Particle image velocimetry (PIV) is an essential method in experimental fluid dynamics. In recent years, the development of deep learning-based methods has inspired new approaches to tackle the PIV problem, which considerably improves the accuracy of PIV. However, the supervised learning of PIV is driven by large volumes of data with ground truth information. Therefore, the authors consider unsupervised PIV methods. There has been some work on unsupervised PIV, but they are not nearly as effective as supervised learning PIV. The authors try to improve the effectiveness and accuracy of unsupervised PIV by adding classical PIV methods and physical constraints. In this paper, the authors propose an unsupervised PIV method combined with the cross-correlation method and divergence-free constraint, which obtains better performance than other unsupervised PIV methods. The authors compare some classical PIV methods and some deep learning methods, such as LiteFlowNet, LiteFlowNet-en, and UnLiteFlowNet with the authors' model on the synthetic dataset. Besides, the authors contrast the results of LiteFlowNet, UnLiteFlowNet and the authors' model on experimental particle images. As a result, the authors' model shows comparable performance with classical PIV methods as well as supervised PIV methods and outperforms the previous unsupervised PIV method in most flow cases. K E Y W O R D S neural network, particle image velocimetry, unsupervised learning | INTRODUCTIONParticle Image Velocimetry (PIV) is one of the most essential measurement methods in experimental fluid mechanics. PIV is a non-intrusive method to detect the fluid flow, so it is widely used in optical, quantitative, and non-contact surface or fluid motion analysis [1]. To conduct a PIV experiment, some tiny particles are necessary. These particles are assumed to follow the flow dynamics. By the illumination of lasers, the particles in the fluid are visible. We can infer the velocity field by comparing the particles in two images, which are generated in a short time interval [2].There are two main techniques used for performing classical PIV: cross-correlation and variational optical flow methods. Cross-correlation methods could provide a sparse motion field by searching the maximum of the crosscorrelation between two interrogation windows of an image pair [3]. The window deformation iterative multi-gridThis is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
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