Predictive Nonlinear Modeling by Koopman Mode Decomposition
Predictive Nonlinear Modeling by Koopman Mode Decomposition
复制标题
通过库普曼模式分解进行预测非线性建模
DOI：
10.1109/icdmw51313.2020.00118
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Kuboyama Tetsuji
中科院分区：
文献类型：
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作者：
Kusaba Akira;Shin Kilho;Shepard Dave;Kuboyama Tetsuji
机器学习在时间序列分析中有无数的应用：控制智能电网、检测机械故障和分析股票价格。傅立叶模态分解 (FMD) 是最常见的分析方法，因为它将时间序列分解为有限的波形分量或模态，但其主要缺点是 FMD 假设每个模态都有恒定的幅度，而这一假设在现实世界的数据中很少成立。相比之下，库普曼模式分解（KMD）可以检测幅度呈指数增加或减少的模式，尽管它主要应用于诊断数据错误，而不是预测。 KMD 无法应用于预测的部分原因是数学公式的缺陷。本文旨在弥补这一缺点：它提供了 KMD 的数学精确公式作为实用工具。反过来，这个公式使我们能够开发一种新颖的实用方法来预测未来数据。我们使用合成数据和真实等离子体流数据进一步证明了我们方法的有效性。
Machine learning has countless applications in time series analysis: controlling smart grids, detecting mechanical failures, and analyzing stock prices. Fourier mode decomposition (FMD) is the most common method of analysis because it decomposes time series into finite waveform components, or modes, but its principal shortcoming is that FMD assumes every mode has a constant amplitude, an assumption that rarely holds in real-world data. In contrast, Koopman mode decomposition (KMD) can detect modes with exponentially-increasing or - decreasing amplitudes, although it has mostly been applied to diagnosing data errors, not to prediction. What has kept KMD from being applied to prediction is partly a shortcoming in a mathematical formulation. This paper seeks to remedy that shortcoming: it provides a mathematically-precise formulation of KMD as a practical tool. This formulation, in turn, allows us to develop a novel practical method for prediction of future data. We further demonstrate our method's effectiveness using both synthetic data and real plasma flow data.