Machine learning-based identification of precursors of extreme events in chaotic systems

Abstract

Abrupt and rapid high-amplitude changes in a dynamical system’s states known as extreme events appear in many processes occurring in nature, such as drastic climate patterns, rogue waves, or avalanches. These events often entail catastrophic effects, therefore their description and prediction is of great importance. Nevertheless, because of their chaotic nature, their modelling poses a great problem up to this day.

This Master thesis focuses on researching the applicability of a modularity-based clustering technique to identify precursors of rare and extreme events in chaotic systems. A data-driven identification framework based on clustering of system states, probability transition matrices and state space tessellation was developed and tested on six different reduced-order systems. As a final stage, the framework was applied to a two-dimensional model of turbulence (the Kolmogorov flow) which exhibits extreme events in the form of quasi-relaminarisation with extreme dissipation of kinetic energy. The proposed framework provides a way to identify pathways towards extreme events and predict their occurrence from a probabilistic standpoint. The clustering algorithm identifies the precursor states leading to extreme events and allows for a statistical description of the system’s states.