  We investigate a hybrid PDE/Monte Carlo technique for the variance reduced
simulation of an agent-based multiscale model for tumor growth. The variance
reduction is achieved by combining a simulation of the stochastic agent-based
model on the microscopic scale with a deterministic solution of a simplified
(coarse) partial differential equation (PDE) on the macroscopic scale as a
control variable. We show that this technique is able to significantly reduce
the variance with only the (limited) additional computational cost associated
with the deterministic solution of the coarse PDE. We illustrate the
performance with numerical experiments in different regimes, both in the
avascular and vascular stage of tumor growth.
