Self-supervised reservoir computing with spatial-temporal encoding for identifying critical transitions

Anticipating critical transitions and identifying bifurcation types in complex systems remains a major challenge due to high dimensionality and limited labeled data. In this study, we propose spatial-to-temporal auto reservoir computing, a self-supervised approach of reservoir computing designed to detect early warning signals of critical transitions and identify the corresponding bifurcation types, including transcritical, period-doubling, and Neimark-Sacker bifurcations. Grounded on Takens’ embedding theorem, it performs spatial-to-temporal information transformation via a reservoir structure, by encoding high-dimensional spatial data into the temporal dynamics of a single representative variable. This ultralow one-dimensional representation is obtained in a self-supervised and analytical manner, making it particularly suited for critical transition analyses in time-varying, high-dimensional systems. In addition, based on the Poincaré recurrence principle, the proposed method captures the structural information of the local phase space by constructing a spatial neighborhood network centered at each input state to enhance the robustness. The proposed method is validated on synthetic models and real-world datasets across multiple domains including paleoclimate, ecology and physiology, consistently achieving high accuracy and robustness under varying noise levels and parameter choices. Anticipating critical transitions is essential across diverse fields. Here, the authors propose a method, which enables early warning of critical transitions and identification of bifurcation types by converting high-dimensional spatial information into one-dimensional temporal dynamics.