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

arXiv: https://arxiv.org/abs/2603.13789 · HTML: https://mlsanity.com/paper/2603.13789/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 45 references that are in the map.
- First posted on arXiv 14 Mar 2026.

## Builds on (most cited first, 8 of 8)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation](https://mlsanity.com/paper/2309.01745/) (2023)
- [Stochastic Latent Transformer: Efficient Modelling of Stochastically Forced Zonal Jets](https://mlsanity.com/paper/2310.16741/) (2023)
- [Dynamical errors in machine learning forecasts](https://mlsanity.com/paper/2504.11074/) (2025)
- [Spatio-temporal Dynamical Indices for Complex Systems](https://mlsanity.com/paper/2412.10069/) (2024)
- [XAI4Extremes: An interpretable machine learning framework for understanding extreme-weather precursors under climate change](https://mlsanity.com/paper/2503.08163/) (2025)

## Built on by (most cited first, 2 of 2)

- [Dynamics-Aware Weighting for Deep Learning Forecasts of Chaotic Systems](https://mlsanity.com/paper/2608.22277/) (2026)
- [Noise-Induced Predictability Redistribution Across Forecast Horizons of Extreme Events in Chaotic Dynamics](https://mlsanity.com/paper/2609.27877/) (2026)

## Abstract (arXiv)

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 ≈ 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.