  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.
