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Optimizing Markovian modeling of chaotic systems with recurrent neural networks

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  • Cechin, Adelmo L.
  • Pechmann, Denise R.
  • de Oliveira, Luiz P.L.

Abstract

In this paper, we propose a methodology for optimizing the modeling of an one-dimensional chaotic time series with a Markov Chain. The model is extracted from a recurrent neural network trained for the attractor reconstructed from the data set. Each state of the obtained Markov Chain is a region of the reconstructed state space where the dynamics is approximated by a specific piecewise linear map, obtained from the network. The Markov Chain represents the dynamics of the time series in its statistical essence. An application to a time series resulted from Lorenz system is included.

Suggested Citation

  • Cechin, Adelmo L. & Pechmann, Denise R. & de Oliveira, Luiz P.L., 2008. "Optimizing Markovian modeling of chaotic systems with recurrent neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1317-1327.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:5:p:1317-1327
    DOI: 10.1016/j.chaos.2006.10.018
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    Cited by:

    1. Mirzaee, Hossein, 2009. "Linear combination rule in genetic algorithm for optimization of finite impulse response neural network to predict natural chaotic time series," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2681-2689.
    2. Mirzaee, Hossein, 2009. "Long-term prediction of chaotic time series with multi-step prediction horizons by a neural network with Levenberg–Marquardt learning algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1975-1979.
    3. Sangiorgio, Matteo & Dercole, Fabio, 2020. "Robustness of LSTM neural networks for multi-step forecasting of chaotic time series," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Cheng, Wei & Wang, Yan & Peng, Zheng & Ren, Xiaodong & Shuai, Yubei & Zang, Shengyin & Liu, Hao & Cheng, Hao & Wu, Jiagui, 2021. "High-efficiency chaotic time series prediction based on time convolution neural network," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. Sangiorgio, Matteo & Dercole, Fabio & Guariso, Giorgio, 2021. "Forecasting of noisy chaotic systems with deep neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).

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