Lyapunov exponents estimation via automatic differentiation: A modern approach inspired by machine learning
Marek Balcerzak1, S Leo Kingston1,2,3
1Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland.
Abstract:
Automatic Differentiation (AD) is a powerful technique for computing derivatives of functions defined by code and serves as the workhorse of modern machine learning. In this paper, we leverage AD for the estimation of Lyapunov exponents, a fundamental tool for analyzing the stability and chaotic behavior of dynamical systems. We present example applications of this approach and conduct a comprehensive evaluation of its accuracy and computational efficiency. Our results demonstrate that the AD-based method achieves accuracy comparable to existing techniques while offering superior performance for high-dimensional systems. This advantage is particularly relevant in the study of complex networks and other large-scale dynamical systems.
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