Control-aware echo state networks (Ca-ESN) for the suppression of
  extreme events
Alberto Racca Luca Magri
Extreme event are sudden large-amplitude changes in the state or observables
of chaotic nonlinear systems, which characterize many scientific phenomena.
Because of their violent nature, extreme events typically have adverse
consequences, which call for methods to prevent the events from happening. In
this work, we introduce the control-aware echo state network (Ca-ESN) to
seamlessly combine ESNs and control strategies, such as
proportional-integral-derivative and model predictive control, to suppress
extreme events. The methodology is showcased on a chaotic-turbulent flow, in
which we reduce the occurrence of extreme events with respect to traditional
methods by two orders of magnitude. This works opens up new possibilities for
the efficient control of nonlinear systems with neural networks.