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Equivalence of machine learning models in modeling chaos

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  • Chen, Xiaolu
  • Weng, Tongfeng
  • Li, Chunzi
  • Yang, Huijie

Abstract

Recent advances have demonstrated that machine learning models are effective methods for predicting chaotic systems. Although short-term chaos prediction can be successfully realized by seemingly different machine learning models, an intriguing question of their correlation is still unknown. Here, we focus on three commonly used machine learning models that are reservoir computing, long-short term memory networks, and deep belief networks, respectively. We find that these selected models present almost identical long-term statistical properties as that of a learned chaotic system. Specifically, we show that these machine learning models have the same correlation dimension and recurrence time. Furthermore, by sharing a common signal, we realize synchronization, cascading synchronization, and coupled synchronization among machine learning models. Our findings reveal the equivalence of machine learning models in characterizing and modeling chaotic systems.

Suggested Citation

  • Chen, Xiaolu & Weng, Tongfeng & Li, Chunzi & Yang, Huijie, 2022. "Equivalence of machine learning models in modeling chaos," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p2:s0960077922010104
    DOI: 10.1016/j.chaos.2022.112831
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    References listed on IDEAS

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    1. Chen, Xiaolu & Weng, Tongfeng & Gu, Changgui & Yang, Huijie, 2019. "Synchronizing hyperchaotic subsystems with a single variable: A reservoir computing approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    2. Chen, Xiaolu & Weng, Tongfeng & Li, Chunzi & Yang, Huijie, 2022. "Synchronization of reservoir computing models via a nonlinear controller," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    3. Hu, Wancheng & Zhang, Yibin & Ma, Rencai & Dai, Qionglin & Yang, Junzhong, 2022. "Synchronization between two linearly coupled reservoir computers," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    4. 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).
    5. Weng, Tongfeng & Song, Jia & Yang, Huijie & Gu, Changgui & Zhang, Jie & Small, Michael, 2020. "Synchronization of reservoir computers with applications to communications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    6. Uribarri, Gonzalo & Mindlin, Gabriel B., 2022. "Dynamical time series embeddings in recurrent neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    7. Fischer, Thomas & Krauss, Christopher, 2018. "Deep learning with long short-term memory networks for financial market predictions," European Journal of Operational Research, Elsevier, vol. 270(2), pages 654-669.
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    Citations

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    Cited by:

    1. Ke, Shaowei & Zhao, Chen, 2024. "From local utility to neural networks," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    2. Chen, Xiaolu & Weng, Tongfeng & Yang, Huijie, 2023. "Synchronization of spatiotemporal chaos and reservoir computing via scalar signals," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Weng, Tongfeng & Chen, Xiaolu & Ren, Zhuoming & Yang, Huijie & Zhang, Jie & Small, Michael, 2023. "Synchronization of multiple mobile reservoir computing oscillators in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    4. Naudé, Wim, 2023. "Artificial Intelligence and the Economics of Decision-Making," IZA Discussion Papers 16000, Institute of Labor Economics (IZA).

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