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 (DSMC) coupled to a Monte Carlo sampling in the random space. To this end, exploiting the knowledge of the corresponding mean-field approximation we develop novel mean-field Control Variate (MFCV) 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 opinion formation model for collective phenomena.

翻译：在本文中,我们将最近引入的多种纤维控制变异,用于对Boltzmann等式的不确定性进行量化,将其扩大到多试剂系统研究中产生的动能模型。对于这些特别明显具有不确定性影响的现象,已经开发了几种平衡状态通常未知的模型。特别是,我们的目标是开发高效的数字方法,通过直接模拟蒙特卡洛(DSMC)和随机空间的蒙特卡洛(Monte Carlo)取样来解决阶段空间的动能方程。为此,我们利用对相应的平均近似值的知识,开发了新型的中位控制Variate(MFCV)方法,这些方法能够显著减少随机空间标准蒙特卡洛取样方法的差异。我们用一些基于传统模型的数字模型,包括财富交流和集体现象形成观点模型来核实这些观测结果。