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Learning Hamiltonian dynamics with reservoir computing.

Han Zhang1, Huawei Fan1, Liang Wang1

  • 1School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710119, China.

Physical Review. E
|September 16, 2021
PubMed
Summary
This summary is machine-generated.

Reservoir computing (RC) reconstructs complex Hamiltonian dynamics from limited data. This machine learning approach accurately predicts system evolution and maps entire Kolmogorov-Arnold-Moser (KAM) diagrams without prior knowledge of equations.

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Area of Science:

  • Nonlinear dynamics
  • Machine learning
  • Complex systems

Background:

  • Reconstructing Hamiltonian dynamics from time series data is challenging, especially with unknown system Hamiltonians.
  • Understanding Kolmogorov-Arnold-Moser (KAM) diagrams is crucial for characterizing Hamiltonian systems.

Purpose of the Study:

  • To demonstrate reservoir computing (RC) as a method for reconstructing KAM dynamics diagrams from limited time-series data.
  • To show RC can predict system evolution and replicate ergodic properties without prior knowledge of the Hamiltonian.

Main Methods:

  • Utilizing reservoir computing (RC), a machine learning technique, to analyze time-series data from Hamiltonian systems.
  • Employing a parameter-aware RC architecture to reconstruct the KAM diagram by training on data from a limited set of parameters.

Main Results:

  • The trained RC accurately predicts short-term system state evolution and long-term ergodic properties.
  • The parameter-aware RC successfully reconstructs the entire KAM dynamics diagram with high precision.
  • The method's efficacy is validated on the double-pendulum oscillator and the standard map.

Conclusions:

  • Reservoir computing effectively learns Hamiltonian dynamics from data, even without explicit knowledge of the governing equations.
  • RC offers a powerful and efficient approach for reconstructing complex dynamical system diagrams and properties.