Source-linked AI summary
Predicting catastrophes in nonlinear dynamical systems by compressive sensing
Wen-Xu Wang, Rui Yang, Ying-Cheng Lai, Vassilios Kovanis, Celso Grebogi
TL;DR
The paper addresses predicting catastrophes when nonlinear-system equations are unknown and only time series are available. It reconstructs the system with series expansions and compressive sensing, demonstrating accurate prediction in chaotic examples, including robustness to noise and short data records.
Problem
Predicting catastrophes is difficult when nonlinear-system equations are unknown, while accurately inferring such equations from time series remains largely unsolved.
Method
The method expands vector fields or maps in a suitable basis and estimates their coefficients from time-series measurements using compressive sensing.
Results
The predicted Hénon, Lorenz, and Rössler systems reproduce the relevant dynamics, while accurate coefficient prediction requires fewer measurements than candidate terms when the system is sparse.
Takeaways & Limitations
The approach can estimate many terms from short time series, supporting real-time catastrophe prediction through bifurcation analysis of the reconstructed system.
Takeaways & Limitations
The method may not work for high-dimensional or stochastic systems, where Bayesian inference is suggested as a possible alternative.
Abstract
from arXiv · showhide
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.