Koopman mode expansions between simple invariant solutions

Koopman analysis of Burgers equation

(2018) Jacob Page et al.   Physical Review Fluids

Deep learning for universal linear embeddings of nonlinear dynamics

(2018) Bethany Lusch et al.   Nature Communications

Study of dynamics in post-transient flows using Koopman mode decomposition

(2017) Hassan Arbabi et al.   Physical Review Fluids

Extracting spatial–temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition

(2016) Bingni W. Brunton et al.   JOURNAL OF NEUROSCIENCE METHODS

Multiresolution Dynamic Mode Decomposition

(2016) J. Nathan Kutz et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Correspondence between Koopman mode decomposition, resolvent mode decomposition, and invariant solutions of the Navier-Stokes equations

(2016) Ati S. Sharma et al.   Physical Review Fluids

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

(2016) Steven L. Brunton et al.   PLoS One

A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition

(2015) Matthew O. Williams et al.   JOURNAL OF NONLINEAR SCIENCE

Spanwise-localized solutions of planar shear flows

(2014) J. F. Gibson et al.   JOURNAL OF FLUID MECHANICS

A doubly localized equilibrium solution of plane Couette flow

(2014) E. Brand et al.   JOURNAL OF FLUID MECHANICS

Streamwise and doubly-localised periodic orbits in plane Poiseuille flow

(2014) Stefan Zammert et al.   JOURNAL OF FLUID MECHANICS

Genesis of Streamwise-Localized Solutions from Globally Periodic Traveling Waves in Pipe Flow

(2014) M. Chantry et al.   PHYSICAL REVIEW LETTERS

Sparsity-promoting dynamic mode decomposition

(2014) Mihailo R. Jovanović et al.   PHYSICS OF FLUIDS

Koopman-mode decomposition of the cylinder wake

(2013) Shervin Bagheri   JOURNAL OF FLUID MECHANICS

Invariant recurrent solutions embedded in a turbulent two-dimensional Kolmogorov flow

(2013) Gary J. Chandler et al.   JOURNAL OF FLUID MECHANICS

Streamwise-Localized Solutions at the Onset of Turbulence in Pipe Flow

(2013) M. Avila et al.   PHYSICAL REVIEW LETTERS

Analysis of Fluid Flows via Spectral Properties of the Koopman Operator

(2012) Igor Mezić   Annual Review of Fluid Mechanics

The Significance of Simple Invariant Solutions in Turbulent Flows

(2011) Genta Kawahara et al.   Annual Review of Fluid Mechanics

Dynamic mode decomposition of numerical and experimental data

(2010) PETER J. SCHMID   JOURNAL OF FLUID MECHANICS

Streamwise vortices in shear flows: harbingers of transition and the skeleton of coherent structures

(2010) PHILIP HALL et al.   JOURNAL OF FLUID MECHANICS

Traveling-waves consistent with turbulence-driven secondary flow in a square duct

(2010) Markus Uhlmann et al.   PHYSICS OF FLUIDS

Equilibrium and travelling-wave solutions of plane Couette flow

(2009) J. F. GIBSON et al.   JOURNAL OF FLUID MECHANICS

Spectral analysis of nonlinear flows

(2009) CLARENCE W. ROWLEY et al.   JOURNAL OF FLUID MECHANICS

Visualizing the geometry of state space in plane Couette flow

(2008) J. F. GIBSON et al.   JOURNAL OF FLUID MECHANICS