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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/7/973 |
| _version_ | 1797589369050103808 |
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| author | Mu Qiao Yanchun Liang Adriano Tavares Xiaohu Shi |
| author_facet | Mu Qiao Yanchun Liang Adriano Tavares Xiaohu Shi |
| author_sort | Mu Qiao |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-11T01:06:43Z |
| format | Article |
| id | doaj.art-5d9e63c5ca0d4d90b2aff9bc76f4d37d |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T01:06:43Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-5d9e63c5ca0d4d90b2aff9bc76f4d37d2023-11-18T19:12:48ZengMDPI AGEntropy1099-43002023-06-0125797310.3390/e25070973Multilayer Perceptron Network Optimization for Chaotic Time Series ModelingMu Qiao0Yanchun Liang1Adriano Tavares2Xiaohu Shi3School of Mathematics, Jilin University, Changchun 130021, ChinaKey Laboratory of Symbol Computation and Knowledge Engineering of the Ministry of Education, College of Computer Science and Technology, Jilin University, 2699 Qianjin Street, Changchun 130012, ChinaDepartment of Industrial Electronics, School of Engineering, University of Minho, 4800-058 Guimares, PortugalKey Laboratory of Symbol Computation and Knowledge Engineering of the Ministry of Education, College of Computer Science and Technology, Jilin University, 2699 Qianjin Street, Changchun 130012, ChinaChaotic 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.https://www.mdpi.com/1099-4300/25/7/973chaotic time seriesmultilayer perceptron networkgeneralized degrees of freedomAkaike information criterionmaximal Lyapunov exponent |
| spellingShingle | Mu Qiao Yanchun Liang Adriano Tavares Xiaohu Shi Multilayer Perceptron Network Optimization for Chaotic Time Series Modeling Entropy chaotic time series multilayer perceptron network generalized degrees of freedom Akaike information criterion maximal Lyapunov exponent |
| 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 | chaotic time series multilayer perceptron network generalized degrees of freedom Akaike information criterion maximal Lyapunov exponent |
| url | https://www.mdpi.com/1099-4300/25/7/973 |
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