Data-driven early warning of Gaussian white noise-induced critical transitions

Many complex systems are frequently subject to the influence of uncertain disturbances, which can exert a profound effect on the critical transitions (CTs), potentially resulting in catastrophic consequences. Consequently, it is of uttermost importance to provide warnings for noise-induced CTs in various applications. Although capturing certain generic symptoms of transition behaviors from observational and simulated data poses a challenging problem, this work attempts to extract information regarding CTs from simulated data of a Gaussian white noise-induced tri-stable system. Using the extended dynamic mode decomposition (EDMD) algorithm, we initially obtain finite-dimensional approximations of both the stochastic Koopman operator and the generator. Subsequently, the drift parameters and the noise intensity within the system are identified from the simulated data. Utilizing the identified system, the parameter-dependent basin of the unsafe regime (PDBUR) is quantified, enabling data-driven early warning of Gaussian white noise-induced CTs. Finally, an error analysis is carried out to verify the effectiveness of the data-driven results. Our findings may serve as a paradigm for understanding and predicting noise-induced CTs in complex systems based on data.