# Using Machine Learning to predict extreme events in the H'enon map

arXiv: https://arxiv.org/abs/2002.10268 · HTML: https://mlsanity.com/paper/2002.10268/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2020.

## Built on by (most cited first, 5 of 5)

- [Optimized ensemble deep learning framework for scalable forecasting of dynamics containing extreme events](https://mlsanity.com/paper/2106.08968/) (2021)
- [Model-free prediction of emergence of extreme events in a parametrically driven nonlinear dynamical system by Deep Learning](https://mlsanity.com/paper/2107.08819/) (2021)
- [Model-assisted deep learning of rare extreme events from partial observations](https://mlsanity.com/paper/2111.04857/) (2021)
- [Prediction of Occurrence of Extreme Events using Machine Learning](https://mlsanity.com/paper/2110.09304/) (2021)
- [Lorenz System State Stability Identification using Neural Networks](https://mlsanity.com/paper/2106.08489/) (2021)

## Abstract (arXiv)

Machine Learning (ML) inspired algorithms provide a flexible set of tools for analyzing and forecasting chaotic dynamical systems. We here analyze the performance of one algorithm for the prediction of extreme events in the two-dimensional H'enon map at the classical parameters. The task is to determine whether a trajectory will exceed a threshold after a set number of time steps into the future. This task has a geometric interpretation within the dynamics of the H'enon map, which we use to gauge the performance of the neural networks that are used in this work. We analyze the dependence of the success rate of the ML models on the prediction time T , the number of training samples NT and the size of the network Np. We observe that in order to maintain a certain accuracy, NT propto exp(2 h T) and Np propto exp(hT), where h is the topological entropy. Similar relations between the intrinsic chaotic properties of the dynamics and ML parameters might be observable in other systems as well.