Nonparametric forecasting of low-dimensional dynamical systems
Nonparametric forecasting of low-dimensional dynamical systems
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DOI：
10.1103/physreve.91.032915
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发表时间：
2015-03-19
影响因子：
2.4
通讯作者：
Harlim, John
中科院分区：
文献类型：
--
作者：
Berry, Tyrus;Giannakis, Dimitrios;Harlim, John
本文提出了一种用于预测低维流形上的随机动力系统的非参数建模方法。关键思想是在平滑的基础上表示离散移位图，这可以通过扩散图算法获得。在大数据的限制下，该方法在适应不变测度的基础上收敛到潜在动力学的半群解的伽辽金投影。这种方法允许人们通过无方程建模来量化非平凡动力系统的不确定性（实际上，演化概率分布）。我们在各种示例上验证了我们的方法，包括环面上的非均匀各向异性随机微分方程、混沌洛伦兹三维模型以及用作厄尔尼诺南方涛动代理的 Nino-3.4 数据集。
This paper presents a nonparametric modeling approach for forecasting stochastic dynamical systems on low-dimensional manifolds. The key idea is to represent the discrete shift maps on a smooth basis which can be obtained by the diffusion maps algorithm. In the limit of large data, this approach converges to a Galerkin projection of the semigroup solution to the underlying dynamics on a basis adapted to the invariant measure. This approach allows one to quantify uncertainties (in fact, evolve the probability distribution) for nontrivial dynamical systems with equation-free modeling. We verify our approach on various examples, ranging from an inhomogeneous anisotropic stochastic differential equation on a torus, the chaotic Lorenz three-dimensional model, and the Nino-3.4 data set which is used as a proxy of the El Nino Southern Oscillation.