Cascade Reservoir Outflow Simulation Based on Physics-Constrained Random Forest

Accurate reservoir outflow simulation is crucial for water resource management. However, traditional machine learning-based simulation methods have not sufficiently considered the physical constraints of reservoir operation, which may lead to unrealistic issues such as negative outflows or water levels exceeding the reservoir’s own limitations. This study integrates physical constraints into the random forest (RF) model using the Sigmoid function, constructing a physics-constrained random forest model (PC-RF) for cascade reservoir outflow simulation. A stratified sampling strategy based on hydrological year types is used to create the training and validation datasets. The coefficient of determination (R2) and root mean square error (RMSE) are used to evaluate the model’s performance for medium- to long-term predictions of reservoir outflows on a 10-day time scale. Additionally, the mean decrease in impurity method is used to assess the importance of input features, thereby enhancing the model’s interpretability. The application the Yalong River cascade reservoir indicates that (1) compared to traditional RF, the PC-RF achieved significant breakthroughs, with an increase of 37.13% in the R2 and a decrease of 60.04% in the RMSE when simulating outflows from the Lianghekou Reservoir, with all reservoirs maintaining an R2 above 0.95, with no instances of unrealistic outcomes; (2) PC-RF effectively integrated historical operational patterns with top three features being previous period outflow, current inflow, and previous period inflow, providing interpretable insights for operational decision-making. The PC-RF model demonstrates high accuracy and practical potential in cascade reservoir outflow simulation, providing valuable applications for cascade reservoir management and water resource optimization.