Physics-informed neural network for open channel flow velocity prediction

This study presents a physics-informed neural network (PINN) framework for predicting open channel flow velocity, integrating traditional hydraulic principles with modern deep learning techniques when limited data are available. The framework combines a multi-branch neural architecture with a composite loss function that enforces physical consistency through established hydrological principles, including the continuity condition, location-dependent Manning's equation, and geometric constraints. Unlike conventional PINN implementations that require dense spatiotemporal discretization, this approach is specifically designed for sparse data conditions (or local data), utilizing a surrogate model that assimilates limited sensor-based measurements while embedding key physical–empirical laws. The model achieves superior predictive performance compared to traditional machine learning baselines, demonstrating a 40% reduction in mean absolute percentage error relative to standard approaches. Moreover, the framework maintains physical consistency, predicting location-dependent Manning coefficients that align with established hydraulic engineering literature and achieving accurate hydraulic radius predictions across diverse channel configurations. These results suggest that integrating physical constraints effectively compensates for data sparsity, offering a promising solution for applications such as hydrokinetic power assessment where both accuracy and physical plausibility are essential.