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Area of Science:

  • Dynamical Systems and Chaos Theory
  • Computational Mathematics
  • Machine Learning

Background:

  • Automatic Differentiation (AD) is crucial for modern machine learning, enabling efficient derivative computation.
  • Lyapunov exponents are fundamental metrics for assessing the stability and chaotic nature of dynamical systems.
  • Existing methods for Lyapunov exponent estimation can be computationally intensive, especially for high-dimensional systems.

Purpose of the Study:

  • To apply Automatic Differentiation (AD) for estimating Lyapunov exponents.
  • To evaluate the accuracy and computational efficiency of an AD-based approach for Lyapunov exponent estimation.
  • To demonstrate the utility of AD in analyzing complex and large-scale dynamical systems.

Main Methods:

  • Leveraging Automatic Differentiation (AD) to compute the necessary derivatives for Lyapunov exponent calculation.
  • Developing and implementing an AD-based algorithm for Lyapunov exponent estimation.
  • Conducting comprehensive numerical experiments to assess performance.

Main Results:

  • The AD-based method achieves accuracy comparable to established techniques.
  • The proposed approach demonstrates superior computational efficiency, particularly for high-dimensional systems.
  • Successful application examples in analyzing complex networks and large-scale dynamical systems were presented.

Conclusions:

  • Automatic Differentiation provides an effective and efficient tool for Lyapunov exponent estimation.
  • The AD-based method offers a significant advantage for studying high-dimensional and complex dynamical systems.
  • This approach enhances the analysis of system stability and chaotic behavior in various scientific domains.