Isometric Transformation Invariant and Equivariant Graph Convolutional Networks
This addresses the need for computationally efficient models in physical simulations, offering a domain-specific incremental improvement over existing equivariant models.
The paper tackles the problem of learning isometric transformation invariant and equivariant features for graphs embedded in Euclidean spaces, such as in physical simulations, by proposing IsoGCNs, which achieve competitive performance on geometrical and physical simulation tasks and scale to graphs with 1M vertices with faster inference than conventional finite element analysis.
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 physical simulations. A crucial requirement for applying graphs in Euclidean spaces to physical simulations is learning and inferring the isometric transformation invariant and equivariant features in a computationally efficient manner. In this paper, we propose a set of transformation invariant and equivariant models based on graph convolutional networks, called IsoGCNs. We demonstrate that the proposed model has a competitive performance compared to state-of-the-art methods on tasks related to geometrical and physical simulation data. Moreover, the proposed model can scale up to graphs with 1M vertices and conduct an inference faster than a conventional finite element analysis, which the existing equivariant models cannot achieve.