Framework for a variational Bayesian convolutional network for velocity field prediction and uncertainty quantification of a pump-jet propulsor

This study provides the framework for a variational Bayesian convolutional neural network (VB-CNN) to quickly predict the wake velocity field of a pump-jet propulsor and quantify uncertainty. For engineering application and experiments, the wake velocity field of the propulsor can be obtained by using discrete pressure points when the model is trained. The weight distribution of the neural network is altered from a point distribution to a probability distribution using the variational Bayesian method, which also takes into account the prior knowledge of datasets. VB-CNN produces superior results to the convolutional neural network method in small datasets and can quantify uncertainty. This study investigates the differences between the velocity field of computational fluid dynamics and the predictions for the velocity field obtained by the CNN method and the VB-CNN method. The uncertainty distribution of the predicted velocity fields is analyzed according to the 95% confidence interval. Different geometric models are used to verify the generalization of the VB-CNN and CNN models. The results indicate that the VB-CNN method has higher accuracy than the CNN method. Furthermore, the VB-CNN method has superior prediction performance for the velocity field contour and velocity gradient. The maximum error for the velocity field prediction is within 2.33% at different axial positions. The best linear correlation coefficient reached 0.9911. The VB-CNN and CNN models have lower uncertainty at lower rotation speeds and higher uncertainty at higher rotation speeds.