Early warning indicators via latent stochastic dynamical systems

TL;DR

This paper introduces a novel framework using latent stochastic dynamical systems and anisotropic diffusion maps to detect early warning signals of abrupt transitions in complex systems, validated on EEG data.

Contribution

It develops a new approach combining latent dynamics and diffusion maps to identify early warnings, with three effective indicators derived from low-dimensional manifold representations.

Findings

Indicators successfully detect tipping points in EEG data

Framework bridges latent dynamics with high-dimensional observations

Potential for automatic labeling of complex time series

Abstract

Detecting early warning indicators for abrupt dynamical transitions in complex systems or high-dimensional observation data is essential in many real-world applications, such as brain diseases, natural disasters, and engineering reliability. To this end, we develop a novel approach: the directed anisotropic diffusion map that captures the latent evolutionary dynamics in the low-dimensional manifold. Then three effective warning signals (Onsager-Machlup Indicator, Sample Entropy Indicator, and Transition Probability Indicator) are derived through the latent coordinates and the latent stochastic dynamical systems. To validate our framework, we apply this methodology to authentic electroencephalogram (EEG) data. We find that our early warning indicators are capable of detecting the tipping point during state transition. This framework not only bridges the latent dynamics with real-world data but also shows the potential ability for automatic labeling on complex high-dimensional time series.