Enhancing Riverbed Elevation Estimation: Comparison of Gradually Varied Flow Solvers and Physics-Informed Neural Networks

Accurate river bathymetry is essential for hydrodynamic flood modelling, as river channels convey substantial water volumes that critically influence flow dynamics. However, obtaining reliable bathymetric data remains a formidable challenge due to logistical constraints and uncertainties associated with traditional field surveys and remote sensing methods. Gradually varied flow (GVF) solvers have emerged as a promising alternative, leveraging readily observable parameters－river width, water surface elevation, and discharge－to estimate riverbed elevations. With the advent of the Surface Water and Ocean Topography (SWOT) satellite mission, the availability of high-resolution water surface elevation observations at unprecedented spatial and temporal scales presents new opportunities to enhance GVF-based bathymetric estimation methods. These solvers have demonstrated superior performance compared to solutions based on hydraulic geometry and uniform flow solvers using Manning's equation, particularly in capturing spatial variability in natural river systems. Rather than reconstructing the full cross-sectional profile, GVF solvers focus on estimating an average riverbed elevation at each cross section, balancing the need for accurate channel representation with the practical constraints of data acquisition.

This research investigates the potential of Physics-Informed Neural Networks (PINNs) as a complementary approach to GVF solvers for riverbed elevation estimation. GVF solvers apply physical principles of gradually varied flow, optimizing the riverbed profile to minimize discrepancies between observed and simulated water surface elevations. PINNs, in contrast, incorporate governing physical laws into neural network architectures, allowing for accurate predictions from sparse datasets while maintaining physical realism. By comparing the performance, accuracy, and limitations of both methods, this study aims to assess their relative effectiveness in addressing the complexities of river bathymetry. The findings of this study will contribute to the development of more effective and efficient methods for riverbed elevation estimation, enhancing our understanding of river dynamics and improving hydrodynamic modeling capabilities.