Dynamics-informed deep learning for predicting extreme events

Predicting extreme events in high-dimensional chaotic dynamical systems remains a fundamental challenge because these events are rare, intermittent and often driven by transient dynamical mechanisms that are difficult to identify from limited observations. We propose a fully data-driven framework for real-time forecasting of extreme events based on an interpretable, mechanism-aware precursor that tracks the transient instabilities preceding event onset. Specifically, we use the finite-time Lyapunov exponent (FTLE) as the precursor, computed directly from state snapshots through a reduced-order, equation-agnostic formulation. By restricting the instability dynamics to an adaptively evolving subspace spanned by optimal time-dependent (OTD) modes, the method substantially reduces the computational cost of classical FTLE evaluation while retaining the dominant transiently amplifying directions. The resulting FTLE sequence serves as input to a transformer-based model that forecasts the system observable at future lead times, enabling long-lead prediction of extreme events. We demonstrate the framework on Kolmogorov flow, a canonical model of intermittent turbulence. The results show that explicitly encoding transient instability mechanisms substantially extends extreme-event prediction horizons compared to baseline observable-based approaches.