Conventional data-driven models, including pure machine learning models, frequently exhibit a deficiency in explicit physical consistency. This paper presents a hydrodynamically-informed neural network framework designed to enhance stage–discharge modeling and flood forecasting. Drawing from the Saint–Venant equations, a set of hydrodynamic descriptors, including the Froude number ( Fr ) and temporal derivatives of water level and discharge, is identified and integrated as input features into a Back Propagation (BP) neural network. This learned hydraulic relationship is subsequently coupled with a hydrodynamic model, serving as a dynamic downstream boundary condition. Validation across four diverse Chinese basins confirms that incorporating Fr effectively resolves multi-valued (looped) rating curves, achieving a Nash–Sutcliffe Efficiency ( NSE ) of up to 0.99. In real-time forecasting trials, at a 6 h lead time, the framework maintains high accuracy ( NSE ≈ 0.98) due to inherent hydrodynamic inertia. However, at a 24 h lead time, the dynamic recursive update scheme significantly outperforms traditional methods; it mitigates cumulative forecast drift, reducing peak discharge relative errors by 10% and improving the NSE from 0.86 to 0.96. These quantitative results demonstrate that bridging machine learning with hydrodynamic principles provides a robust and physically consistent solution for flood forecasting in non-stationary hydraulic environments.
Yang et al. (2026) studied this question.