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Predicting chaotic time series by means of reservoir computing

Räth, Christoph and Aumeier, Jonas and herteux, Joschka and Haluszczynski, Alexander (2020) Predicting chaotic time series by means of reservoir computing. 45th conference of the middle european cooperation in statistical physics, 2020-09-14 - 2020-09-16, Online conference.

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It has been demonstrated that in the realm of complex systems not only exact predic-tions of multivariate time series with large time horizons become possible but also the longterm behavior of the underlying dynamical system (its climate) can well be reproducedusing machine learning techniques. This is achieved by using reservoir computing (RC), which represents a special kind ofrecurrent neural networks (RNN). The core of the model is a network called reservoir,which is a complex network with loops. Input data are fed into the nodes of the reservoir,which are connected according to a predefined network topology (mostly random net-works). Only the weights of the linear output layer transforming the reservoir response tooutput variables are subject to optimization via linear regression. This makes the learningextremely fast and omits the vanishing gradient problem of other RNNs.Here, we investigate the question of statistical stability of short and long term predictionsand find that the ability to exactly forecast the correct trajectory as well as the reconstruc-tion of the long-term climate measured by the correlation dimension and largest Lyapunovexponent strongly varies among different realizations of the same reservoir setup [1]. Thus,special care must be taken in selecting the good predictions.To improve upon the statistical robustness of the prediction results we tested differentnetwork topologies, namely (random) Erd ̈os Renyi, small world and scale free networksfor the reservoir. While the small world reservoir showed slightly better results for theLorenz system than a random network, the scale-free network performed worse, where thedifference to the other two network types is much pronounced for the Roessler system [1]. In-depth studies reveal that the nodes which contribute most to the output signal are notthose, which have most connections in the network. Thus scale-free networks with somehighly connected nodes do not represent the suitable topology for this kind of predictiontask. Furthermore, we demonstrate that a controlled node removal and a suitable chosenweighting function significantly increase the prediction performance - even with a muchsmaller reservoir [2]. Studying and interpreting these results in detail will give new insights about the essentialrequirements for the emergence of complex behavior in nonlinear dynamical systems. [1] A. Haluszczynski & C. Räth, Chaos 29, 103143 (2019) [2] A. Haluszczynski, J. Aumeier, J. Herteux & C. Räth, Chaos 30, 063136 (2020)

Item URL in elib:https://elib.dlr.de/136165/
Document Type:Conference or Workshop Item (Speech)
Title:Predicting chaotic time series by means of reservoir computing
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Haluszczynski, AlexanderLMU MünchenUNSPECIFIEDUNSPECIFIED
Refereed publication:No
Open Access:No
Gold Open Access:No
In ISI Web of Science:No
Keywords:komplexe System, künstliche Intelligenz, Reservoir Computing, Zeitserienanalyse, Vorhersage
Event Title:45th conference of the middle european cooperation in statistical physics
Event Location:Online conference
Event Type:international Conference
Event Start Date:14 September 2020
Event End Date:16 September 2020
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 - Research under Space Conditions
DLR - Research theme (Project):R - Komplexe Plasmen / Data analysis (old)
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Materials Physics in Space > Research Group Complex Plasma
Deposited By: Räth, Christoph
Deposited On:02 Oct 2020 09:18
Last Modified:24 Apr 2024 20:38

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