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Predicting spatio-temporal time series using dimension reduced local states

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Isensee,  Jonas
Research Group Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Datseris,  George
Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Parlitz,  Ulrich
Research Group Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Isensee, J., Datseris, G., & Parlitz, U. (2020). Predicting spatio-temporal time series using dimension reduced local states. Journal of Nonlinear Science, 30, 713-735. doi:10.1007/s00332-019-09588-7.


Cite as: https://hdl.handle.net/21.11116/0000-0005-1996-6
Abstract
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.