  We propose Echo State Networks (ESNs) to predict the statistics of extreme
events in a turbulent flow. We train the ESNs on small datasets that lack
information about the extreme events. We asses whether the networks are able to
extrapolate from the small imperfect datasets and predict the heavy-tail
statistics that describe the events. We find that the networks correctly
predict the events and improve the statistics of the system with respect to the
training data in almost all cases analysed. This opens up new possibilities for
the statistical prediction of extreme events in turbulence.
