A physics-informed neural network method for modeling one-dimensional water flow without roughness coefficient input

Roughness coefficients significantly influence flow resistance and are critical for accurate one-dimensional (1-D) river flow simulations. However, obtaining reliable roughness data in natural rivers is challenging due to spatial variability and measurement difficulties, leading to substantial uncertainty in hydraulic modeling. To address this, we propose a novel Physics-Informed Neural Network Roughness Estimation (PINN-RE) framework, which augments traditional PINNs by incorporating a dedicated neural network for predicting spatially distributed roughness. By coupling the roughness and the hydrodynamic field via the loss function governed by the Saint-Venant Equations, PINN-RE enables the simultaneous learning of spatially distributed roughness coefficients and hydrodynamics. The framework is evaluated using four scenario groups with varying roughness distributions. Results show that PINN-RE markedly improves hydrodynamic prediction accuracy compared to the conventional PINN, reducing the water depth error from 8.24% to 1.75% in a linear roughness case. Sensitivity analysis reveals a U-shaped error trend with sampling frequency, minimized at 300 points per station and the model is more sensitive to sampling frequency than to station count. Moreover, we analyze the relative importance of different physical quantities in the partial differential equation loss and find that the contribution of roughness is 10–50 times greater than that of water depth or discharge. These findings show the dominant role of roughness in 1-D flow modeling and demonstrate that PINN-RE not only offers a physically consistent and data-efficient solution to roughness identification, but also enhances the understanding of physical parameter interactions in river channels.