The DOI matches its Crossref record; 40 of the 40 references it cites were found in a registry or an index.
Higher Order Dynamic Mode Decomposition
Open accessAbstract
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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Citations
Cites
Deterministic Nonperiodic Flow
Lorenz, E. N. (1963) · Journal of the Atmospheric Sciences · doi:10.1175/1520-0469(1963)020<0130:dnf>2.0.co;2 · Cited by 19,398
Detecting strange attractors in turbulence
Takens, F. (1981) · Lecture Notes in Mathematics · doi:10.1007/bfb0091924 · Cited by 10,459 · cited 4×
“In this sense, HODMD can be seen as a synergic combination of standard DMD and Takens’ delay embedding and could be useful for the delay-embedding community, which is very interested in forecasting.”
MethodInfluentialHydrodynamic and Hydromagnetic Stability
Chandrasekhar, S., & Gillis, J. (1962) · Physics Today · doi:10.1063/1.3058072 · Cited by 10,329
Dynamic mode decomposition of numerical and experimental data
SCHMID, P. J. (2010) · Journal of Fluid Mechanics · doi:10.1017/s0022112010001217 · Cited by 5,915
Discovering governing equations from data by sparse identification of nonlinear dynamical systems
Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1517384113 · Cited by 4,796
Packard, N. H., Crutchfield, J. P., Farmer, J. D., & Shaw, R. S. (1980) · Physical Review Letters · doi:10.1103/physrevlett.45.712 · Cited by 3,869
Hamiltonian Systems and Transformation in Hilbert Space
Koopman, B. O. (1931) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.17.5.315 · Cited by 2,383
Spectral analysis of nonlinear flows
ROWLEY, C. W., MEZIĆ, I., BAGHERI, S., SCHLATTER, P., & HENNINGSON, D. S. (2009) · Journal of Fluid Mechanics · doi:10.1017/s0022112009992059 · Cited by 2,324
Extracting qualitative dynamics from experimental data
Broomhead, D. S., & King, G. P. (1986) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(86)90031-x · Cited by 2,278
Sauer, T., Yorke, J. A., & Casdagli, M. (1991) · Journal of Statistical Physics · doi:10.1007/bf01053745 · Cited by 2,045
Cited by
Dynamic Mode Decomposition and Its Variants
Schmid, P. J. (2022) · Annual Review of Fluid Mechanics · doi:10.1146/annurev-fluid-030121-015835 · Cited by 640
Discovery of nonlinear multiscale systems: Sampling strategies and embeddings
Champion, K. P., Brunton, S. L., & Kutz, J. N. (2019) · SIAM Journal on Applied Dynamical Systems · doi:10.1137/18m1188227 · Cited by 171
Metadata
- Authors
- Le Clainche, S., & Vega, J. M.
- Venue
- SIAM Journal on Applied Dynamical Systems
- Published
- 2017-01
- Volume
- 16
- Issue
- 2
- Pages
- 882-925
- ISSN
- 1536-0040 (ISSN-L)
- OpenAlex
- W2613314665
- Cited by
- 417
- References
- 40
- FWCI
- 12.02
- Type
- journal article
- Language
- en
- Open access
- green
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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