Mechanisms and Pathways of Extreme Events in Partially-Observed Stochastic Dynamical Systems

Extreme events occur across the natural, engineering, and socioeconomic sciences, where rare but high-impact episodes can lead to disproportionate consequences that pose major challenges for prediction and risk management. Existing studies have mainly focused on the statistics, sampling, forecasting, and attribution of extremes from observable variables. In this paper, we develop a mathematical framework for studying the mechanisms and pathways of extreme events in partially-observed stochastic dynamical systems with hidden variables. By integrating data assimilation with information-theoretic and trajectory-based diagnostics, we infer latent precursor dynamics from observations, quantify their uncertainty, and determine how their influence propagates toward observed extreme events. Conditional Gaussian models provide a tractable analytical setting for deriving closed-form diagnostics, while the framework extends through numerical methods. The analysis proceeds from two complementary perspectives. From a trajectory-wise viewpoint, we compare filtering and smoothing distributions to identify the onset of hidden precursors and quantify temporal influence. From a statistical viewpoint, we construct event-conditioned hidden-state distributions to identify sensitive triggering directions, latent pathways, and multiple classes of extreme-event mechanisms through clustering. Three numerical examples illustrate the methodology. In an intermittent stochastic model, hidden damping dynamics emerge before observed bursts, where discrepancies between the filter and smoother provide an onset diagnostic. In a stochastic model with damping and forcing, separate damping-induced, forcing-driven, and mixed pathways to extremes are identified. In a nonlinear topographic-flow model, distinct mechanisms and pathways for blocking and unblocking patterns associated with observed extreme events are revealed.