Early warning prediction: Onsager-Machlup vs Schr\"{o}dinger

TL;DR

This paper introduces a new early-warning framework combining manifold learning and stochastic modeling, using Schr"odinger bridge theory to improve prediction sensitivity and robustness for critical transitions like epileptic seizures.

Contribution

It develops a novel Score Function indicator based on Schr"odinger bridge theory, enhancing early-warning detection in high-dimensional complex systems.

Findings

Higher sensitivity and robustness in epilepsy prediction

Enables earlier identification of critical points

Captures dynamic features before and after seizure onset

Abstract

Predicting critical transitions in complex systems, such as epileptic seizures in the brain, represents a major challenge in scientific research. The high-dimensional characteristics and hidden critical signals further complicate early-warning tasks. This study proposes a novel early-warning framework that integrates manifold learning with stochastic dynamical system modeling. Through systematic comparison, six methods including diffusion maps (DM) are selected to construct low-dimensional representations. Based on these, a data-driven stochastic differential equation model is established to robustly estimate the probability evolution scoring function of the system. Building on this, a new Score Function (SF) indicator is defined by incorporating Schr\"{o}dinger bridge theory to quantify the likelihood of significant state transitions in the system. Experiments demonstrate that this indicator exhibits higher sensitivity and robustness in epilepsy prediction, enables earlier identification of critical points, and clearly captures dynamic features across various stages before and after seizure onset. This work provides a systematic theoretical framework and practical methodology for extracting early-warning signals from high-dimensional data.