Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multi-fidelity methods for uncertainty propagation in kinetic equations   The construction of efficient methods for uncertainty quantification in
kinetic equations represents a challenge due to the high dimensionality of the
models: often the computational costs involved become prohibitive. On the other
hand, precisely because of the curse of dimensionality, the construction of
simplified models capable of providing approximate solutions at a
computationally reduced cost has always represented one of the main research
strands in the field of kinetic equations. Approximations based on suitable
closures of the moment equations or on simplified collisional models have been
studied by many authors. In the context of uncertainty quantification, it is
therefore natural to take advantage of such models in a multi-fidelity setting
where the original kinetic equation represents the high-fidelity model, and the
simplified models define the low-fidelity surrogate models. The scope of this
article is to survey some recent results about multi-fidelity methods for
kinetic equations that are able to accelerate the solution of the uncertainty
quantification process by combining high-fidelity and low-fidelity model
evaluations with particular attention to the case of compressible and
incompressible hydrodynamic limits. We will focus essentially on two classes of
strategies: multi-fidelity control variates methods and bi-fidelity stochastic
collocation methods. The various approaches considered are analyzed in light of
the different surrogate models used and the different numerical techniques
adopted. Given the relevance of the specific choice of the surrogate model, an
application-oriented approach has been chosen in the presentation.

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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th