reaches of the Hei River, and the accuracy was evaluated by the Nash–Sutcliffe efficiency coefficient, root mean square error and Pearson correlation coefficient. The physical consistency of the model was evaluated by the volume error, relative error, and peak flow relative difference. The results showed that the PG-LSTM model had higher accuracy and physical consistency than the traditional LSTM model. The fitting accuracy between the measured and predicted values was 0.97, which is higher than that of the traditional LSTM model (0.89). In addition, the closer the subbasin was to the outlet of the basin, the better the effect of the PG-LSTM model. This model improvement method demonstrated high streamflow prediction accuracy and interpretability, providing a scientific basis for water resource planning and management. • A physically guided LSTM model achieves high precision and physical consistency. • A novel LSTM loss function is proposed where physical weights dominate over data weights. • Model performance varies with the same physical mechanisms at different locations.