  We introduce a framework for generating samples of a distribution given a
finite number of its moments, targeted to particle-based solutions of kinetic
equations and rarefied gas flow simulations. Our model, referred to as the
Wasserstein-Entropy distribution (WE), couples a physically-motivated
Wasserstein penalty term to the traditional maximum-entropy distribution (MED)
functions, which serves to regularize the latter. The penalty term becomes
negligible near the local equilibrium, reducing the proposed model to the MED,
known to reproduce the hydrodynamic limit. However, in contrast to the standard
MED, the proposed WE closure can cover the entire physically realizable moment
space, including the so-called Junk line. We also propose an efficient Monte
Carlo algorithm for generating samples of the unknown distribution which is
expected to outperform traditional non-linear optimization approaches used to
solve the MED problem. Numerical tests demonstrate that, given moments up to
the heat flux -- that is equivalent to the information contained in the
Chapman-Enskog distribution -- the proposed methodology provides a reliable
closure in the collision-dominated and early transition regime. Applications to
larger rarefaction demand information from higher-order moments, which can be
incorporated within the proposed closure.
