Transfer Operators from Optimal Transport Plans for Coherent Set Detection

TL;DR

This paper introduces a novel approach combining optimal transport and transfer operators to detect coherent sets in complex flows, providing a noise-robust and computationally efficient method for flow analysis.

Contribution

It develops a new framework that leverages unbalanced regularized optimal transport to analyze flow coherence and reconstruct dynamics from limited distribution data.

Findings

Optimal transport effectively identifies coherent flow regions.

Unbalanced regularization enhances noise robustness.

Method efficiently reconstructs flow dynamics from minimal data.

Abstract

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.