Hierarchy of extreme-event predictability in turbulence revealed by machine learning
This work addresses the challenge of quantifying predictability for turbulence extremes, which is important for fields like weather forecasting and fluid dynamics, though it is incremental as it applies existing machine learning methods to a specific domain.
The researchers tackled the problem of predicting extreme events in turbulence by training an autoregressive conditional diffusion model on simulations and using a skill score to quantify event-wise predictability horizons, finding that enstrophy extremes have forecast skill ranging from about 1 to over 4 Lyapunov times, controlled by large-scale structures.
Extreme-event predictability in turbulence is strongly state dependent, yet event-by-event predictability horizons are difficult to quantify without access to governing equations or costly perturbation ensembles. Here we train an autoregressive conditional diffusion model on direct numerical simulations of the two-dimensional Kolmogorov flow and use a CRPS-based skill score to define an event-wise predictability horizon. Enstrophy extremes exhibit a pronounced hierarchy: forecast skill persists from $\approx 1$ to $> 4$ Lyapunov times across events. Spectral filtering shows that these horizons are controlled predominantly by large-scale structures. Extremes are preceded by intense strain cores organizing quadrupolar vortex packets, whose lifetime sharply separates long- from short-horizon events. These results identify coherent-structure persistence as a governing mechanism for the predictability of turbulence extremes and provide a data-driven route to diagnose predictability limits from observations.