  A molecule's 2D representation consists of its atoms, their attributes, and
the molecule's covalent bonds. A 3D (geometric) representation of a molecule is
called a conformer and consists of its atom types and Cartesian coordinates.
Every conformer has a potential energy, and the lower this energy, the more
likely it occurs in nature. Most existing machine learning methods for
molecular property prediction consider either 2D molecular graphs or 3D
conformer structure representations in isolation. Inspired by recent work on
using ensembles of conformers in conjunction with 2D graph representations, we
propose $\mathrm{E}$(3)-invariant molecular conformer aggregation networks. The
method integrates a molecule's 2D representation with that of multiple of its
conformers. Contrary to prior work, we propose a novel 2D-3D aggregation
mechanism based on a differentiable solver for the \emph{Fused
Gromov-Wasserstein Barycenter} problem and the use of an efficient conformer
generation method based on distance geometry. We show that the proposed
aggregation mechanism is $\mathrm{E}$(3) invariant and propose an efficient GPU
implementation. Moreover, we demonstrate that the aggregation mechanism helps
to significantly outperform state-of-the-art molecule property prediction
methods on established datasets.
