Unsupervised Learning for Anticipating Critical Transitions

Anticipating critical transitions in complex dynamical systems is often hindered by the need for explicit knowledge of the bifurcation parameter. We present a fully data-driven framework that combines a variational autoencoder with reservoir computing to overcome this limitation. The variational autoencoder autonomously extracts latent driving factors from time-series data in an unsupervised manner, providing effective control parameters for the reservoir computer to forecast imminent transitions. This approach eliminates dependence on prior parameter knowledge and enables direct prediction from raw observations. By linking inferred latent variables to the system's dynamical evolution, the framework establishes a general paradigm for identifying and predicting critical transitions in nonlinear systems. Its effectiveness is demonstrated on benchmark examples, including the spatiotemporal Kuramoto-Sivashinsky system, and the method naturally extends to systems influenced by multiple parameters or with incomplete state information.