Early warning prediction: Onsager-Machlup vs Schr\"{o}dinger
🤖 AI Summary
This study addresses the challenge of early warning for critical transitions in high-dimensional complex systems—such as epileptic seizures—where high dimensionality and concealed critical signals hinder detection. The authors propose a novel framework that integrates manifold learning with stochastic dynamical modeling: diffusion maps are employed to construct a low-dimensional embedding, upon which a data-driven stochastic differential equation model is built. Innovatively, Schrödinger bridge theory is introduced in conjunction with Onsager–Machlup path probabilities to formulate a new Score Function that quantifies transition likelihood between states. This work represents the first application of Schrödinger bridge theory to early-warning systems, significantly enhancing sensitivity and robustness to critical points in seizure prediction and enabling earlier, more reliable identification of multi-stage dynamic features.
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
early warning prediction
critical transitions
high-dimensional data
epileptic seizures
stochastic dynamical systems
Innovation
Methods, ideas, or system contributions that make the work stand out.
early warning prediction
manifold learning
stochastic differential equation
Schrödinger bridge
Score Function
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