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Open AccessArticle

On the Potential of Time Delay Neural Networks to Detect Indirect Coupling between Time Series

by Riccardo Rossi 1,*,†, Andrea Murari 2,† and Pasquale Gaudio 1
1
Department of Industrial Engineering, University of Rome “Tor Vergata”, via del Politecnico 1, 00100 Roma, Italy
2
Consorzio RFX (CNR, ENEA, INFN, Universita di Padova, Acciaierie Venete SpA), Corso Stati Uniti 4, 35127 Padova, Italy
*
Author to whom correspondence should be addressed.
These authors contributed equally to the work.
Entropy 2020, 22(5), 584; https://doi.org/10.3390/e22050584
Received: 17 April 2020 / Revised: 8 May 2020 / Accepted: 19 May 2020 / Published: 21 May 2020
Determining the coupling between systems remains a topic of active research in the field of complex science. Identifying the proper causal influences in time series can already be very challenging in the trivariate case, particularly when the interactions are non-linear. In this paper, the coupling between three Lorenz systems is investigated with the help of specifically designed artificial neural networks, called time delay neural networks (TDNNs). TDNNs can learn from their previous inputs and are therefore well suited to extract the causal relationship between time series. The performances of the TDNNs tested have always been very positive, showing an excellent capability to identify the correct causal relationships in absence of significant noise. The first tests on the time localization of the mutual influences and the effects of Gaussian noise have also provided very encouraging results. Even if further assessments are necessary, the networks of the proposed architecture have the potential to be a good complement to the other techniques available in the market for the investigation of mutual influences between time series. View Full-Text
Keywords: time series; indirect coupling; time delay neural networks; Lorenz system time series; indirect coupling; time delay neural networks; Lorenz system
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Rossi, R.; Murari, A.; Gaudio, P. On the Potential of Time Delay Neural Networks to Detect Indirect Coupling between Time Series. Entropy 2020, 22, 584.

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