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Good and bad predictions: Assessing and improving the replication of chaotic attractors by means of reservoir computing

Haluszczynski, Alexander and Räth, Christoph (2019) Good and bad predictions: Assessing and improving the replication of chaotic attractors by means of reservoir computing. Chaos, 29, p. 103143. American Institute of Physics (AIP). DOI: 10.1063/1.5118725 ISSN 1054-1500

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Official URL: https://aip.scitation.org/doi/10.1063/1.5118725

Abstract

The prediction of complex nonlinear dynamical systems with the help of machine learning techniques has become increasingly popular. In particular, reservoir computing turned out to be a very promising approach especially for the reproduction of the long-term properties of a nonlinear system. Yet, a thorough statistical analysis of the forecast results is missing. Using the Lorenz and Rössler system, we statistically analyze the quality of prediction for different parametrizations - both the exact short-term prediction as well as the reproduction of the longterm properties (the climate) of the system as estimated by the correlation dimension and largest Lyapunov exponent. We find that both short- and long-term predictions vary significantly among the realizations. Thus, special care must be taken in selecting the good predictions as realizations, which deliver better short-term prediction also tend to better resemble the long-term climate of the system. Instead of only using purely random Erdös-Renyi networks, we also investigate the benefit of alternative network topologies such as small world or scalefree networks and show which effect they have on the prediction quality. Our results suggest that the overall performance with respect to the reproduction of the climate of both the Lorenz and Rössler system is worst for scale-free networks. For the Lorenz system, there seems to be a slight benefit of using small world networks, while for the Rössler system, small world and Erdös-Renyi networks performed equivalently well. In general, the observation is that reservoir computing works for all network topologies investigated here.

Item URL in elib:https://elib.dlr.de/129947/
Document Type:Article
Title:Good and bad predictions: Assessing and improving the replication of chaotic attractors by means of reservoir computing
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Haluszczynski, AlexanderLMUUNSPECIFIED
Räth, ChristophChristoph.Raeth (at) dlr.deUNSPECIFIED
Date:25 October 2019
Journal or Publication Title:Chaos
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:29
DOI :10.1063/1.5118725
Page Range:p. 103143
Publisher:American Institute of Physics (AIP)
ISSN:1054-1500
Status:Published
Keywords:Machine Learning, Complex Systems, Prediction, Reservoir Computing, Networks, Attractors
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Research under Space Conditions
DLR - Research area:Raumfahrt
DLR - Program:R FR - Forschung unter Weltraumbedingungen
DLR - Research theme (Project):R - Komplexe Plasmen / Data analysis
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Materials Physics in Space > Research Group Complex Plasma
Deposited By: Räth, Christoph
Deposited On:04 Nov 2019 09:19
Last Modified:04 Nov 2019 09:19

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