  The forecasting of high-dimensional, spatiotemporal nonlinear systems has
made tremendous progress with the advent of model-free machine learning
techniques. However, in real systems it is not always possible to have all the
information needed; only partial information is available for learning and
forecasting. This can be due to insufficient temporal or spatial samplings, to
inaccessible variables or to noisy training data. Here, we show that it is
nevertheless possible to forecast extreme events occurrence in incomplete
experimental recordings from a spatiotemporally chaotic microcavity laser using
reservoir computing. Selecting regions of maximum transfer entropy, we show
that it is possible to get higher forecasting accuracy using nonlocal data vs
local data thus allowing greater warning times, at least twice the time horizon
predicted from the nonlinear local Lyapunov exponent.
