Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems
Author(s)
Farazmand, Mohammad M; Sapsis, Themistoklis P.
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Drawing upon the bursting mechanism in slow-fast systems, we propose indicators for the prediction of such rare extreme events which do not require a priori known slow and fast coordinates. The indicators are associated with functionals defined in terms of optimally time-dependent (OTD) modes. One such functional has the form of the largest eigenvalue of the symmetric part of the linearized dynamics reduced to these modes. In contrast to other choices of subspaces, the proposed modes are flow invariant and therefore a projection onto them is dynamically meaningful. We illustrate the application of these indicators on three examples: a prototype low-dimensional model, a body-forced turbulent fluid flow, and a unidirectional model of nonlinear water waves. We use Bayesian statistics to quantify the predictive power of the proposed indicators.
Date issued
2016-09Department
Massachusetts Institute of Technology. Department of Mechanical EngineeringJournal
Physical Review E
Publisher
American Physical Society
Citation
Farazmand, Mohammad, and Themistoklis P. Sapsis. “Dynamical Indicators for the Prediction of Bursting Phenomena in High-Dimensional Systems.” Physical Review E 94.3 (2016): n. pag. © 2016 American Physical Society
Version: Final published version
ISSN
2470-0045
2470-0053