Flow completion network: Inferring the fluid dynamics from incomplete flow information using graph neural networks

This paper introduces a novel neural network—a flow completion network (FCN)—to infer the fluid dynamics, including the flow field and the force acting on the body, from the incomplete data based on a graph convolution attention network. The FCN is composed of several graph convolution layers and spatial attention layers. It is designed to infer the velocity field and the vortex force contribution of the flow field when combined with the vortex force map method. Compared with other neural networks adopted in fluid dynamics, the FCN is capable of dealing with both structured data and unstructured data. The performance of the proposed FCN is assessed by the computational fluid dynamics (CFD) data on the flow field around a circular cylinder. The force coefficients predicted by our model are validated against those obtained directly from CFD. Moreover, it is shown that our model effectively utilizes the existing flow field information and the gradient information simultaneously, giving better performance than the traditional convolution neural network (CNN)-based and deep neural network (DNN)-based models. Specifically, among all the cases of different Reynolds numbers and different proportions of the training dataset, the results show that the proposed FCN achieves a maximum norm mean square error of 5.86% in the test dataset, which is much lower than those of the traditional CNN-based and DNN-based models (42.32% and 15.63%, respectively).