Estimating the Finite Time Lyapunov Exponent from Sparse Lagrangian Trajectories

We propose a simple numerical algorithm to estimate the finite time Lyapunov exponent (FTLE) in dynamical systems from only a sparse number of Lagrangian particle trajectories. The method first reconstructs the flow field using the radial basis function (RBF) and then uses either the Lagrangian or the Eulerian approach to determine the corresponding flow map. We also develop a simple algorithm based on the Schur complement for updating, rather than recomputing, the reconstruction in the RBF when new trajectory data is made available in applications. We will demonstrate the effectiveness of the proposed method using examples from autonomous and aperiodic flows, and also measurements from real-life data.