Using Machine Learning to predict extreme events in the Hénon map

Martin Lellep, Jonathan Prexl, Moritz Linkmann, Bruno Eckhardt

Research output: Contribution to journalArticlepeer-review

Abstract

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 Hénon 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 Hénon 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∝exp(2hT) and Np∝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.
Original languageEnglish
Article number013113
Number of pages9
JournalChaos
Volume30
Issue number1
Early online date9 Jan 2020
DOIs
Publication statusPublished - 31 Jan 2020

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