  Anisotropic patchy particles have become an archetypical statistical model
system for associating fluids. Here we formulate an approach to the
Kern-Frenkel model via classical density functional theory to describe the
positionally and orientationally resolved equilibrium density distributions in
flat wall geometries. The density functional is split into a reference part for
the orientationally averaged density and an orientational part in mean-field
approximation. To bring the orientational part into a kernel form suitable for
machine learning techniques, an expansion into orientational invariants and the
proper incorporation of single-particle symmetries is formulated. The
mean-field kernel is constructed via machine learning on the basis of hard wall
simulation data. Results are compared to the well-known random-phase
approximation which strongly underestimates the orientational correlations
close to the wall. Successes and shortcomings of the mean-field treatment of
the orientational part are highlighted and perspectives are given for attaining
a full density functional via machine learning.
