Published:
Springer Science and Business Media LLC, 2020
Published in:
Journal of Nonlinear Science, 30 (2020) 3, Seite 713-735
Language:
English
DOI:
10.1007/s00332-019-09588-7
ISSN:
0938-8974;
1432-1467
Origination:
Footnote:
Description:
AbstractWe 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.