HODMD: Higher Order Dynamic Mode Decomposition. This paper deals with an extension of dynamic mode decomposition (DMD), which is appropriate to treat general periodic and quasi-periodic dynamics, and transients decaying to periodic and quasi-periodic attractors, including cases (not accessible to standard DMD) that show limited spatial complexity but a very large number of involved frequencies. The extension, labeled as higher order dynamic mode decomposition, uses time-lagged snapshots and can be seen as superimposed DMD in a sliding window. The new method is illustrated and clarified using some toy model dynamics, the Stuart--Landau equation, and the Lorenz system. In addition, the new method is applied to (and its robustness is tested in) some permanent and transient dynamics resulting from the complex Ginzburg--Landau equation (a paradigm of pattern forming systems), for which standard DMD is seen to only uncover trivial dynamics, and the thermal convection in a rotating spherical shell subject to a radial gravity field.
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References in zbMATH (referenced in 8 articles )
Showing results 1 to 8 of 8.
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- Le Clainche, Soledad; Vega, José M.: A review on reduced order modeling using DMD-based methods (2020)
- Pan, Shaowu; Duraisamy, Karthik: On the structure of time-delay embedding in linear models of non-linear dynamical systems (2020)
- Peherstorfer, Benjamin: Sampling low-dimensional Markovian dynamics for preasymptotically recovering reduced models from data with operator inference (2020)
- Champion, Kathleen P.; Brunton, Steven L.; Kutz, J. Nathan: Discovery of nonlinear multiscale systems: sampling strategies and embeddings (2019)
- Pascarella, G.; Fossati, M.; Barrenechea, G.: Adaptive reduced basis method for the reconstruction of unsteady vortex-dominated flows (2019)
- Le Clainche, Soledad; Vega, José M.: Spatio-temporal Koopman decomposition (2018)