@inbook{beda93fc70c14b23aa1e9109218e5ab9,
title = "An Introduction to Uncertainty Quantification for Kinetic Equations and Related Problems",
abstract = "We overview some recent results in the field of uncertainty quantification for kinetic equations and related problems with random inputs. Uncertainties may be due to various reasons, such as lack of knowledge on the microscopic interaction details or incomplete information at the boundaries or on the initial data. These uncertainties contribute to the curse of dimensionality and the development of efficient numerical methods is a challenge. After a brief introduction on the main numerical techniques for uncertainty quantification in partial differential equations, we focus our survey on some of the recent progress on multi-fidelity methods and stochastic Galerkin methods for kinetic equations.",
keywords = "Boltzmann equation, Euler equations, Kinetic models, Multi-fidelity methods, Stochastic Galerkin methods, Uncertainty quantification",
author = "Lorenzo Pareschi",
note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",
year = "2021",
month = feb,
day = "15",
doi = "10.1007/978-3-030-67104-4\_5",
language = "English",
isbn = "978-3-030-67103-7",
series = "SEMA SIMAI Springer Series",
publisher = "Springer",
pages = "141--181",
editor = "Giacomo Albi and Sara Merino-Aceituno and Alessia Nota and Mattia Zanella",
booktitle = "Trails in Kinetic Theory",
}