This paper enhances the Physics-Informed Neural Networks (PINNs) method to effectively model the hydrodynamics of real-world river networks with irregular cross-sections. Firstly, we pre-process hydraulic parameters to optimize training speed without compromising accuracy, achieving a 91.67% acceleration compared to traditional methods. To address the vanishing gradient problem, layer normalization is also incorporated into the architecture. We also introduce novel physical constraints—water level range and junction node equations—to ensure effective training convergence and enrich the model with additional physical insights. Two practical case studies using HEC-RAS benchmarks demonstrate that our improved PINN method can predict river network hydrodynamics with less data and is less sensitive to time step size, allowing for longer computational time steps. Incorporating physical knowledge, our enhanced PINN methodology emerges as an efficient and promising avenue for modeling the complexities of hydrodynamic processes in natural river networks.