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

2015 ◽  
Vol 25 (6) ◽  
pp. 1307-1346 ◽  
Author(s):  
Matthew O. Williams ◽  
Ioannis G. Kevrekidis ◽  
Clarence W. Rowley
Keyword(s):  
Dynamic Mode Decomposition ◽  
Data Driven ◽  
Dynamic Mode ◽  
Koopman Operator ◽  
Mode Decomposition

scholarly journals Detecting regime transitions in time series using dynamic mode decomposition

2020 ◽  
Author(s):  
Georg Gottwald ◽  
Federica Gugole
Keyword(s):  
Time Series ◽  
Reconstruction Error ◽  
Reanalysis Data ◽  
Dynamic Mode Decomposition ◽  
Transient Dynamics ◽  
Dynamic Mode ◽  
Koopman Operator ◽  
Regime Changes ◽  
Fast Relaxation ◽  
Mode Decomposition

<p>We employ the framework of the Koopman operator and dynamic mode decomposition to devise a computationally cheap and easily implementable method to detect transient dynamics and regime changes in time series. We argue that typically transient dynamics experiences the full state space dimension with subsequent fast relaxation towards the attractor. In equilibrium, on the other hand, the dynamics evolves on a slower time scale on a lower dimensional attractor. The reconstruction error of a dynamic mode decomposition is used to monitor the inability of the time series to resolve the fast relaxation towards the attractor as well as the effective dimension of the dynamics. We illustrate our method by detecting transient dynamics in the Kuramoto-Sivashinsky equation. We further apply our method to atmospheric reanalysis data; our diagnostics detects the transition from a predominantly negative North Atlantic Oscillation (NAO) to a predominantly positive NAO around 1970, as well as the recently found regime change in the Southern Hemisphere atmospheric circulation around 1970.</p>

scholarly journals Data‐driven identification of the spatiotemporal structure of turbulent flows by streaming dynamic mode decomposition

2022 ◽  
Author(s):  
Rui Yang ◽  
Xuan Zhang ◽  
Philipp Reiter ◽  
Detlef Lohse ◽  
Olga Shishkina ◽  
...  
Keyword(s):  
Turbulent Flows ◽  
Dynamic Mode Decomposition ◽  
Data Driven ◽  
Dynamic Mode ◽  
Spatiotemporal Structure ◽  
Mode Decomposition
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