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<p>Chaotic time series prediction has widespread applications in fields such as energy, finance, and sea clutter, but the multidimensional chaotic time series therein exhibit more complex nonlinear properties, making it often difficult to balance the ability and efficiency of extracting multidimensional chaotic time series information in previous studies. To balance the two, we propose an improved model based on Single-Layer Perception (SLP) and Multilayer Perceptron (MLP), called Time-mixing Broad Learning System (TBLS). Firstly, the data from phase space reconstruction of multidimensional chaotic time series are mixed. Secondly, the temporal information is extracted by modelling along the direction of each feature time axis using Time-mixing MLP. Finally, due to the complexity and nonlinearity of chaotic time series, a BLS MLP is designed. The BLS MLP consists of a Feature-map MLP and a Feature-enhance MLP. The Feature-map MLP maps the data extracted with temporal information into a high-dimensional space to reveal the nonlinear features. Subsequently, Feature-enhance MLP extracts the feature information in the high dimensional space. TBLS, a lightweight network composed entirely of MLPs, is better at extracting nonlinear information than earlier MLP-based models, which makes it more appropriate for chaotic time series and enhances its predictive performance. Additionally, TBLS shows reduced computational complexity and resource usage compared to earlier hybrid models. This superior performance is further validated by comparative studies against existing models on both simulated datasets (Lorenz and Rossler) and real-world datasets (power consumption). The code for this paper is publicly available at <a href="https://github.com/4Aver/Time-mixing-Broad-Learning-System">https://github.com/4Aver/Time-mixing-Broad-Learning-System</a>.</p>

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Time-mixing broad learning system for predicting multidimensional chaotic time series

  • 期刊论文

  • 发表日期：

    2025年9月15日

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  • Liyun Su,
  • Chunquan Pan,
  • Lang Xiong

摘要

Chaotic time series prediction has widespread applications in fields such as energy, finance, and sea clutter, but the multidimensional chaotic time series therein exhibit more complex nonlinear properties, making it often difficult to balance the ability and efficiency of extracting multidimensional chaotic time series information in previous studies. To balance the two, we propose an improved model based on Single-Layer Perception (SLP) and Multilayer Perceptron (MLP), called Time-mixing Broad Learning System (TBLS). Firstly, the data from phase space reconstruction of multidimensional chaotic time series are mixed. Secondly, the temporal information is extracted by modelling along the direction of each feature time axis using Time-mixing MLP. Finally, due to the complexity and nonlinearity of chaotic time series, a BLS MLP is designed. The BLS MLP consists of a Feature-map MLP and a Feature-enhance MLP. The Feature-map MLP maps the data extracted with temporal information into a high-dimensional space to reveal the nonlinear features. Subsequently, Feature-enhance MLP extracts the feature information in the high dimensional space. TBLS, a lightweight network composed entirely of MLPs, is better at extracting nonlinear information than earlier MLP-based models, which makes it more appropriate for chaotic time series and enhances its predictive performance. Additionally, TBLS shows reduced computational complexity and resource usage compared to earlier hybrid models. This superior performance is further validated by comparative studies against existing models on both simulated datasets (Lorenz and Rossler) and real-world datasets (power consumption). The code for this paper is publicly available at https://github.com/4Aver/Time-mixing-Broad-Learning-System.