  We develop a Genetic Programming-based methodology that enables discovery of
novel functional forms for classical inter-atomic force-fields, used in
molecular dynamics simulations. Unlike previous efforts in the field, that fit
only the parameters to the fixed functional forms, we instead use a novel
algorithm to search the space of many possible functional forms. While a
follow-on practical procedure will use experimental and {\it ab inito} data to
find an optimal functional form for a forcefield, we first validate the
approach using a manufactured solution. This validation has the advantage of a
well-defined metric of success. We manufactured a training set of atomic
coordinate data with an associated set of global energies using the well-known
Lennard-Jones inter-atomic potential. We performed an automatic functional form
fitting procedure starting with a population of random functions, using a
genetic programming functional formulation, and a parallel tempering
Metropolis-based optimization algorithm. Our massively-parallel method
independently discovered the Lennard-Jones function after searching for several
hours on 100 processors and covering a miniscule portion of the configuration
space. We find that the method is suitable for unsupervised discovery of
functional forms for inter-atomic potentials/force-fields. We also find that
our parallel tempering Metropolis-based approach significantly improves the
optimization convergence time, and takes good advantage of the parallel cluster
architecture.
