Lyapunov Exponent

Lyapunov exponents quantify the rate of separation of infinitesimally close trajectories in dynamical systems, providing a measure of system stability and predictability. Current research focuses on leveraging Lyapunov exponents within machine learning frameworks, such as recurrent neural networks, reservoir computing, and physics-informed neural networks, to analyze and model complex systems, including chaotic phenomena and high-dimensional datasets. This work has implications for diverse fields, improving model accuracy in areas like weather forecasting and enabling the development of more robust control systems for autonomous agents by identifying and mitigating instability.