2017/04/01 by Travis Askham, J. Nathan Kutz, Askham, Travis +1 · 7 citations
Decision Sciences · Engineering · #37M02 #49M02 #65P02 #Control Systems and Identification #FOS: Mathematics #Fault Detection and Control Systems #Numerical Analysis (math.NA) #Scientific Measurement and Uncertainty Evaluation
paper · pdf · doi:10.48550/arxiv.1704.02343
openalex publication_date 2017/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.