A physically informed neural network approach for modeling wave transformation in vegetated waters

Prediction of wave propagation in vegetated waters is crucial for the design and maintenance of coastal ecological protection systems. In this study, we propose a Physics-Informed Neural Network (PINN) model that incorporates physical constraints from the Boussinesq equations for modeling wave propagation processes in vegetated waters. The results demonstrate that the PINN model effectively captures the evolution of regular wave propagation in rigid, non-submerged vegetated waters. Compared to conventional numerical models, the PINN approach offers a more efficient preprocessing framework while maintaining comparable simulation accuracy with an average Coefficient of Determination (R²) of 0.942, an average Root Mean Square Error (RMSE) of 1.84 × 10⁻³ m and an average Mean Absolute Error (MAE) of 1.19 × 10⁻³ m. Moreover, the parametric inference framework embedded within PINN enables precise determination of the optimal drag coefficient (C_d) through systematic assimilation of experimental measurements. Additionally, the accuracy of both the simulation and the inferred C_d improves as more external data are integrated into the model.