Variable Projection Methods for an Optimized Dynamic Mode Decomposition
| Autor: | Travis Askham, J. Nathan Kutz |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Dynamical systems theory
Noise (signal processing) Computer science 01 natural sciences 010305 fluids & plasmas 010101 applied mathematics Variable (computer science) Modeling and Simulation Non-linear least squares 0103 physical sciences Dynamic mode decomposition Projection method 0101 mathematics Projection (set theory) Algorithm Analysis SIMPLE algorithm |
| Zdroj: | SIAM Journal on Applied Dynamical Systems. 17:380-416 |
| ISSN: | 1536-0040 |
| DOI: | 10.1137/m1124176 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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