论文标题
从最佳运输计划转移操作员进行连贯的设置检测
Transfer Operators from Optimal Transport Plans for Coherent Set Detection
论文作者
论文摘要
这项研究的主题在于两个领域的交集。一个与分析复杂流中的运输现象有关。为此，我们使用所谓的连贯集：非分散的，可能在流动域中移动的区域。另一个涉及从观察其对度量的作用来重建流场，我们通过最佳运输来解决。我们表明，最佳运输的框架非常适合提供可以基于连贯的分析的正式要求。连贯性的必要噪声要求可以通过不平衡的正则最佳运输的计算有效概念来匹配。此外，鉴于根据布朗运动，粒子的初始粒子和最终分布非常有限的信息，可以将应用的正则化被解释为检索全部动力学的最佳方法。
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 observing 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 distribution of particles moving according to Brownian motion.
