SAE${}^2$F: State-Aware Extreme Event Forecasting for Multivariate Time Series

Extreme values are often treated as isolated tail observations, although the dynamics leading to an extreme event may change substantially before the event occurs. However, existing extreme-event forecasting methods mainly rely on rare-sample modeling and tail-supervision optimization, making it difficult to characterize system state transitions and evolving inter-variable dependency structures before extreme events occur. To address this issue, we propose SAE${}^2$F, a state-aware enhanced framework for extreme-event forecasting. The framework combines local stochastic-dynamics modeling with critical slowing down theory to detect precursor states before extreme values appear, and injects the resulting risk-state information into subsequent forecasting. Furthermore, a Lyapunov consistency constraint converts the second-order statistical reference of local stochastic dynamics into a differentiable training constraint, while a unified risk-state variable $\alpha$ is used to regulate dependency structures and match similar extreme-event patterns, thereby enabling state-conditioned forecasting. Experiments show that SAE${}^2$F consistently improves extreme-event F1 and extreme-point MAE while maintaining competitive overall forecasting performance. The code is available at https://anonymous.4open.science/status/SAEEF-2026.