Estimation of cavitation velocity fields based on limited pressure data through improved U-shaped neural network

In marine applications, estimating velocity fields or other states from limited data are important as it provides a reference for active control. In this work, we propose PVNet (Pressure-Velocity Network), an improved U-shaped neural network (UNet) combined with Transformer Modules and Multi-scale Fusion Modules, to predict velocity fields from pressure on the hydrofoil surface. To improve prediction accuracy, position encodings have been incorporated into the input features. Tests on the cavitation dataset of the NACA66 (National Advisory Committee for Aeronautics) hydrofoil demonstrate that PVNet outperforms traditional models such as shallow neural networks and UNet. In addition, we conducted a quantitative analysis of the impact of input features on prediction performance, providing guidance for the practical arrangement of sampling points. Furthermore, by comparing different positional encodings, we found that reasonable positional encodings can significantly improve prediction accuracy.