Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems

TL;DR

This paper introduces flow-invariant dynamical indicators based on OTD modes for predicting rare bursting events in high-dimensional systems without prior coordinate knowledge, validated across models and fluid flows.

Contribution

It proposes novel indicators derived from OTD modes that are flow invariant and effective for early prediction of bursting phenomena in complex systems.

Findings

Indicators successfully predict bursting events in diverse systems

Bayesian analysis confirms high predictive power

Applicable to low-dimensional models and high-dimensional fluid flows

Abstract

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.