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

Abstract

Abrupt transitions ("tipping") in nonlinear dynamical systems are often accompanied by changes in the geometry of the attracting set, but quantifying such changes from partial and noisy observations in high-dimensional systems remains challenging. We address this problem with a sequential diagnostic framework, Data Assimilation-High dimensional Attractor's Structural Complexity (DA-HASC). First, this method reconstructs system's high-dimensional state using data assimilation from limited and noisy observations. Second, we quantify a structural complexity of the high-dimensional system dynamics from the reconstructed state by manifold learning. Third, we capture underlying changes in the system by splitting the reconstructed timeseries into sliding windows and analyzing the changes in the temporally local attractor's structural complexity. The structural information is provided as graph Laplacian and measured by Von Neumann entropy in this framework. We evaluate DA-HASC on both synthetic and real-world datasets and demonstrate that it can detect tipping under high-dimensionality and imperfect system knowledge. We further discuss how this framework behaves across different tipping mechanisms.