"Dynamic mode decomposition (DMD) is a dimensionality reduction
algorithm developed by Peter Schmid in 2008. Given a time series of
data, DMD computes a set of modes each of which is associated with a
fixed oscillation frequency and decay/growth rate. For linear systems in
particular, these modes and frequencies are analogous to the normal modes of the system, but more generally, they are approximations of the modes and eigenvalues of the composition operator
(also called the Koopman operator). Due to the intrinsic temporal
behaviors associated with each mode, DMD differs from dimensionality
reduction methods such as principal component analysis,
which computes orthogonal modes that lack predetermined temporal
behaviors. Because its modes are not orthogonal, DMD-based
representations can be less parsimonious than those generated by PCA.
However, they can also be more physically meaningful because each mode
is associated with a damped (or driven) sinusoidal behavior in time.
https://en.wikipedia.org/wiki/Dynamic_mode_decomposition
http://faculty.washington.edu/kutz/page1/page13/
On Dynamic Mode Decomposition: Theory and Applications - http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10631
https://arxiv.org/abs/1312.0041
Applied Koopmanism - http://aip.scitation.org/doi/10.1063/1.4772195
Analysis of Fluid Flows via Spectral Properties of the Koopman Operator - http://www.annualreviews.org/doi/10.1146/annurev-fluid-011212-140652
Variants of Dynamic Mode Decomposition: Boundary Condition, Koopman, and Fourier Analyses - http://link.springer.com/article/10.1007%2Fs00332-012-9130-9
"Dynamic mode decomposition (DMD) is an Arnoldi-like method based on the
Koopman operator. It analyzes empirical data, typically generated by
nonlinear dynamics, and computes eigenvalues and eigenmodes of an
approximate linear model. Without explicit knowledge of the dynamical
operator, it extracts frequencies, growth rates, and spatial structures
for each mode."
Model Reduction Using DMD - http://www.sciencedirect.com/science/article/pii/S163107211400103X
Multi-Resolution Dynamic Mode Decomposition - https://arxiv.org/abs/1506.00564
DMDSP – Sparsity-Promoting Dynamic Mode Decomposition - http://people.ece.umn.edu/~mihailo/software/dmdsp/
Sparse DMD in Python - https://github.com/aaren/sparse_dmd
http://aaren.me/thesis/chapters/dynamic-mode-decomposition/
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