  Recent machine learning methods make it possible to model potential energy of
atomic configurations with chemical-level accuracy (as calculated from
ab-initio calculations) and at speeds suitable for molecular dynam- ics
simulation. Best performance is achieved when the known physical constraints
are encoded in the machine learning models. For example, the atomic energy is
invariant under global translations and rotations, it is also invariant to
permutations of same-species atoms. Although simple to state, these symmetries
are complicated to encode into machine learning algorithms. In this paper, we
present a machine learning approach based on graph theory that naturally
incorporates translation, rotation, and permutation symmetries. Specifically,
we use a random walk graph kernel to measure the similarity of two adjacency
matrices, each of which represents a local atomic environment. This Graph
Approximated Energy (GRAPE) approach is flexible and admits many possible
extensions. We benchmark a simple version of GRAPE by predicting atomization
energies on a standard dataset of organic molecules.
