  We consider the motion of interacting particles governed by a coupled system
of ODEs with random initial conditions. Direct computations for such systems
are prohibitively expensive due to a very large number of particles and
randomness requiring many realizations in their locations in the presence of
strong interactions. While there are several approaches that address the above
difficulties, none addresses all three simultaneously. Our goal is to develop
such a computational approach in order to capture the experimentally observed
emergence of correlations in the collective state (patterns due to strong
interactions). Our approach is based on the truncation of the BBGKY hierarchy
that allows one to go beyond the classical Mean Field limit and capture
correlations while drastically reducing the computational complexity. Finally,
we provide an example showing a numerical solution of this nonlinear and
non-local system.
