Unsupervised machine learning for coherent structure identification

The clustering of fluid particle trajectories into coherent structures often requires a priori assumptions about the nature of the coherent subgroups. We present a new method, simultaneous Coherent Structure Coloring (sCSC), which performs unsupervised learning on measured or simulated Lagrangian flow trajectories without anticipating the underlying structure of the data. Unlike common methods, rather than clustering similar states (i.e., particle trajectories), sCSC separates the most dissimilar states via a generalized eigenvalue problem. The set of eigenvector solutions are bifurcated and sequentially applied to the data, yielding a binary dendrogram representation. The number of coherent structures emerges naturally, since many fewer branches are occupied than is combinatorically possible. We demonstrate that sCSC can identify the structures governing fluid transport in both theoretical models and laboratory measurements with two orders of magnitude less data than existing methods and no a priori assumptions.