  Simple models for spherical particles with a soft shell have been shown to
self-assemble into numerous crystal phases and even quasicrystals. However,
most of these models rely on a simple pairwise interaction, which is usually a
valid approximation only in the limit of small deformations, i.e. low
densities. In this work, we consider a many-body yet simple model for the
evaluation of the elastic energy associated with the deformation of a spherical
shell. The resulting energy evaluation, however, is relatively expensive for
direct use in simulations. We significantly reduce the associated numerical
cost by fitting the potential using a set of symmetry functions. We propose a
method for selecting a suitable set of symmetry functions that capture the most
relevant features of the particle environment in a systematic manner. The
fitted interaction potential is then used in Monte Carlo simulations to draw
the phase diagram of the system in two dimensions. The system is found to form
both a fluid and a hexagonal crystal phase.
