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Self-supervised reservoir computing with spatial-temporal encoding for identifying critical transitions
Na Yang1, Jürgen Kurths2,3, Rui Liu4
1School of Mathematics, South China University of Technology, Guangzhou, China.
Nature Communications
|June 1, 2026
Summary
This study introduces spatial-to-temporal auto reservoir computing to detect early warning signals of critical transitions in complex systems. The novel self-supervised method accurately identifies bifurcation types and enhances robustness in high-dimensional data.
Area of Science:
- Complex Systems Science
- Dynamical Systems Theory
- Machine Learning for Scientific Discovery
Background:
- Detecting critical transitions and bifurcation types in high-dimensional complex systems is challenging due to limited data.
- Existing methods struggle with the dimensionality and data scarcity inherent in analyzing systems like climate, ecology, and physiology.
- Early warning signals are crucial for predicting abrupt shifts in system behavior.
Purpose of the Study:
- To propose a novel self-supervised method, spatial-to-temporal auto reservoir computing, for early warning signal detection.
- To identify specific bifurcation types (transcritical, period-doubling, Neimark-Sacker) preceding critical transitions.
- To provide a robust analytical tool for time-varying, high-dimensional systems.
Main Methods:
- Employs Takens' embedding theorem for spatial-to-temporal data transformation using a reservoir structure.
- Encodes high-dimensional spatial data into a single, ultralow one-dimensional temporal variable via self-supervision.
- Utilizes the Poincaré recurrence principle and spatial neighborhood networks to capture phase space structure and enhance robustness.
Main Results:
- The proposed method successfully detects early warning signals and identifies bifurcation types with high accuracy.
- Demonstrates consistent performance across synthetic models and real-world datasets in paleoclimate, ecology, and physiology.
- Exhibits robustness against varying noise levels and parameter choices.
Conclusions:
- Spatial-to-temporal auto reservoir computing offers a powerful, self-supervised approach for analyzing critical transitions in complex systems.
- The method's ability to reduce dimensionality while preserving crucial dynamic information makes it highly applicable.
- Validated across diverse scientific domains, this technique holds significant potential for predictive modeling and system understanding.
