Variable projection methods for an optimized dynamic mode decomposition
This work provides a more robust DMD variant for practitioners analyzing noisy, irregularly sampled time-series data from dynamical systems.
The authors present an optimized dynamic mode decomposition (DMD) algorithm using variable projection for nonlinear least squares, enabling analysis of unevenly sampled data. The method reduces bias in noisy conditions compared to standard DMD, as demonstrated on synthetic and real dynamical system data.
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.