WallpaperNet: A $p6mm$-Equivariant Graph Neural Network for Molecule Adsorption on Graphene

We present WallpaperNet, a $p6mm$-group-equivariant graph neural network (GNN) for modeling adsorption of small molecules on graphene. Unlike conventional approaches that freeze surface atoms and operate on large system sizes, our method focuses exclusively on the adsorbate atoms, which allows fast AI-guided design of molecule-graphene composite systems. We encode the symmetry of the underlying hexagonal lattice through Wyckoff-Anchor vector encoding and $D_6$-equivariant attention mechanism.