  An important class of multi-scale flow scenarios deals with an interplay
between kinetic and continuum phenomena. While hybrid solvers provide a natural
way to cope with these settings, two issues restrict their performance.
Foremost, the inverse problem implied by estimating distributions has to be
addressed, to provide boundary conditions for the kinetic solver. The next
issue comes from defining a robust yet accurate switching criterion between the
two solvers. This study introduces a data-driven kinetic-continuum coupling,
where the Maximum-Entropy-Distribution (MED) is employed to parametrize
distributions arising from continuum field variables. Two regression
methodologies of Gaussian-Processes (GPs) and Artificial-Neural-Networks (ANNs)
are utilized to predict MEDs efficiently. Hence the MED estimates are employed
to carry out the coupling, besides providing a switching criterion. To achieve
the latter, a continuum breakdown parameter is defined by means of the Fisher
information distance computed from the MED estimates. We test the performance
of our devised MED estimators by recovering bi-modal densities. Next, MED
estimates are integrated into a hybrid kinetic-continuum solution algorithm.
Here Direct Simulation Monte-Carlo (DSMC) and Smoothed-Particle Hydrodynamics
(SPH) are chosen as kinetic and continuum solvers, respectively. The problem of
monatomic gas inside Sod's shock tube is investigated, where DSMC-SPH coupling
is realized by applying the devised MED estimates. Very good agreements with
respect to benchmark solutions along with a promising speed-up are observed in
our reported test cases.
