Deep Learning Optical Flow with Compound Loss for Dense Fluid Motion Estimation

Flow motion with complex patterns, such as vortex, stagnant flow, and seepage, put forward higher spatial resolution requirements for particle image velocimetry (PIV). With the development of deep learning technology in optical flow estimation, many attempts have been made to introduce deep learning-based optical flow (DLOF) into PIV. Compared with the traditional optical flow method, the DLOF method has the advantages of higher precision, faster calculation speed, and avoiding manual parameter adjustment. However, DLOF research is generally developed based on the basic characteristics of rigid body motion, and its key loss function part still generally uses the L1 (mean absolute error, MAE, L1) or L2 (mean square error, MSE, L2) loss functions, which lack consideration of fluid motion characteristics. Therefore, the current DLOF research has the problems of large angular error and serious curl-divergence loss in fluid motion estimation scenarios with smaller spatial scales than rigid bodies. Based on the prior knowledge of the traditional fluid motion characteristics, this study proposes a fluid loss function for describing the fluid motion characteristics, and combines this loss function with Flownet2. The compound loss (CL) function is combined with the displacement error, angular error, and div-curl smooth loss. The method combined with the loss function in this paper is called FlowNet2-CL-PIV. In order to verify that the compound loss function proposed in this study has a positive impact on the model training results, this paper uses the cosine similarity measure to demonstrate its effectiveness. In addition, the parameter selection of the compound loss function is analyzed and compared, and it is verified that the best training effect can be achieved by adjusting the parameter so that the order of magnitude of each part of the compound loss function is consistent. In order to test the calculation effect of the Flownet2-CL-PIV method proposed in this study, synthetic particle images are used for model training and performance analysis. Simulation results in various flow fields show that the root mean square error (RMSE) and average angular error (AAE) of Flownet2-CL-PIV reach 0.182 pixels and 1.7 degrees, which are 10% and 54% higher than the original model, respectively.