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A data-driven framework for learning hybrid dynamical systems.

Yang Li1, Shengyuan Xu1, Jinqiao Duan2

  • 1School of Automation, Nanjing University of Science and Technology, 200 Xiaolingwei Street, Nanjing 210094, China.

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Summary
This summary is machine-generated.

This study introduces a new data-driven method to uncover hybrid dynamical systems from time series data without needing prior system knowledge. The framework effectively learns governing laws for complex systems, offering broad applicability.

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Area of Science:

  • Dynamical Systems Theory
  • Machine Learning
  • Data Science

Background:

  • Existing data-driven methods for hybrid dynamical systems often require prior knowledge of model structures.
  • Parameter identification is typically limited to pre-defined functions or prescribed forms.

Purpose of the Study:

  • To develop a novel data-driven framework for discovering hybrid dynamical systems directly from time series data.
  • To eliminate the need for prior knowledge about the system's underlying structure or functions.

Main Methods:

  • A dual-loop algorithm is employed to isolate data belonging to individual subsystems.
  • Residual networks are iteratively trained to approximate subsystem dynamics.
  • A fully connected neural network estimates the transition rules between subsystems.

Main Results:

  • The proposed method successfully identifies hybrid dynamical systems across various dimensions and structures.
  • Demonstrated effectiveness and accuracy on several prototypical examples.
  • The framework learns the evolutionary governing laws from data.

Conclusions:

  • This novel framework provides an effective tool for learning hybrid dynamical systems without prior knowledge.
  • The method shows wide applicability for analyzing complex systems from available datasets.