River Surface Velocity and Discharge Estimation Using Optical Flow and Unlabeled Physics-Informed Neural Networks

Area of Science:

• Hydrology and Fluid Dynamics
• Computational Science
• Remote Sensing

Background:

• Accurate quantification of river surface velocity and discharge is crucial for effective flood control and mitigation.
• Traditional contact measurement methods are resource-intensive and challenging during flood events.
• Existing image velocimetry techniques often lack physical interpretability.

Purpose of the Study:

• To develop a novel, physically-grounded algorithm for river flow estimation using Physics-Informed Neural Networks (PINNs).
• To improve the accuracy and interpretability of image-based river flow measurements.
• To provide a safer and more efficient alternative to traditional methods, especially during flood seasons.

Main Methods:

• Integration of a convection-diffusion equation derived from optical flow into a PINN framework.
• Utilizing the convection-diffusion equation as the loss function for PINN training.
• Employing multiple scenarios to train the PINNs without requiring labeled data.

Main Results:

• Demonstrated superior performance in both artificial and natural river channels.
• Achieved low relative errors for discharge measurements (0.66% and -1.75%).
• Achieved low relative errors for mean velocity measurements (0.64% and -2.33%).

Conclusions:

• The proposed PINN-based method offers a physically robust and accurate approach to river flow estimation.
• This technique enhances the reliability and interpretability of image velocimetry for hydrological applications.
• The algorithm provides a significant advancement over existing methods for measuring river surface velocity and discharge.