Performance Comparison of Prediction of Hydraulic Jump Length Under Multiple Neural Network Models

Hydraulic jump is a common physical phenomenon in the field of hydraulic engineering. The essence of hydraulic jump is the conversion and dissipation of a large amount of energy due to the interaction between vortex structures, mainly released in the form of turbulence and water waves. This process significantly reduces the kinetic energy of water flow, thereby mitigating downstream erosion and protecting hydraulic structures, which in turn extends their service life. As a crucial factor in the energy dissipation design of discharge structures, the length of the hydraulic jump is influenced by various factors, including flow velocity, upstream and downstream water depths, riverbed roughness height, and Froude number. In this study, we applied dimensional analysis to identify the key parameters influencing hydraulic jumps on the dataset provided by literature. We utilized a multi-task learning strategy, incorporating a shared feature extraction layer for characteristic modeling of hydraulic jumps within Physics-Informed Neural Networks (PINNs). Furthermore, we compared the performance of PINNs with other data-driven models such as Deep Neural Networks (DNNs), Convolutional Neural Networks (CNNs), and Transformers. The results demonstrated that these models are effective in estimating the length of hydraulic transitions and distinguishing between steady and unsteady hydraulic jump processes. Notably, the PINNs model exhibited better performance than other models, achieving an $\mathbf {R^{2}}$ score of $\mathbf {0.8818}$ , RMSE of 4.4627(cm), MAE of 3.3784(cm), precision of $\mathbf {0.9677}$ and recall of 0.9677 on the test set. These findings are significant for elucidating the characteristics and effects of hydraulic jumps in hydraulic structures, providing a scientific basis for the safe operation and design of practical hydraulic engineering projects.