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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.<\/jats:p>","DOI":"10.3390\/e25070973","type":"journal-article","created":{"date-parts":[[2023,6,26]],"date-time":"2023-06-26T05:39:13Z","timestamp":1687757953000},"page":"973","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Multilayer Perceptron Network Optimization for Chaotic Time Series Modeling"],"prefix":"10.3390","volume":"25","author":[{"given":"Mu","family":"Qiao","sequence":"first","affiliation":[{"name":"School of Mathematics, Jilin University, Changchun 130021, China"},{"name":"Department of Industrial Electronics, School of Engineering, University of Minho, 4800-058 Guimares, Portugal"}]},{"given":"Yanchun","family":"Liang","sequence":"additional","affiliation":[{"name":"Key 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, China"},{"name":"School of Computer Science, Zhuhai College of Science and Technology, Zhuhai 519041, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8316-6927","authenticated-orcid":false,"given":"Adriano","family":"Tavares","sequence":"additional","affiliation":[{"name":"Department of Industrial Electronics, School of Engineering, University of Minho, 4800-058 Guimares, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5115-8137","authenticated-orcid":false,"given":"Xiaohu","family":"Shi","sequence":"additional","affiliation":[{"name":"Key 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, China"},{"name":"School of Computer Science, Zhuhai College of Science and Technology, Zhuhai 519041, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2340056","DOI":"10.1142\/S0218348X2340056X","article-title":"Chaotic behavior of financial dynamical system with generalized fractional operator","volume":"31","author":"Alzaid","year":"2023","journal-title":"Fractals"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Yao, Q., Jahanshahi, H., Batrancea, L.M., Alotaibi, N.D., and Rus, M.-I. 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