Data-driven prediction and control of extreme events in a chaotic flow

An extreme event is a sudden and violent change in the state of a nonlinear system. In fluid dynamics, extreme events can have adverse effects on the system's optimal design and operability, which calls for accurate methods for their prediction and control. In this paper, we propose a data-driven methodology for the prediction and control of extreme events in a chaotic shear flow. The approach is based on echo state networks, which are a type of reservoir computing that learn temporal correlations within a time-dependent data set. The objective is fivefold. First, we exploit ad hoc metrics from binary classification to analyze (1) how many of the extreme events predicted by the network actually occur in the test set (precision) and (2) how many extreme events are missed by the network (recall). We apply a principled strategy for optimal hyperparameter selection, which is key to the networks' performance. Second, we focus on the time-accurate prediction of extreme events. We show that echo state networks are able to predict extreme events well beyond the predictability time, i.e., up to more than five Lyapunov times. Third, we focus on the long-term prediction of extreme events from a statistical point of view. By training the networks with data sets that contain nonconverged statistics, we show that the networks are able to learn and extrapolate the flow's long-term statistics. In other words, the networks are able to extrapolate in time from relatively short time series. Fourth, we design a simple and effective control strategy to prevent extreme events from occurring. The control strategy decreases the occurrence of extreme events up to one order of magnitude with respect to the uncontrolled system. Finally, we analyze the robustness of the results for a range of Reynolds numbers. We show that the networks perform well across a wide range of regimes. This work opens up new possibilities for the data-driven prediction and control of extreme events in chaotic systems.