Application of the Db-PINN model in predicting hydraulic jump flow fields under different Froude numbers

Abstract

We propose a hybrid model driven by both data and physics, termed Double-branched Physics-Informed Neural Network (Db-PINN), which enhances the synergy between data-driven and physical mechanisms methods, effectively improving the accuracy of predicting the hydraulic jump flow field and energy dissipation rate. The core architecture of the model is based on Convolutional Neural Networks (CNNs), which extract detailed features of the hydraulic jump flow field. In combination with a branch network, Deep Neural Networks (DNNs) are used to compute the residuals of partial differential equations, ensuring adherence to physical laws. Additionally, considering hardware resource constraints, the Db-PINN model incorporates a mini-batch algorithm to reduce dependence on GPU memory size, thus meeting the model’s need to process large-scale datasets. When compared to numerical simulation results, the model demonstrates high accuracy and generalization capability in predicting the velocity distribution and turbulence characteristics of the hydraulic jump flow field.