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Flow visualization technologies such as particle tracking velocimetry (PTV)are broadly used in understanding the all-pervasiveness three-dimensional (3D)turbulent flow from nature and industrial processes. Despite the advances in 3Dacquisition techniques, the developed motion estimation algorithms in particletracking remain great challenges of large particle displacements, denseparticle distributions and high computational cost. By introducing a novel deepneural network based on recurrent Graph Optimal Transport, called GotFlow3D, wepresent an end-to-end solution to learn the 3D fluid flow motion fromdouble-frame particle sets. The proposed network constructs two graphs in thegeometric and feature space and further enriches the original particlerepresentations with the fused intrinsic and extrinsic features learnt from agraph neural network. The extracted deep features are subsequently utilized tomake optimal transport plans indicating the correspondences of particle pairs,which are then iteratively and adaptively retrieved to guide the recurrent flowlearning. Experimental evaluations, including assessments on numericalexperiments and validations on real-world experiments, demonstrate that theproposed GotFlow3D achieves state-of-the-art performance against bothrecently-developed scene flow learners and particle tracking algorithms, withimpressive accuracy, robustness and generalization ability, which can providedeeper insight into the complex dynamics of broad physical and biologicalsystems.

GotFlow3D: Recurrent Graph Optimal Transport for Learning 3D Flow Motion in Particle Tracking