odmd: Python/Matlab implementation of online dynamic mode decomposition (Online DMD) and window dynamic mode decomposition (Window DMD). Online dynamic mode decomposition for time-varying systems. Dynamic mode decomposition (DMD) is a popular technique for modal decomposition, flow analysis, and reduced-order modeling. In situations where a system is time varying, one would like to update the system’s description online as time evolves. This work provides an efficient method for computing DMD in real time, updating the approximation of a system’s dynamics as new data becomes available. The algorithm does not require storage of past data and computes the exact DMD matrix using rank-1 updates. A weighting factor that places less weight on older data can be incorporated in a straightforward manner, making the method particularly well suited to time-varying systems. A variant of the method may also be applied to online computation of “windowed DMD,” in which only the most recent data are used. The efficiency of the method is compared against several existing DMD algorithms: for problems in which the state dimension is less than about 200, the proposed algorithm is the most efficient for real-time computation, and it can be orders of magnitude more efficient than the standard DMD algorithm. The method is demonstrated on several examples, including a time-varying linear system and a more complex example using data from a wind tunnel experiment. In particular, we show that the method is effective at capturing the dynamics of surface pressure measurements in the flow over a flat plate with an unsteady separation bubble.
Keywords for this software
References in zbMATH (referenced in 8 articles , 1 standard article )
Showing results 1 to 8 of 8.
- Alfatlawi, Mustaffa; Srivastava, Vaibhav: An incremental approach to online dynamic mode decomposition for time-varying systems with applications to EEG data modeling (2020)
- Hirsh, Seth M.; Harris, Kameron Decker; Kutz, J. Nathan; Brunton, Bingni W.: Centering data improves the dynamic mode decomposition (2020)
- Prasadan, Arvind; Nadakuditi, Raj Rao: Time series source separation using dynamic mode decomposition (2020)
- Wang, Yanran; Hikihara, Takashi: Two-dimensional swarm formation in time-invariant external potential: modeling, analysis, and control (2020)
- Zhang, Hao; Dawson, Scott T. M.; Rowley, Clarence W.; Deem, Eric A.; Cattafesta, Louis N.: Evaluating the accuracy of the dynamic mode decomposition (2020)
- Jayaraman, Balaji; Lu, Chen; Whitman, Joshua; Chowdhary, Girish: Sparse feature map-based Markov models for nonlinear fluid flows (2019)
- Zhang, Hao; Rowley, Clarence W.; Deem, Eric A.; Cattafesta, Louis N.: Online dynamic mode decomposition for time-varying systems (2019)
- Maćešić, Senka; Črnjarić-Žic, Nelida; Mezić, Igor: Koopman operator family spectrum for nonautonomous systems (2018)