Dynamic mode decomposition for multiscale nonlinear physics
Dynamic mode decomposition for multiscale nonlinear physics
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DOI：
10.1103/physreve.99.063311
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发表时间：
2019-06-20
影响因子：
2.4
通讯作者：
Kutz, J. Nathan
中科院分区：
文献类型：
--
作者：
Dylewsky, Daniel;Tao, Molei;Kutz, J. Nathan
我们提出了一个数据驱动的方法分离复杂的，多尺度系统到其组成的时间尺度组件使用递归实现的动态模式分解（DMD）。局部线性模型建立从窗口的数据子集，和主导的时间尺度发现使用谱聚类的特征值。这种方法为每个识别的分量产生时间序列数据，其总和为输入信号的忠实重构。它与多分辨率分析（MRA）领域中的大多数其他方法不同，因为它（1）同时考虑空间和时间相干性，使其对组件之间的尺度重叠更具鲁棒性，以及（2）在每个尺度上产生局部动态的闭合形式表达式，可用于任何或所有组件的短期预测。我们的技术是多分辨率动态模式分解（mrDMD）的扩展，广义处理更广泛的各种多尺度系统，更忠实地重建其孤立的组件。在本文中，我们提出了一个概述，我们的算法和结果的两个例子的物理系统，并简要讨论了一些优点和潜在的预测应用的技术。
We present a data-driven method for separating complex, multiscale systems into their constituent timescale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed subsets of the data, and dominant timescales are discovered using spectral clustering on their eigenvalues. This approach produces time series data for each identified component, which sum to a faithful reconstruction of the input signal. It differs from most other methods in the field of multiresolution analysis (MRA) in that it (1) accounts for spatial and temporal coherencies simultaneously, making it more robust to scale overlap between components, and (2) yields a closed-form expression for local dynamics at each scale, which can be used for short-term prediction of any or all components. Our technique is an extension of multi-resolution dynamic mode decomposition (mrDMD), generalized to treat a broader variety of multiscale systems and more faithfully reconstruct their isolated components. In this paper we present an overview of our algorithm and its results on two example physical systems, and briefly discuss some advantages and potential forecasting applications for the technique.