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Multilayer Perceptron Network Optimization for Chaotic Time Series Modeling

Chaotic time series are widely present in practice, but due to their characteristics—such as internal randomness, nonlinearity, and long-term unpredictability—it is difficult to achieve high-precision intermediate or long-term predictions. Multi-layer perceptron (MLP) networks are an effective tool...

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Detalles Bibliográficos
Autores principales: Qiao, Mu, Liang, Yanchun, Tavares, Adriano, Shi, Xiaohu
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10378385/
https://www.ncbi.nlm.nih.gov/pubmed/37509920
http://dx.doi.org/10.3390/e25070973
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author Qiao, Mu
Liang, Yanchun
Tavares, Adriano
Shi, Xiaohu
author_facet Qiao, Mu
Liang, Yanchun
Tavares, Adriano
Shi, Xiaohu
author_sort Qiao, Mu
collection PubMed
description Chaotic time series are widely present in practice, but due to their characteristics—such as internal randomness, nonlinearity, and long-term unpredictability—it is difficult to achieve high-precision intermediate or long-term predictions. Multi-layer perceptron (MLP) networks are an effective tool for chaotic time series modeling. Focusing on chaotic time series modeling, this paper presents a generalized degree of freedom approximation method of MLP. We then obtain its Akachi information criterion, which is designed as the loss function for training, hence developing an overall framework for chaotic time series analysis, including phase space reconstruction, model training, and model selection. To verify the effectiveness of the proposed method, it is applied to two artificial chaotic time series and two real-world chaotic time series. The numerical results show that the proposed optimized method is effective to obtain the best model from a group of candidates. Moreover, the optimized models perform very well in multi-step prediction tasks.
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spelling pubmed-103783852023-07-29 Multilayer Perceptron Network Optimization for Chaotic Time Series Modeling Qiao, Mu Liang, Yanchun Tavares, Adriano Shi, Xiaohu Entropy (Basel) Article Chaotic time series are widely present in practice, but due to their characteristics—such as internal randomness, nonlinearity, and long-term unpredictability—it is difficult to achieve high-precision intermediate or long-term predictions. Multi-layer perceptron (MLP) networks are an effective tool for chaotic time series modeling. Focusing on chaotic time series modeling, this paper presents a generalized degree of freedom approximation method of MLP. We then obtain its Akachi information criterion, which is designed as the loss function for training, hence developing an overall framework for chaotic time series analysis, including phase space reconstruction, model training, and model selection. To verify the effectiveness of the proposed method, it is applied to two artificial chaotic time series and two real-world chaotic time series. The numerical results show that the proposed optimized method is effective to obtain the best model from a group of candidates. Moreover, the optimized models perform very well in multi-step prediction tasks. MDPI 2023-06-24 /pmc/articles/PMC10378385/ /pubmed/37509920 http://dx.doi.org/10.3390/e25070973 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Qiao, Mu
Liang, Yanchun
Tavares, Adriano
Shi, Xiaohu
Multilayer Perceptron Network Optimization for Chaotic Time Series Modeling
title Multilayer Perceptron Network Optimization for Chaotic Time Series Modeling
title_full Multilayer Perceptron Network Optimization for Chaotic Time Series Modeling
title_fullStr Multilayer Perceptron Network Optimization for Chaotic Time Series Modeling
title_full_unstemmed Multilayer Perceptron Network Optimization for Chaotic Time Series Modeling
title_short Multilayer Perceptron Network Optimization for Chaotic Time Series Modeling
title_sort multilayer perceptron network optimization for chaotic time series modeling
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10378385/
https://www.ncbi.nlm.nih.gov/pubmed/37509920
http://dx.doi.org/10.3390/e25070973
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