Online dynamic mode decomposition for time-varying systems

Hao Zhang, Clarence Worth Rowley, Eric A. Deem, Louis N. Cattafesta

Research output: Contribution to journalArticlepeer-review

102 Scopus citations


Dynamic mode decomposition (DMD) is a popular technique for modal decomposition, ow 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 effiective at capturing the dynamics of surface pressure measurements in the ow over a at plate with an unsteady separation bubble.

Original languageEnglish (US)
Pages (from-to)1586-1609
Number of pages24
JournalSIAM Journal on Applied Dynamical Systems
Issue number3
StatePublished - 2019

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modeling and Simulation


  • Data-driven modeling
  • Dynamic mode decomposition
  • Online methods
  • Rank-1 updating algorithm
  • System identification
  • Time-varying systems


Dive into the research topics of 'Online dynamic mode decomposition for time-varying systems'. Together they form a unique fingerprint.

Cite this