The topic of this study lies in the intersection of two fields. One is related with analyzing transport phenomena in complicated flows. For this purpose, we use so-called coherent sets: non-dispersing, possibly moving regions in the flow’s domain. The other is concerned with reconstructing a flow field from observations of its action on a measure, which we address by optimal transport. We show that the framework of optimal transport is well suited for delivering the formal requirements on which a coherent-set analysis can be based on. The necessary noise-robustness requirement of coherence can be matched by the computationally efficient concept of unbalanced regularized optimal transport. Moreover, the applied regularization can be interpreted as an optimal way of retrieving the full dynamics given the extremely restricted information of an initial and a final particle distribution moving according to Brownian motion.

本研究的主题在于两个领域的交集。一是与分析复杂流中的传输现象有关。为此，我们使用所谓的相干集：流域中的非分散、可能移动的区域。另一个是从观察流场对测量的作用来重建流场，我们通过最佳传输来解决。我们表明，最优传输的框架非常适合提供可作为连贯集分析基础的形式要求。相干性的必要噪声鲁棒性要求可以通过不平衡正则化最优传输的计算效率概念来匹配。而且，