Regensburg 2022 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 8: Data Analytics for Complex Systems (joint session DY/SOE)

DY 8.1: Vortrag

Montag, 5. September 2022, 15:00–15:15, H18

Estimating covariant Lyapunov vectors from data — •Nahal Sharafi, Christoph Martin und Sarah Hallerberg — Hamburg University of Applied Sciences, Hamburg, Germany

Covariant Lyapunov vectors characterize the directions along which perturbations in dynamical systems grow. They have also been studied as predictors of critical transitions and extreme events. For many applications, it is necessary to estimate these vectors from data since model equations are unknown for many interesting phenomena. We propose a novel approach for estimating covariant Lyapunov vectors based on data records without knowing the underlying equations of the system. In contrast to previous approaches, our approach can be applied to high-dimensional datasets. We demonstrate that this purely data-driven approach can accurately estimate covariant Lyapunpov vectors from data records generated by low and high-dimensional dynamical systems. Additionally we test for the robustness against noise in a low-dimensional dynamical system.