Using machine learning to predict extreme events in the Hénon map

Martin Lellep; Jonathan Prexl; Moritz Linkmann; Bruno Eckhardt

doi:10.1063/1.5121844

Using machine learning to predict extreme events in the Hénon map

Chaos. 2020 Jan;30(1):013113. doi: 10.1063/1.5121844.

Authors

Martin Lellep¹, Jonathan Prexl², Moritz Linkmann¹, Bruno Eckhardt¹

Affiliations

¹ Physics Department, Philipps-University of Marburg, D-35032 Marburg, Germany.
² Department of Civil, Geo and Environmental Engineering, Technical University of Munich, D-80333 Munich, Germany.

PMID: 32013508
DOI: 10.1063/1.5121844

Abstract

Machine Learning (ML) inspired algorithms provide a flexible set of tools for analyzing and forecasting chaotic dynamical systems. We analyze here 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 N_T, and the size of the network N_p. We observe that in order to maintain a certain accuracy, N_T∝exp⁡(2hT) and N_p∝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.