  This paper deals with the Monte-Carlo methods for evaluating expectations of
functionals of solutions to McKean-Vlasov Stochastic Differential Equations
(MV-SDE) with drifts of super-linear growth. We assume that the MV-SDE is
approximated in the standard manner by means of an interacting particle system
and propose two importance sampling (IS) techniques to reduce the variance of
the resulting Monte Carlo estimator. In the \emph{complete measure change}
approach, the IS measure change is applied simultaneously in the coefficients
and in the expectation to be evaluated. In the \emph{decoupling} approach we
first estimate the law of the solution in a first set of simulations without
measure change and then perform a second set of simulations under the
importance sampling measure using the approximate solution law computed in the
first step.
  For both approaches, we use large deviations techniques to identify an
optimisation problem for the candidate measure change. The decoupling approach
yields a far simpler optimisation problem than the complete measure change,
however, we can reduce the complexity of the complete measure change through
some symmetry arguments. We implement both algorithms for two examples coming
from the Kuramoto model from statistical physics and show that the variance of
the importance sampling schemes is up to 3 orders of magnitude smaller than
that of the standard Monte Carlo. The computational cost is approximately the
same as for standard Monte Carlo for the complete measure change and only
increases by a factor of 2--3 for the decoupled approach. We also estimate the
propagation of chaos error and find that this is dominated by the statistical
error by one order of magnitude.
