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Bayesian framework for simulation of dynamical systems from multidimensional data using recurrent neural network.

Aleksei Seleznev1, Dmitry Mukhin1, Andrey Gavrilov1

  • 1Institute of Applied Physics of the Russian Academy of Science, 46 Ul'yanov Street, 603950 Nizhny Novgorod, Russia.

Chaos (Woodbury, N.Y.)
|January 3, 2020
PubMed
Summary
This summary is machine-generated.

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This study introduces a novel recurrent neural network method for creating data-driven dynamical models from time series. The approach effectively reconstructs low-dimensional dynamics and evolution operators, successfully modeling atmospheric low-frequency variability.

Area of Science:

  • Dynamical systems theory
  • Machine learning
  • Atmospheric science

Background:

  • Dynamical models are crucial for understanding complex systems.
  • Extracting meaningful dynamics from noisy, high-dimensional time series data remains a challenge.
  • Existing methods often struggle with joint reconstruction of embeddings and evolution operators.

Purpose of the Study:

  • To propose a novel data-driven method for building dynamical models from multidimensional time series.
  • To develop a recurrent neural network architecture capable of joint embedding and evolution operator reconstruction.
  • To validate the method on both synthetic and real-world atmospheric data.

Main Methods:

  • Utilizing a specifically structured recurrent neural network for joint reconstruction.

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  • Employing Bayesian optimization for model structure and data-generating law hypothesis.
  • Constructing a cost function for model learning based on Bayesian optimization.
  • Testing the method on noisy, low-dimensional dynamical systems and a high-dimensional atmospheric model.

    • Main Results:

    • Successfully reconstructed low-dimensional dynamical components and evolution operators from noisy data.
    • Developed a data-driven model for the low-frequency variability (LFV) of Earth's midlatitude atmosphere using a quasigeostrophic model.
    • Demonstrated accurate reproduction of key atmospheric LFV regimes in simulations.

    Conclusions:

    • The proposed recurrent neural network method offers a robust approach for data-driven dynamical modeling.
    • The technique effectively handles noisy, high-dimensional data, including complex atmospheric systems.
    • This method advances the ability to model and understand complex dynamical phenomena from observational data.