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.

介绍了控制感知回声状态网络（Ca-ESN），用于无缝结合 ESNs 和控制策略，如比例积分微分控制和模型预测控制，以抑制极端事件，并在混沌湍流流动中展示了这一方法，相对于传统方法将极端事件的发生率降低了两个数量级，为用神经网络有效控制非线性系统开辟了新的可能性。