Isometric Transformation Invariant and Equivariant Graph Convolutional Networks

Graphs correspond to one of the most important data structures used to represent pairwise relations between objects. Specifically, using the graphs embedded in the Euclidean space is essential to solve real problems, such as object detection, structural chemistry analysis, and physical simulation. A crucial requirement to employ the graphs in the Euclidean space is to learn the isometric transformation invariant and equivariant features. In the present paper, we propose a set of the transformation invariant and equivariant models called IsoGCNs that are based on graph convolutional networks. We discuss an example of IsoGCNs that corresponds to differential equations. We also demonstrate that the proposed model achieves high prediction performance on the considered finite element analysis dataset and can scale up to the graphs with 1M vertices.