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国际不确定性的量化期刊

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ISSN 打印: 2152-5080

ISSN 在线: 2152-5099

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MEAN-FIELD CONTROL VARIATE METHODS FOR KINETIC EQUATIONS WITH UNCERTAINTIES AND APPLICATIONS TO SOCIOECONOMIC SCIENCES

卷 12, 册 1, 2022, pp. 61-84
DOI: 10.1615/Int.J.UncertaintyQuantification.2021037960
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摘要

In this paper, we extend a recently introduced multi-fidelity control variate for the uncertainty quantification of the Boltzmann equation to the case of kinetic models arising in the study of multiagent systems. For these phenomena, where the effect of uncertainties is particularly evident, several models have been developed whose equilibrium states are typically unknown. In particular, we aim to develop efficient numerical methods based on solving the kinetic equations in the phase space by direct simulation Monte Carlo coupled to a Monte Carlo sampling in the random space. To this end, by exploiting the knowledge of the corresponding mean-field approximation we develop novel mean-field control variate methods that are able to strongly reduce the variance of the standard Monte Carlo sampling method in the random space. We verify these observations with several numerical examples based on classical models, including wealth exchanges and the opinion formation model for collective phenomena.

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对本文的引用
  1. Liu Liu, Pareschi Lorenzo, Zhu Xueyu, A bi-fidelity stochastic collocation method for transport equations with diffusive scaling and multi-dimensional random inputs, Journal of Computational Physics, 462, 2022. Crossref

  2. Medaglia Andrea, Tosin Andrea, Zanella Mattia, Monte Carlo stochastic Galerkin methods for non-Maxwellian kinetic models of multiagent systems with uncertainties, Partial Differential Equations and Applications, 3, 4, 2022. Crossref

  3. Franceschi J., Pareschi L., Zanella M., From agent-based models to the macroscopic description of fake-news spread: the role of competence in data-driven applications, Partial Differential Equations and Applications, 3, 6, 2022. Crossref

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