Isometric Transformation Invariant and Equivariant Graph Convolutional Networks

Graphs are one of the most important data structures for representing pairwise relations between objects. Specifically, a graph embedded in a Euclidean space is essential to solving real problems, such as object detection, structural chemistry analyses, and physical simulation. A crucial requirement to applying a graph in a Euclidean space is learning the isometric transformation invariant and equivariant features. In the present paper, we propose a set of transformation invariant and equivariant models based on graph convolutional networks (GCNs), called IsoGCNs. We demonstrate that the proposed model outperforms state-of-the-art methods on tasks related with geometrical and physical data. Moreover, the proposed model can scale up to the graphs with 1M vertices and conduct an inference faster than a conventional finite element analysis.