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Abrupt and rapid high-amplitude changes in a dynamical system's states knownas extreme event appear in many processes occurring in nature, such as drasticclimate patterns, rogue waves, or avalanches. These events often entailcatastrophic effects, therefore their description and prediction is of greatimportance. However, because of their chaotic nature, their modellingrepresents a great challenge up to this day. The applicability of a data-drivenmodularity-based clustering technique to identify precursors of rare andextreme events in chaotic systems is here explored. The proposed identificationframework based on clustering of system states, probability transition matricesand state space tessellation was developed and tested on two different chaoticsystems that exhibit extreme events: the Moehliss-Faisst-Eckhardt model ofself-sustained turbulence and the 2D Kolmogorov flow. Both exhibit extremeevents in the form of bursts in kinetic energy and dissipation. It is shownthat the proposed framework provides a way to identify pathways towards extremeevents and predict their occurrence from a probabilistic standpoint. Theclustering algorithm correctly identifies the precursor states leading toextreme events and allows for a statistical description of the system's statesand its precursors to extreme events.

Clustering-based Identification of Precursors of Extreme Events in Chaotic Systems