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Dynamical time series embeddings in recurrent neural networks

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  • Uribarri, Gonzalo
  • Mindlin, Gabriel B.

Abstract

Time series forecasting has historically been a key research problem in science and engineering. In recent years, machine learning algorithms have proven to be a very successful data-driven approach in this area. In particular, Recurrent Neural Networks (RNNs) represent the state-of-the-art algorithms in many sequential tasks. In this paper we train Long Short Term Memory networks (LSTM), which are a type of RNNs, to make predictions in time series corresponding to the observation of a single variable of a chaotic system. We show that, under certain conditions, networks learn to generate an embedding of the data in their inner sate that is topologically equivalent to the original strange attractor. Remarkably, this resembles standard forecasting methods from nonlinear science in which the time series is embedded in a multi-valued space using Takens's delay embedding mechanism.

Suggested Citation

  • Uribarri, Gonzalo & Mindlin, Gabriel B., 2022. "Dynamical time series embeddings in recurrent neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    • Handle: RePEc:eee:chsofr:v:154:y:2022:i:c:s0960077921009668
    DOI: 10.1016/j.chaos.2021.111612
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    References listed on IDEAS

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    1. 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).
    2. Omer Berat Sezer & Mehmet Ugur Gudelek & Ahmet Murat Ozbayoglu, 2019. "Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019," Papers 1911.13288, arXiv.org.
    3. David S. Stoffer & Hernando Ombao, 2012. "Editorial: Special issue on time series analysis in the biological sciences," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(5), pages 701-703, September.
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    Cited by:

    1. Zhang, Hai & Chen, Xinbin & Ye, Renyu & Stamova, Ivanka & Cao, Jinde, 2023. "Adaptive quasi-synchronization analysis for Caputo delayed Cohen–Grossberg neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 49-65.
    2. Fainstein, Facundo & Catoni, Josefina & Elemans, Coen P.H. & Mindlin, Gabriel B., 2023. "The reconstruction of flows from spatiotemporal data by autoencoders," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    3. Sun, Ying & Zhang, Luying & Yao, Minghui, 2023. "Chaotic time series prediction of nonlinear systems based on various neural network models," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    4. Chen, Xiaolu & Weng, Tongfeng & Li, Chunzi & Yang, Huijie, 2022. "Equivalence of machine learning models in modeling chaos," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).

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