Early warning prediction: Onsager-Machlup vs Schrödinger
This work addresses the problem of early seizure prediction for medical applications, representing an incremental improvement with a novel hybrid method.
The study tackled the challenge of predicting critical transitions like epileptic seizures in complex systems by proposing a novel early-warning framework that integrates manifold learning with stochastic dynamical system modeling, resulting in a new Score Function indicator that shows higher sensitivity and robustness, enabling earlier identification of critical points in epilepsy prediction.
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 Schrödinger 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.