Isometric Transformation Invariant and Equivariant Graph Convolutional Networks

Masanobu Horie, Naoki Morita, Toshiaki Hishinuma, Yu Ihara, Naoto Mitsume

Keywords: Machine Learning, Graph Neural Network, Invariance, Equivariance, Simulation, Mesh

Abstract: 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.

One-sentence Summary: We developed isometric transformation invariant and equivariant graph convolutional networks, which shows high prediction performance and computational efficiency.

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Code: [ yellowshippo/isogcn-iclr2021](https://github.com/yellowshippo/isogcn-iclr2021)