# Capturing Extreme Events in Turbulence using an Extreme Variational Autoencoder (xVAE)

arXiv: https://arxiv.org/abs/2502.04685 · HTML: https://mlsanity.com/paper/2502.04685/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 48 references that are in the map.
- First posted on arXiv 7 Feb 2025.

## Builds on (most cited first, 9 of 9)

- [β-Variational autoencoders and transformers for reduced-order modelling of fluid flows](https://mlsanity.com/paper/2304.03571/) (2023)
- [The Why and How of Nonnegative Matrix Factorization](https://mlsanity.com/paper/1401.5226/) (2014)
- [A Perspective on Machine Learning Methods in Turbulence Modelling](https://mlsanity.com/paper/2010.12226/) (2020)
- [Data-Driven POD-Galerkin Reduced Order Model for Turbulent Flows](https://mlsanity.com/paper/1907.09909/) (2019)
- [Grasping Extreme Aerodynamics on a Low-Dimensional Manifold](https://mlsanity.com/paper/2305.08024/) (2023)
- [Advances in Statistical Modeling of Spatial Extremes](https://mlsanity.com/paper/2007.00774/) (2020)
- [Dynamics of a data-driven low-dimensional model of turbulent minimal Couette flow](https://mlsanity.com/paper/2301.04638/) (2023)
- [A Physics-Informed Vector Quantized Autoencoder for Data Compression of Turbulent Flow](https://mlsanity.com/paper/2201.03617/) (2022)
- [Stochastic dynamical modeling of turbulent flows](https://mlsanity.com/paper/1908.09487/) (2019)

## Built on by (most cited first, 1 of 1)

- [Phase-Type Variational Autoencoders for Heavy-Tailed Data](https://mlsanity.com/paper/2603.01800/) (2026)

## Abstract (arXiv)

Turbulent flow fields are characterized by extreme events that are statistically intermittent and carry a significant amount of energy and physical importance. To emulate these flows, we introduce the extreme variational Autoencoder (xVAE), which embeds a max-infinitely divisible process with heavy-tailed distributions into a standard VAE framework, enabling accurate modeling of extreme events. xVAEs are neural network models that reduce system dimensionality by learning non-linear latent representations of data. We demonstrate the effectiveness of xVAE in large-eddy simulation data of wildland fire plumes, where intense heat release and complex plume-atmosphere interactions generate extreme turbulence. Comparisons with the commonly used Proper Orthogonal Decomposition (POD) modes show that xVAE is more robust in capturing extreme values and provides a powerful uncertainty quantification framework using variational Bayes. Additionally, xVAE enables analysis of the so-called copulas of fields to assess risks associated with rare events while rigorously accounting for uncertainty, such as simultaneous exceedances of high thresholds across multiple locations. The proposed approach provides a new direction for studying realistic turbulent flows, such as high-speed aerodynamics, space propulsion, and atmospheric and oceanic systems that are characterized by extreme events.