Physics-informed neural networks for inversion of river flow and geometry with shallow water model

The river flow transports sediment, resulting in the formation of alternating sandbars in the riverbed. The underlying physics is characterized by the interaction between flow and river geometry, necessitating an understanding of their inseparable relationship. However, the dynamics of river flow with alternating sandbars are hard to understand due to the difficulty of measuring flow depth and riverbed geometry during floods with current technology. This study implements an innovative approach utilizing physics-informed neural networks (PINNs) to estimate important hydraulic variables in rivers that are difficult to measure directly. The method uses sparse yet obtainable flow velocity and water level data. The governing equations of motion, continuity, and the constant discharge condition based on the mass conservation principle are integrated into the neural network as physical constraints. This approach enables the completion of sparse velocity fields and the inversion of flow depth, riverbed elevation, and roughness coefficients without requiring direct training data for these variables. Validation was performed using model experiment data and numerical simulations derived from these experiments. Results indicate that the accuracy of the estimations is relatively robust to the number of training data points, provided their spatial resolution is finer than the wavelength of the sandbars. The inclusion of mass conservation as a redundant constraint significantly improved the convergence and accuracy of the model. This PINNs-based approach, using measurable data, offers a new way to quantify complex river flows on alternating sandbars without significant updates to conventional methods, providing new insights into river physics.