sVltege / DMD-for-ergodic-systems

Computing the discrete spectrum of the Koopman operator using Dynamic Mode Decomposition

DMD-for-ergodic-systems

This folder shows the application of Dynamic Mode Decomposition (DMD) algorithm for computing the eigenvalues and eigenfunctions of the Koopman operator for dynamical systems with ergodic attractors following the paper
"Ergodic Theory, Dynamic Mode Decomposition and Computation of Koopman scpectral properties" SIAM Journal on Applied Dynamical Systems, by Hassan Arbabi & Igor Mezic, 2017

The examples in the root folder:

Lorenz_POD: computation of a POD basis for observables on chaotic Lorenz attractor,
QPeriodicCavityFlow: computation of Koopman eigenvalues for quais-periodic nonlinear flows using Exact Hankel-DMD, VanDerPol_phase: computation of asymptotic phase for trajectories of Van der Pol oscillator.

The DMD routines in the +DMD folder:

Hankel-DMD (algorithm suggested in the above paper), companion-matrix DMD (Rowley et al 2009, Journal of Fluid Mechanics) SVD-enhanced DMD (Schmid 2010, Journal of Fluid Mechanics) EXACT_DMD (Tu et al 2015, Journal of Computational Dynamics)

send comments and questions to [e-mail]

H. Arbabi

November 2017