Machine Learning for Identifying Lagrangian Coherent Structures in Geophysical Flows

Lagrangian coherent structures (LCS) are time-varying material surfaces that delineate dynamically distinct regions in general dynamical systems. LCS are the extensions of stable and unstable manifolds in static dynamical systems to general time dependent systems. Literature has shown that LCS are instrumental in controlling transport in geophysical flows. In particular, it has be shown that LCS can be used to predict evolution of biological phenomena, predict contaminant dispersion, maintain sensor in their desired regions and to extract fuel efficient navigation pathways for autonomous agents. Prior research has also established that LCS can be identified by a variety of dynamical systems methods. However, these methods are computationally expensive and often confound high shear regions in the flow field with true invariant features that inform its topology.

In this work we propose using machine learning techniques to identify the location and evolution of LCS in geophysical flows. Deep learning tools have revolutionized a wide range of scientific disciplines in the last few years due to its remarkable effectiveness in handling large sets of data. These techniques have proven to be particularly adept at identifying coherent patterns in data that may not be apparent to a human inspector, making it an ideal candidate for capturing and extracting invariant features in geophysical data sets. In this work, we propose a convolutional neural network to locate LCS in a given data set. We use finite time lyapunov exponent (FTLE) computations to obtain the "ground truth" information about the LCS for training purposes. In addition to flow velocity data, we use the locations of critical points in the flow field such as saddle and stable equilibria, as inputs to the network. A novel feature extractor termed "entropy compass" is used to locate these equilibria in the raw data set. Inclusion of these equilibria as inputs would potentially enable the network to distinguish high shear regions from true invariant features. The network will be trained and tested on different data sets with different spatial and temporal scales to ensure that it is able to identify LCS in any given data set.