Application of PINNs to Define Roughness Coefficients for Channel Flow Problems

This paper considers the possibility of using Physics-Informed Neural Networks (PINNs) to study the hydrological processes of model river sections. A fully connected neural network is used for the approximation of the Saint-Venant equations in both 1D and 2D formulations. This study addresses the problem of determining the velocities, water level, discharge, and area of water sections in 1D cases, as well as the inverse problem of calculating the roughness coefficient. To evaluate the applicability of PINNs for modeling flows in channels, it seems reasonable to start with cases where exact reference solutions are available. For the 1D case, we examined a rectangular channel with a given length, width, and constant roughness coefficient. An analytical solution is obtained to calculate the discharge and area of the water section. Two-dimensional 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 calculation in Delft3D code took about 2 min. The influence of PINN hyperparameters on the prediction quality was studied. Finally, the absolute error value was assessed. The prediction error of the roughness coefficient n value in the 2D case for the inverse problem did not exceed 10%. A typical training process took from 2.5 to 3.5 h and the prediction process took 5–10 s using developed PINN models on a server with Nvidia A100 40GB GPU.