Dynamic mode decomposition: an alternative algorithm for full-rank datasets. (English) Zbl 1531.65277
Summary: Dynamic mode decomposition (DMD) is a modal decomposition technique that describes high-dimensional dynamic data using coupled spatial-temporal modes. It combines the main features of performing principal component analysis (PCA) in space, and power spectral analysis in time. The method is equation-free in the sense that it does not require knowledge of the underlying governing equations and is entirely data-driven. The purpose of this paper is to introduce a new algorithm for computing the dynamic mode decomposition in the case of full rank data. The new approach is more economical from a computational point of view, which is an advantage when working with large datasets.
MSC:
| 65P99 | Numerical problems in dynamical systems |
| 37M10 | Time series analysis of dynamical systems |
| 65F55 | Numerical methods for low-rank matrix approximation; matrix compression |
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
Keywords:
algorithms for dynamic mode decomposition; singular value decomposition; Koopman operator; equation-freeReferences:
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