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

arXiv: https://arxiv.org/abs/2204.11682 · HTML: https://mlsanity.com/paper/2204.11682/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 70 references that are in the map.
- First posted on arXiv 25 Apr 2022.

## Builds on (most cited first, 6 of 6)

- [Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/1910.05266/) (2019)
- [Echo state networks are universal](https://mlsanity.com/paper/1806.00797/) (2018)
- [Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model](https://mlsanity.com/paper/1803.04779/) (2018)
- [Robust Optimization and Validation of Echo State Networks for learning chaotic dynamics](https://mlsanity.com/paper/2103.03174/) (2021)
- [Echo State Networks trained by Tikhonov least squares are L2(μ) approximators of ergodic dynamical systems](https://mlsanity.com/paper/2005.06967/) (2020)
- [Physics-Informed Echo State Networks](https://mlsanity.com/paper/2011.02280/) (2020)

## Built on by (most cited first, 6 of 6)

- [Optimal training of finitely-sampled quantum reservoir computers for forecasting of chaotic dynamics](https://mlsanity.com/paper/2409.01394/) (2024)
- [Robust quantum reservoir computers for forecasting chaotic dynamics: generalized synchronization and stability](https://mlsanity.com/paper/2506.22335/) (2025)
- [Modelling spatiotemporal turbulent dynamics with the convolutional autoencoder echo state network](https://mlsanity.com/paper/2211.11379/) (2022)
- [On the relationship between Koopman operator approximations and neural ordinary differential equations for data-driven time-evolution predictions](https://mlsanity.com/paper/2411.12940/) (2024)
- [Control-aware echo state networks (Ca-ESN) for the suppression of extreme events](https://mlsanity.com/paper/2308.03095/) (2023)
- [Clustering-based Identification of Precursors of Extreme Events in Chaotic Systems](https://mlsanity.com/paper/2306.16291/) (2023)

## Abstract (arXiv)

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 dataset. The objective is five-fold. First, we exploit ad-hoc metrics from binary classification to analyse (i) how many of the extreme events predicted by the network actually occur in the test set (precision), and (ii) 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 datasets that contain non-converged 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 analyse the robustness of the results for a range of Reynolds numbers. We show that the networks perform well across a wide range of regimes.