Presentation: 2025 ND EPSCoR Annual conference 

October 21, 2025, NDSU Memorial Union, Fargo, North Dakota

SKM-PINNs: A super-resolution process of bathymetry inversion from UAV imaging data for small and medium rivers using Physics-Informed Neural Networks

Measurement of river bathymetry is critical for many civil engineering applications. However, direct measurement methods is typically costly and challenging in remote locations, especially under flooding. Recent advances in deep learning have shown promise for bathymetric inversion from remote sensing data. Yet, these approaches are limited for site-specific locations. In this study, a novel bathymetry inversion method (SKM-PINN) from Uncrew Air Vehicles (UAV) data is developed using Physics-Informed Neural Networks (PINNs). Our novel methodology employed the Shiono-Knight Model (SKM) for shallow water equations (SWEs), which is embedded in the loss function of the neural network to infer water depth from surface velocity field. Our new approach transforms the two-dimensional SWEs into one-dimensional ordinary differential equation, which leads to fast convergence during the training of neural network. This approach addresses the most challenging issue of PINNs in applying bathymetry inversion for natural streams where the flow field can be highly complex. The SKM-PINNs is validated for both synthetic and field measurement data, which can reach the accuracy root mean square errors below 0.15~m across multiple cross-sections. The results show that SKM-PINNs is highly reliable and robust in predicting water depth in both pools and riffles, using a minimum information from UAV measurements. This work provides a cost-effective framework for high-resolution bathymetric mapping using readily available UAV technology.