Characterizing Extreme Events in Dynamical Systems through Sensitivity-Based Modal Decomposition
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Extreme and rare events are common features of many chaotic dynamical systems found in nature, such as earthquakes, solar coronal mass ejections, and rapid fluctuations in turbulent flows. While the events may be rare, they can pose a threat to safe and resilient operations; therefore it is critical to model, forecast, and even mitigate these events if possible. In this work, we utilize the Covariance Balancing Reduction using Adjoint Snapshots (CoBRAS) method to identify a descriptive sets of low-dimensional coordinates for characterizing extreme events that arise from nonlinear differential equations. We demonstrate the utility of these coordinates to characterize extreme events across a diverse set of systems including excitations of networks of coupled FitzHugh-Nagumo oscillators, localized rogue waves from a modified nonlinear Schrödinger equation, and energy dissipation in the 2D Kolmogorov flow. For each example, we exploit insight from the coordinates to develop simple models for forecasting and suppressing extreme events by introducing control.
