Graph-enhanced Neural Operator for Missing Velocities Infilling in River Surface Velocimetry

Measuring river surface velocity enables river discharge estimation, a fundamental task for hydrologists, environmental scientists, and water resource managers. While traditional image-based velocimetry methods are often effective, they struggle to produce complete velocity fields under complex environmental conditions. Poor lighting, reflective glare, lack of visible surface features, or excessive turbulence can all result in regions where feature tracking fails, leading to gaps in the resolved velocity field. Addressing these gaps through the reconstruction of missing velocity measurements is an important research challenge. Recently, researchers have employed deep learning to address various hydrology problems, demonstrating promising improvements. In this work, we propose a neural operator-based model to address the challenge of missing velocities in river surface velocimetry. Specifically, our model is based on the Fourier neural operator with a graph-enhanced lifting layer. It is trained on the river surface velocimetry reconstruction task using a self-supervised paradigm. Once trained, it can be used to infer missing velocities in unseen samples. Experiments conducted on a dataset collected from a river in the Netherlands demonstrate our approach’s ability to accurately infill missing surface velocities, even when faced with large amounts of missing data. We attribute this robustness to the neural operator’s ability to learn continuous functions, which enhances our model’s capacity for high-level feature representation and extraction. Our findings suggest that the reconstructed velocity fields produced by our model can act as reliable ground truth data for deep learning-based methods. In the future, we aim to improve our model’s performance and generalization by incorporating additional data collected from a wider range of rivers and under varying environmental conditions.