Knowledge-driven multi-output Gaussian process for ventilated cavity morphology prediction

The accurate characterization and dynamic prediction of ventilated cavity morphology are critical to revealing the unsteady shedding mechanism of ventilated cavitation. In the present study, an integrated data-driven and knowledge-driven framework is developed for cavity morphology extraction and prediction based on high-speed images and sparse experimental data. A U-Net-based image segmentation method is employed to extract the cavity length L and the cavity diameter D under transient conditions. The extracted results provide reliable data for the subsequent modeling. A multi-output Gaussian process (MOGP) model is further established to predict the time-averaged cavity length and cavity diameter from the Froude number (Fr) and the ventilation rate (C_Q). The positive dependence of the cavity dimensions on the ventilation rate is incorporated into the model as physical knowledge. This treatment effectively suppresses the non-physical oscillations that arise under small-sample condition. The results show that the root mean squared error (RMSE) is reduced by 59.6% for L and 69.6% for D, while the corresponding R² values increase to 0.985 and 0.978. Furthermore, the cavity aspect ratio is employed to characterize the coupled axial–radial evolution of the cavity morphology. The present work provides practical guidance for the analysis and prediction of ventilated cavity morphology.