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Deciphering complexity: machine learning insights into the chaos

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  • Lazare Osmanov

    (Free University of Tbilisi)

Abstract

We introduce new machine learning techniques for analyzing chaotic dynamical systems. The main goal of this study is to develop a simple method for calculating the Lyapunov exponent using only two trajectory data points, in contrast to traditional methods that require averaging procedures. Additionally, we explore phase transition graphs to analyze the shift from regular periodic to chaotic dynamics, focusing on identifying “almost integrable” trajectories where conserved quantities deviate from whole numbers. Furthermore, we identify “integrable regions” within chaotic trajectories. These methods are tested on two dynamical systems: “two objects moving on a rod” and the “Henon–Heiles” system. Graphic abstract

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  • Lazare Osmanov, 2025. "Deciphering complexity: machine learning insights into the chaos," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 98(1), pages 1-10, January.
    • Handle: RePEc:spr:eurphb:v:98:y:2025:i:1:d:10.1140_epjb_s10051-024-00840-y
    DOI: 10.1140/epjb/s10051-024-00840-y
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    References listed on IDEAS

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    1. Yashar D. Hezaveh & Laurence Perreault Levasseur & Philip J. Marshall, 2017. "Fast automated analysis of strong gravitational lenses with convolutional neural networks," Nature, Nature, vol. 548(7669), pages 555-557, August.
    2. Gaspard, Pierre, 1997. "Chaos and hydrodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 240(1), pages 54-67.
    3. Long-Gang Pang & Kai Zhou & Nan Su & Hannah Petersen & Horst Stöcker & Xin-Nian Wang, 2018. "An equation-of-state-meter of quantum chromodynamics transition from deep learning," Nature Communications, Nature, vol. 9(1), pages 1-6, December.
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