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.

本文提出了一种基于循环图优化传输的深度神经网络解决大颗粒位移、高计算成本等问题，在几何和特征空间构建两个图，并且从图神经网络中获得融合的内部和外部特征用于优化传输计划，从而可以对粒子对进行对应关系的迭代适应式检索以指导循环流学习，实验结果证明该方法在粒子跟踪方面取得了最先进性能。

GotFlow3D：循环图峰值传输用于粒子跟踪中学习三维流动运动

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

We propose a new method to estimate Wasserstein distances and optimal
transport plans between two probability distributions from samples in high
dimension. Unlike plug-in rules that simply replace the true distributions by
their empirical counterparts, our method promotes couplings with low transport
rank, a new structural assumption that is similar to the nonnegative rank of a
matrix. Regularizing based on this assumption leads to drastic improvements on
high-dimensional data for various tasks, including domain adaptation in
single-cell RNA sequencing data. These findings are supported by a theoretical
analysis that indicates that the transport rank is key in overcoming the curse
of dimensionality inherent to data-driven optimal transport.

本文章提出了一种新的方法来估计高维中两个概率分布之间的 Wasserstein 距离和最优传输方案，该方法可以在各种任务中获得显著的改进，包括单细胞 RNA 测序数据的领域适应性。该方法基于低运输秩的耦合，解决了数据驱动最优传输中的维数灾难，并得到了理论分析的支持。