Predicting Spatio-temporal Time Series Using Dimension Reduced Local States

被引：13
|
作者：
Isensee, Jonas [1 ,2 ]
Datseris, George [1 ,2 ]
Parlitz, Ulrich [1 ,2 ]
机构：
[1] Max Planck Inst Dynam & Self Org, Fassberg 17, D-37077 Gottingen, Germany
[2] Georg August Univ Gottingen, Inst Dynam Komplexer Syst, Friedrich Hund Pl 1, D-37077 Gottingen, Germany
来源：
JOURNAL OF NONLINEAR SCIENCE | 2020年 / 30卷 / 03期
关键词：
Data driven modelling; Nearest neighbours prediction; Spatio-temporal chaos; DYNAMICS; MODEL;
D O I：
10.1007/s00332-019-09588-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present a method for both cross-estimation and iterated time series prediction of spatio-temporal dynamics based on local modelling and dimension reduction techniques. Assuming homogeneity of the underlying dynamics, we construct delay coordinates of local states and then further reduce their dimensionality through Principle Component Analysis. The prediction uses nearest neighbour methods in the space of dimension reduced states to either cross-estimate or iteratively predict the future of a given frame. The effectiveness of this approach is shown for (noisy) data from a (cubic) Barkley model, the Bueno-Orovio-Cherry-Fenton model, and the Kuramoto-Sivashinsky model.
引用
收藏
页码：713 / 735
页数：23
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