Data-adaptive harmonic spectra and multilayer Stuart-Landau models
Data-adaptive harmonic spectra and multilayer Stuart-Landau models
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DOI：
10.1063/1.4989400
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发表时间：
2017-09-01
期刊：
影响因子：
2.9
通讯作者：
Kondrashov, Dmitri
中科院分区：
文献类型：
--
作者：
Chekroun, Mickael D.;Kondrashov, Dmitri
多元时间序列的调和分解被认为是我们采用的积分算子的方法与周期半群核。谱分解定理推导出，涵盖了重要的情况下，从混合不变测度的两次统计。对应的特征值可以按傅立叶频率分组，并且实际上在每个频率处被给定为取决于数据的互谱矩阵的奇异值。这些特征值服从，此外，变分原理，使我们能够自然地定义一个多维功率谱。本征模，就他们而言，表现出的数据自适应字符体现在他们的相位，这使我们反过来定义一个多维相位谱。由此产生的数据自适应谐波（DAH）模式允许将数据驱动的建模工作减少到按频率堆叠的基本模型，仅通过相同的噪声实现在不同的频率处耦合。特别是，DAH分解提取时间相关系数堆叠傅立叶频率，可以有效地建模提供的时间相关性的衰减是足够好的解决一类的多层随机模型（MSM）在这里定制的随机斯图尔特-朗道振荡器。应用洛伦兹96模型和随机热方程驱动的时空白色噪声被认为是。在这两种情况下，DAH分解允许提取时空模式，揭示嵌入相空间中动态的关键特征。多层Stuart-Landau模型（MSLM）成功地模拟了相应的时间演化场的典型模式，以及它们的发生统计。(C)2017年作者。
Harmonic decompositions of multivariate time series are considered for which we adopt an integral operator approach with periodic semigroup kernels. Spectral decomposition theorems are derived that cover the important cases of two-time statistics drawn from a mixing invariant measure. The corresponding eigenvalues can be grouped per Fourier frequency and are actually given, at each frequency, as the singular values of a cross-spectral matrix depending on the data. These eigenvalues obey, furthermore, a variational principle that allows us to define naturally a multidimensional power spectrum. The eigenmodes, as far as they are concerned, exhibit a data-adaptive character manifested in their phase which allows us in turn to define a multidimensional phase spectrum. The resulting data-adaptive harmonic (DAH) modes allow for reducing the data-driven modeling effort to elemental models stacked per frequency, only coupled at different frequencies by the same noise realization. In particular, the DAH decomposition extracts time-dependent coefficients stacked by Fourier frequency which can be efficiently modeled-provided the decay of temporal correlations is sufficiently well-resolved-within a class of multilayer stochastic models (MSMs) tailored here on stochastic Stuart-Landau oscillators. Applications to the Lorenz 96 model and to a stochastic heat equation driven by a space-time white noise are considered. In both cases, the DAH decomposition allows for an extraction of spatio-temporal modes revealing key features of the dynamics in the embedded phase space. The multilayer Stuart-Landau models (MSLMs) are shown to successfully model the typical patterns of the corresponding time-evolving fields, as well as their statistics of occurrence. (C) 2017 Author(s).