Hierarchy of extreme-event predictability in turbulence revealed by machine learning

TL;DR

This study uses machine learning to analyze the predictability of extreme events in turbulence, revealing a hierarchy of predictability horizons linked to large-scale structures and coherent structures.

Contribution

It introduces a data-driven approach with an autoregressive diffusion model to quantify event-wise predictability horizons in turbulence.

Findings

Extreme events have predictability horizons from about 1 to over 4 Lyapunov times.

Large-scale structures predominantly control the predictability horizons.

Persistent coherent structures like vortex packets influence long- and short-term predictability.

Abstract

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.