Simulation of Reservoir Group Outflow Using LSTM with a Knowledge-Guided Loss Function Coordinated by the MDUPLEX Algorithm

Global climate change and spatiotemporal heterogeneity in water resources exacerbate supply-demand imbalances. Accurate outflow simulation for joint reservoir group operations thus becomes critical for scientific water resources management. Existing data-driven models like the Long Short-Term Memory (LSTM) lack the robust integration of physical constraints. Traditional mechanistic methods, by contrast, lack generality and stability under complex hydrological conditions. To address this limitation, we propose MDUPLEX-KG-LSTM—a physically constrained data-driven model for reservoir outflow simulation. The model incorporates multi-round DUPLEX (MDUPLEX) data partitioning, which ensures statistical homogeneity across training, validation, and test datasets. It also features a Knowledge-Guided (KG) loss function that embeds core physical constraints: water balance, dead water level, flood season restricted water level, and inter-reservoir re-regulation mechanisms. Additionally, it adopts an LSTM network optimized via Particle Swarm Optimization (PSO) for enhanced predictive performance. We validate the model using daily hydrological data from 2010 to 2025 for three reservoirs in the Wujiaqu Irrigation District of Xinjiang, China. The model exhibits exceptional stability and predictive accuracy across key evaluation metrics: Nash–Sutcliffe Efficiency (NSE) ≥ 0.82, Pearson correlation coefficient (r) > 0.94, Root Mean Square Error (RMSE) ≤ 1.50 m3/s, and Water Balance Index (WBI) ≤ 0.016. It outperforms conventional data-driven and mechanistic models in extreme flow simulation scenarios. It also eliminates unphysical negative outflow values in all predictive results. The model achieves 100% compliance with flood control standards and an irrigation guarantee rate of no less than 86%. This study advances the development of physically constrained data-driven modeling for water resources engineering. It provides reliable methodological support for the intelligent operation of reservoir groups in smart water conservancy systems. The model also balances training cost and inference efficiency effectively. It demonstrates verified scalability for reservoir groups of varying scales, fully meeting the operational deployment requirements of smart water systems.