A hybrid model with a physics-constrained neural network to improve hydrodynamic prediction

“Accurate hydrodynamic prediction is vital for water transfer systems to ensure delivery efficiency and prevent damage. Traditional physics-based models use predefined or estimated offtake discharges as lateral boundaries, neglecting interactions between real-time hydraulic states and future offtake discharge, then causing water level predictive errors. To address this, we propose a hybrid model with a physics-constrained neural network (PcNN) for real-time offtake discharge prediction. The PcNN employs long short-term memory (LSTM), incorporating physical constraints into the input layer and loss function from prior knowledge and a hydrodynamic model. Applied to a large-scale water transfer system in China, the hybrid model improves offtake discharge prediction by 30 %–70 % over the baseline and boosts water level forecasting, with Nash-Sutcliffe efficiency coefficients reaching 0.84 and 0.92 in upstream and downstream sections. The results demonstrate its effectiveness in integrating system hydrodynamics with data patterns, offering a robust tool for real-time decision support in water resource management.”

(Citation: Liu, W., Guan, G., Tian, X., et.al. – A hybrid model with a physics-constrained neural network to improve hydrodynamic prediction – Environmental Modelling & Software 194(2025)106699 – https://doi.org/10.1016/j.envsoft.2025.106699)