Unsupervised probing critical transitions in complex systems using generative diffusion models

This is the authors' abstract. We don't add key points for this paper.

Critical transitions can irreversibly change complex systems, making anticipation a fundamental challenge. Machine learning is increasingly used for early warning, but many approaches require transition labels or control information. Probabilistic time-series forecasting models naturally produce predictive uncertainty by generating future trajectories from observations. Here we show that this uncertainty changes with system dynamics near critical transitions. Across three networked systems, uncertainty patterns depend on model architecture and system dynamics. Among the four models, the diffusion model that explicitly estimates the history-dependent endpoint variance of the forward diffusion process consistently exhibits a localized uncertainty collapse across the tested systems. Controlled analyses link the collapse to reduced diversity among generated futures and to transition mechanisms and dynamical regimes represented in training data. Mediterranean Sea data show similar predictive-uncertainty changes near transitions in empirical systems. Beyond quantifying forecast reliability, predictive uncertainty could therefore be further developed as a label-free complement to existing early-warning approaches for tracking dynamical changes in complex systems.