Machine learning prediction of critical transition and system collapse

Hua-Wei Fan,Ling-Wei Kong,Celso Grebogi,Ying-Cheng Lai

doi:10.1103/physrevresearch.3.013090

Abstract

ACKNOWLEDGMENTS We would like to acknowledge support from the Vannevar Bush Faculty Fellowship program sponsored by the Basic Research Office of the Assistant Secretary of Defense for Research and Engineering and funded by the Office of Naval Research through Grant No. N00014-16-1-2828.

Highlights

In nonlinear and complex dynamical systems, a catastrophic collapse is often preceded by transient chaos
We develop a machine learning framework based on reservoir computing to predict critical transition and transient chaos in nonlinear dynamical systems
For a number of representative target systems described by nonlinear ordinary or partial differential equations, a reservoir machine so trained is able to predict the dynamics at all the training parameter points accurately for about four or five Lyapunov times, and can predict the critical point and transient chaos reliably and accurately

Summary

INTRODUCTION

In nonlinear and complex dynamical systems, a catastrophic collapse is often preceded by transient chaos. We develop a machine learning framework based on reservoir computing to predict critical transition and transient chaos in nonlinear dynamical systems. We demonstrate that our proposed machine learning framework can accomplish the two goals with three examples: a three-species food chain model [2] in ecology in which a catastrophic transition leads to transient chaos and species extinction, an electrical power system susceptible to voltage collapse through transient chaos [1], and the Kuramoto-Sivashinsky system [33,34] in the regime of transient spatiotemporal chaos [35]. We show that, training a reservoir network of reasonable size, e.g., 1000 nodes, with time-series data taken from three parameter values in the normal chaotic regime, the machine is able to predict the collapse point and transient chaos for parameter values beyond the critical point. Can the machine predict that the system does exhibit a critical transition, it is capable of revealing some basic physics about the system, i.e., the nature of transient chaos as characterized by the lifetime distribution

RESERVOIR COMPUTING WITH AN ADDITIONAL

Chaotic food chain system

Power system model

One-dimensional Kuramoto-Sivashinsky system

An alternative machine learning approach

DISCUSSION