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

TL;DR

This paper introduces the extreme variational Autoencoder (xVAE), a neural network model that effectively captures and analyzes extreme events in turbulent flows, outperforming traditional methods like POD in modeling rare, high-energy phenomena.

Contribution

The paper presents xVAE, a novel deep learning framework embedding heavy-tailed distributions into VAE to accurately model and quantify extreme turbulence events in complex flow data.

Findings

xVAE outperforms POD in capturing extreme turbulence events.

xVAE provides a robust uncertainty quantification framework.

xVAE enables risk assessment of rare events through copula analysis.

Abstract

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.