When no explicit equations are known on the macroscopic level, the equation-free framework offers a methodology to compute the macroscopic system dynamics using only a description on the microscopic level. Short bursts of the
microscopic simulation code are combined with appropriate lifting (initialization) and restriction (averaging) operators to cross the boundaries between micro- and macroscopic scale. The resulting time integrator defines the
so-called coarse time stepper and enables the microscopic code to perform system-level tasks.
In this work we use Molecular Dynamics as the microscopic simulator and investigate the difficulties that can arise when using this type of microscopic description. An important issue is the appropriate initialization of the
microscopic simulator in order to obtain the correct coarse dynamics. We will define good lifting and restriction operators, based on kernel density estimation, which are suited for use in the equation-free framework. We present a model problem where we aim at calculating a coarse steady state of a time evolving probability density function, and use it as an illustration for the proposed operators.