Data-driven sequential analysis of tipping in high-dimensional complex systems

Detecting tipping points in the Earth system is a significant challenge, particularly given the high dimensionality, observational sparsity and noisiness in real climatological data. Even in the most classical Bifurcation-induced tipping(B-tipping) with quasi-static forcing, conventional Early Warning Signals based on Critical Slowing Down often struggle with these complexities and can yield false positives in non-tipping scenarios. To address these limitations, we propose a tipping analysis indicator:  High-dimensional Attractor’s Structural Complexity (HASC).

From reconstructed high-dimensional states from partial observations, we extract geometrical structures of trajectories using manifold learning method based graph approximation (Uniform Manifold Approximation and Projection) but without dimension reduction. We quantify the time-evolution of the system's structural complexity using the spectral property of the graph Laplacian, Von Neumann Entropy.

We show that HASC serves as a warning indicator of structural degeneracy of trajectory on 3box AMOC tipping model in B-tipping setting, and analyze further applications against N-and R-tipping. We also demonstrate its application to a realistic CESM AMOC collapse simulation (+10,000 dimensions). This approach offers a training-free, multivariate, and geometry-aware tool for monitoring regime shifts in complex systems.