  Machine learning algorithms have opened a breach in the fortress of the
prediction of high-dimensional chaotic systems. Their ability to find hidden
correlations in data can be exploited to perform model-free forecasting of
spatiotemporal chaos and extreme events. However, the extensive feature of
these evolutions constitutes a critical limitation for full-size forecasting
processes. Hence, the main challenge for forecasting relevant events is to
establish the set of pertinent information. Here, we identify precursors from
the transfer entropy of the system and a deep Long Short-Term Memory network to
forecast the complex dynamics of a system evolving in a high-dimensional
spatiotemporal chaotic regime. Performances of this triggerable model-free
prediction protocol based on the information flowing map are tested from
experimental data originating from a passive resonator operating in such a
complex nonlinear regime. We have been able to predict the occurrence of
extreme events up to 9 round trips after the detection of precursor, i.e., 3
times the horizon provided by Lyapunov exponents, with 92 % of true positive
predictions leading to 60 % of accuracy.
