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

2026-03-14

AI Summary

This study addresses the state-dependent predictability of extreme events in turbulence, for which no method previously existed to quantify the prediction horizon of individual events without relying on governing equations or ensemble perturbations. Leveraging direct numerical simulation data of two-dimensional Kolmogorov flow, we develop an autoregressive conditional diffusion model and introduce a CRPS-based skill score to define event-level predictability horizons. Our purely data-driven approach reveals, for the first time, that the persistence of large-scale coherent structures governs the predictability of extreme vorticity events. Specifically, a quadrupolar vortex packet organized around a strong strain core consistently precedes extreme events, with its lifetime clearly distinguishing between long- and short-horizon predictions. This work establishes a novel observational pathway to diagnose predictability limits, delineating a hierarchy of predictability across 1–4 Lyapunov timescales.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Web Mining and Content Analysis: Large pretrained models with web data
• Security and Privacy: Large-scale security measurements
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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.

Problem

• extreme-event predictability
• turbulence
• predictability horizon
• coherent structures
• state dependence

Innovation

• extreme-event predictability
• conditional diffusion model
• coherent structures
• turbulence forecasting
• CRPS-based skill score