%0 Journal Article %1 clainche2017higher %A Le Clainche, Soledad %A Vega, José Manuel %D 2017 %I Society for Industrial & Applied Mathematics (SIAM) %J SIAM Journal on Applied Dynamical Systems %K %N 2 %P 882--925 %R 10.1137/15m1054924 %T Higher Order Dynamic Mode Decomposition %U https://epubs.siam.org/doi/10.1137/15M1054924 %V 16 %X 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.

@article{clainche2017higher, abstract = {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.}, added-at = {2021-05-24T03:29:54.000+0200}, author = {Le Clainche, Soledad and Vega, José Manuel}, biburl = {https://www.bibsonomy.org/bibtex/280f9bbb7f22a4647da9c8d77656b5b3f/gdmcbain}, doi = {10.1137/15m1054924}, interhash = {1853a16496b9d8a3911e54643e03a7a9}, intrahash = {80f9bbb7f22a4647da9c8d77656b5b3f}, journal = {{SIAM} Journal on Applied Dynamical Systems}, keywords = {}, month = jan, number = 2, pages = {882--925}, publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})}, timestamp = {2021-05-24T03:29:54.000+0200}, title = {Higher Order Dynamic Mode Decomposition}, url = {https://epubs.siam.org/doi/10.1137/15M1054924}, volume = 16, year = 2017 }