Higher Order Dynamic Mode Decomposition
Higher Order Dynamic Mode Decomposition
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DOI：
10.1137/15m1054924
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发表时间：
2017-01-01
影响因子：
2.1
通讯作者：
Vega, Jose M.
中科院分区：
文献类型：
--
作者：
Le Clainche, Soledad;Vega, Jose M.
本文讨论了动态模式分解（DMD）的扩展，它适用于处理一般周期和准周期动力学，以及衰减到周期和准周期吸引子的瞬态，包括空间复杂性有限但涉及大量频率的情况（标准 DMD 无法访问）。该扩展被标记为高阶动态模式分解，使用时滞快照，可以看作是滑动窗口中的叠加 DMD。使用一些玩具模型动力学、Stuart Landau 方程和 Lorenz 系统来说明和阐明新方法。此外，新方法还应用于复杂的 Ginzburg Landau 方程（图案形成系统的范例）产生的一些永久和瞬态动力学（并测试了其鲁棒性），对于这些方程，标准 DMD 只能揭示微不足道的动力学，以及受径向重力场影响的旋转球壳中的热对流。
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.