Abstract: To address the complex multi-valuedness of stage-discharge relationships in mid-lower river reaches and the weak generalizability of traditional data-driven models, this paper proposes a generalized modeling approach integrating hydrodynamic mechanisms. Based on the Saint-Venant equations, a physical feature set comprising water level (Z), temporal rates of change (dZ/dt, dQ/dt), and Froude number (Fr) is coupled with a BP neural network. Nine representative cross-sections across China's seven major river basins are selected for evaluation. Results show that Fr significantly enhances the capture of complex hydrodynamic features, achieving Nash-Sutcliffe Efficiencies (E_NS) approaching 1. However, improvements from dZ/dt and dQ/dt are site-dependent, excelling in deep-channel sections but limited elsewhere by data noise. The proposed framework demonstrates robust cross-basin universality, effectively overcoming the downstream boundary limitations of traditional models and providing reliable support for real-time flood forecasting and digital twin applications.