Clustering-based Identification of Precursors of Extreme Events in
  Chaotic Systems
Urszula Golyska Nguyen Anh Khoa Doan
Abrupt and rapid high-amplitude changes in a dynamical system's states known
as extreme event 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. However, because of their chaotic nature, their modelling
represents a great challenge up to this day. The applicability of a data-driven
modularity-based clustering technique to identify precursors of rare and
extreme events in chaotic systems is here explored. The proposed identification
framework based on clustering of system states, probability transition matrices
and state space tessellation was developed and tested on two different chaotic
systems that exhibit extreme events: the Moehliss-Faisst-Eckhardt model of
self-sustained turbulence and the 2D Kolmogorov flow. Both exhibit extreme
events in the form of bursts in kinetic energy and dissipation. It is shown
that the proposed framework provides a way to identify pathways towards extreme
events and predict their occurrence from a probabilistic standpoint. The
clustering algorithm correctly identifies the precursor states leading to
extreme events and allows for a statistical description of the system's states
and its precursors to extreme events.