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Learning noise-induced transitions by multi-scaling reservoir computing

Author

Listed:
  • Zequn Lin

    (University of Electronic Science and Technology of China
    Beijing Normal University
    Westlake University
    Westlake University)

  • Zhaofan Lu

    (Beijing Normal University)

  • Zengru Di

    (Beijing Normal University)

  • Ying Tang

    (University of Electronic Science and Technology of China
    Beijing Normal University
    University of Electronic Science and Technology of China)

Abstract

Noise is usually regarded as adversarial to extracting effective dynamics from time series, such that conventional approaches usually aim at learning dynamics by mitigating the noisy effect. However, noise can have a functional role in driving transitions between stable states underlying many stochastic dynamics. We find that leveraging a machine learning model, reservoir computing, can learn noise-induced transitions. We propose a concise training protocol with a focus on a pivotal hyperparameter controlling the time scale. The approach is widely applicable, including a bistable system with white noise or colored noise, where it generates accurate statistics of transition time for white noise and specific transition time for colored noise. Instead, the conventional approaches such as SINDy and the recurrent neural network do not faithfully capture stochastic transitions even for the case of white noise. The present approach is also aware of asymmetry of the bistable potential, rotational dynamics caused by non-detailed balance, and transitions in multi-stable systems. For the experimental data of protein folding, it learns statistics of transition time between folded states, enabling us to characterize transition dynamics from a small dataset. The results portend the exploration of extending the prevailing approaches in learning dynamics from noisy time series.

Suggested Citation

  • Zequn Lin & Zhaofan Lu & Zengru Di & Ying Tang, 2024. "Learning noise-induced transitions by multi-scaling reservoir computing," Nature Communications, Nature, vol. 15(1), pages 1-10, December.
  • Handle: RePEc:nat:natcom:v:15:y:2024:i:1:d:10.1038_s41467-024-50905-w
    DOI: 10.1038/s41467-024-50905-w
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    References listed on IDEAS

    as
    1. Ying Tang & Jing Liu & Jiang Zhang & Pan Zhang, 2024. "Learning nonequilibrium statistical mechanics and dynamical phase transitions," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    2. Bethany Lusch & J. Nathan Kutz & Steven L. Brunton, 2018. "Deep learning for universal linear embeddings of nonlinear dynamics," Nature Communications, Nature, vol. 9(1), pages 1-10, December.
    3. Daniel J. Gauthier & Erik Bollt & Aaron Griffith & Wendson A. S. Barbosa, 2021. "Next generation reservoir computing," Nature Communications, Nature, vol. 12(1), pages 1-8, December.
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