  We introduce the Hierarchically Interacting Particle Neural Network (HIP-NN)
to model molecular properties from datasets of quantum calculations. Inspired
by a many-body expansion, HIP-NN decomposes properties, such as energy, as a
sum over hierarchical terms. These terms are generated from a neural network--a
composition of many nonlinear transformations--acting on a representation of
the molecule. HIP-NN achieves state-of-the-art performance on a dataset of 131k
ground state organic molecules, and predicts energies with 0.26 kcal/mol mean
absolute error. With minimal tuning, our model is also competitive on a dataset
of molecular dynamics trajectories. In addition to enabling accurate energy
predictions, the hierarchical structure of HIP-NN helps to identify regions of
model uncertainty.
