Predicting catastrophes in nonlinear dynamical systems by compressive sensing

TL;DR

This paper introduces a method to predict catastrophes in nonlinear dynamical systems by using compressive sensing to estimate system equations from time series data, even when the system is unknown.

Contribution

The novel approach combines function series expansion with compressive sensing to forecast system failures without prior knowledge of the system equations.

Findings

Successfully predicts catastrophes in chaotic systems

Accurately estimates system equations from limited data

Applicable to systems with unknown dynamics

Abstract

An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the system equations are completely unknown and only time series reflecting the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field or map of the underlying system into a suitable function series and then to use the compressive-sensing technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic systems are provided to demonstrate our idea.