Source-linked AI summary
Machine learning prediction of critical transition and system collapse
Ling-Wei Kong, Hua-Wei Fan, Celso Grebogi, Ying-Cheng Lai
TL;DR
The paper addresses model-free prediction of parameter-driven critical transitions and collapse when only time series are available, including the difficulty of recognizing long transients. It adds the bifurcation parameter as an input to a reservoir computer trained in the normal chaotic regime. The resulting machine predicts critical values and transient-collapse behavior, including average transient lifetimes.
Problem
Model-free prediction is needed for critical transitions and collapse from measured time series when equations are unknown, and long transients can resemble sustained chaos.
Source: p. 1Method
A reservoir computer receives the bifurcation parameter through an added input channel and is trained on time series from a few safe-regime parameter values.
Source: pp. 1–2Results
The method predicts critical parameter values and transient-chaos statistics, including collapse and average transient lifetime in the electrical-power and food-chain examples.
Source: pp. 3–5Takeaways & Limitations
The framework can forecast transition and transient-collapse statistics without training on post-critical system behavior.
Source: pp. 2, 5Prediction error increases when training parameter values lie farther from the critical transition point, consistent with a low-order approximation near training points.
Source: pp. 4–5
Abstract
from arXiv · showhide
To predict a critical transition due to parameter drift without relying on model is an outstanding problem in nonlinear dynamics and applied fields. A closely related problem is to predict whether the system is already in or if the system will be in a transient state preceding its collapse. We develop a model free, machine learning based solution to both problems by exploiting reservoir computing to incorporate a parameter input channel. We demonstrate that, when the machine is trained in the normal functioning regime with a chaotic attractor (i.e., before the critical transition), the transition point can be predicted accurately. Remarkably, for a parameter drift through the critical point, the machine with the input parameter channel is able to predict not only that the system will be in a transient state, but also the average transient time before the final collapse.