期刊
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
卷 17, 期 1, 页码 380-416出版社
SIAM PUBLICATIONS
DOI: 10.1137/M1124176
关键词
dynamic mode decomposition; inverse linear systems; variable projection algorithm; inverse differential equations
资金
- Air Force Office of Scientific Research (AFOSR) [FA9550-15-1-0385]
- Defense Advanced Research Projects Agency (DARPA) [HR0011-16-C-0016]
The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple algorithm for computing an optimized version of the DMD for data which may be collected at unevenly spaced sample times. By making use of the variable projection method for nonlinear least squares problems, the algorithm is capable of solving the underlying nonlinear optimization problem efficiently. We explore the performance of the algorithm with some numerical examples for synthetic and real data from dynamical systems and find that the resulting decomposition displays less bias in the presence of noise than standard DMD algorithms. Because of the flexibility of the algorithm, we also present some interesting new options for DMD-based analysis.
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