Abstract
We generalize the concept of local states (LS) for the prediction of high-dimensional, potentially mixed chaotic systems. The construction of generalized local states (GLS) relies on defining distances between time series on the basis of their (non-)linear correlations. We demonstrate the prediction capabilities of our approach based on the reservoir computing (RC) paradigm using the Kuramoto-Sivashinsky (KS), the Lorenz-96 (L96) and a combination of both systems. In the mixed system a separation of the time series belonging to the two different systems is made possible with GLS. More importantly, prediction remains possible with GLS, where the LS approach must naturally fail. Applications for the prediction of very heterogeneous time series with GLSs are briefly outlined.
Highlights
Tremendous advances in predicting the short- and longterm behavior of complex systems have been made in recent years by applying machine learning [1,2,3,4,5,6,7]
For high-dimensional systems, Reservoir computing (RC) suffers like other machine learning methods from the “curse of dimensionality” meaning that the number of nodes of the network representing the reservoir has to be considerably larger than the dimensionality of the input data rendering the training unfeasible with a naive RC approach
We have proposed and discussed a generalization of the concept of local states (LS) in the sense of using similarity measure (SM) derived from correlations among time series
Summary
Tremendous advances in predicting the short- and longterm behavior of complex systems have been made in recent years by applying machine learning [1,2,3,4,5,6,7]. The similarity of time series can be defined in a much more general way by deducing a distance measure and a local neighborhood from the correlations among the time series [12]. We employ this approach to define generalized local states (GLS) for the prediction of high-dimensional systems with which some of the shortcomings of the LS approach can be overcome
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