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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 vanilla VAE and the commonly used Proper Orthogonal Decomposition (POD) modes show that xVAE is more robust in capturing extreme values and enables simulation-based uncertainty quantification using variational Bayes. Additionally, xVAE facilitates 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.<\/jats:p>","DOI":"10.1007\/s00521-026-12112-0","type":"journal-article","created":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T03:31:40Z","timestamp":1779852700000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Capturing extreme events in turbulence using an extreme variational autoencoder (xVAE)"],"prefix":"10.1007","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5458-4556","authenticated-orcid":false,"given":"Likun","family":"Zhang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kiran","family":"Bhaganagar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christopher K.","family":"Wikle","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,27]]},"reference":[{"key":"12112_CR1","doi-asserted-by":"crossref","unstructured":"Kolmogorov AN (1991) The local structure of turbulence in incompressible viscous fluid for very large reynolds numbers. 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The authors confirm that all work was conducted in accordance with relevant standards and guidelines, and that the study design and execution did not involve any activities requiring institutional review board oversight. We are committed to fostering an inclusive and equitable research environment, and all authors strived to ensure that research practices were fair, transparent, and considerate of diverse perspectives throughout the study.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Inclusion & Ethics"}},{"value":"All custom code and algorithms used in this study are freely available at the GitHub repository\n                      \n                      under the MIT license. Detailed instructions for downloading, installing, and running the code are provided in the repository\u2019s README file.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Code availability"}}],"article-number":"428"}}