Application of PINN to Define Roughness Coefficient forChannel Flow Problem

This paper considers the possibility of using physics-informed neural networks (PINNs) to study hydrological processes of model river sections. The fully connected neural network is used for approximation of the Saint-Venant equations in both 1D and 2D formulations. The study addresses a forward problem to determine velocities and water level, discharge and area of water section in 1D case, as well as an inverse problem to calculate the roughness coefficient. To evaluate the applicability of PINN for modeling flows in channels, it seems reasonable to start with cases where exact reference solutions are available. For the 1D case the research examines a rectangular channel with given length, width, constant roughness coefficient. An analytical solution is obtained to calculate the discharge and area of water section. The 2D model examples were also examined. The synthetic data were generated in Delft3D code, which included velocity field and water level, for the purpose of PINN training. The influence of PINN hyperparameters on the prediction result was studied. Finally, the absolute error value was assessed. The prediction error of the roughness coefficient n value in 2D case for the inverse problem did not exceed 10%. The one typical training process took from 2.5 to 3.5 hours and the prediction process took 5-10 seconds using developed PINN model on server with Nvidia A100 40GB GPU.