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In this paper, we extend a recently introduced multi-fidelity control variatefor the uncertainty quantification of the Boltzmann equation to the case ofkinetic models arising in the study of multiagent systems. For these phenomena,where the effect of uncertainties is particularly evident, several models havebeen developed whose equilibrium states are typically unknown. In particular,we aim to develop efficient numerical methods based on solving the kineticequations in the phase space by Direct Simulation Monte Carlo (DSMC) coupled toa Monte Carlo sampling in the random space. To this end, exploiting theknowledge of the corresponding mean-field approximation we develop novelmean-field Control Variate (MFCV) methods that are able to strongly reduce thevariance of the standard Monte Carlo sampling method in the random space. Weverify these observations with several numerical examples based on classicalmodels , including wealth exchanges and opinion formation model for collectivephenomena.

Mean-field control variate methods for kinetic equations with uncertainties and applications to socio-economic sciences