Physics-Informed Neural Networks for Hydraulic Monitoring in Water Diversion Projects with Limited Cross-Section Data

Long-distance open-channel water diversion projects, such as China’s South-to-North Water Diversion Project, have significantly mitigated regional water supply-demand imbalances. However, the hydraulic behavior of open channels during water conveyance is highly complex, particularly under abnormal conditions like extreme weather or equipment failures, which can cause abrupt hydraulic changes, rapid water level rises, and even local overtopping or other safety hazards. Therefore, global, real-time, and accurate monitoring of open-channel hydraulics is essential to ensure the project's safe and efficient operation. Hydraulic characteristics of open channels are typically obtained through hydrological monitoring systems and numerical simulations. The reasonable placement and number of monitoring sections in a hydrological system are crucial for balancing monitoring accuracy and construction costs across the entire open channel. Numerical simulation accuracy and reliability depend on clear boundary conditions, precise Manning roughness coefficients, and other key parameters. However, these parameters can vary over time and are often difficult to determine in practical applications. Physics-Informed Neural Networks (PINNs) provide an effective solution to these challenges. This study develops a PINN model to predict the hydraulic characteristics of unsteady flow in open channels by integrating sparse hydrological data with physical laws. The study also examines how the number and placement of monitoring sections affect the accuracy of hydraulic predictions for the entire channel. Results demonstrate that PINNs can achieve high-precision hydraulic predictions along the channel using data from only three optimally placed monitoring sections, with average relative L2 errors below 0.5%. PINNs exhibit strong generalization across diverse boundary conditions, accurately predicting complex flow scenarios and demonstrating significantly higher noise resistance compared to traditional methods. Even with Gaussian noise levels of 10%, PINN predictions maintain relative L2 errors within 3%. Furthermore, PINNs show substantial potential for inverting key parameters such as the Manning roughness coefficient. PINNs offer an efficient and rapid approach to hydraulic predictions for long-distance water conveyance projects, aiding in the design and optimization of monitoring systems while minimizing the number of sensors, equipment, and costs.