  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 3D
acquisition techniques, the developed motion estimation algorithms in particle
tracking remain great challenges of large particle displacements, dense
particle distributions and high computational cost. By introducing a novel deep
neural network based on recurrent Graph Optimal Transport, called GotFlow3D, we
present an end-to-end solution to learn the 3D fluid flow motion from
double-frame particle sets. The proposed network constructs two graphs in the
geometric and feature space and further enriches the original particle
representations with the fused intrinsic and extrinsic features learnt from a
graph neural network. The extracted deep features are subsequently utilized to
make optimal transport plans indicating the correspondences of particle pairs,
which are then iteratively and adaptively retrieved to guide the recurrent flow
learning. Experimental evaluations, including assessments on numerical
experiments and validations on real-world experiments, demonstrate that the
proposed GotFlow3D achieves state-of-the-art performance against both
recently-developed scene flow learners and particle tracking algorithms, with
impressive accuracy, robustness and generalization ability, which can provide
deeper insight into the complex dynamics of broad physical and biological
systems.
