Isometric Transformation Invariant and Equivariant Graph Convolutional Networks
arXiv:2005.06316
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.
arXiv commentPublished as a conference paper at ICLR 2021
References in corpus (16)
- Adam: A Method for Stochastic Optimization
- Neural Message Passing for Quantum Chemistry
- Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks
- Fast Graph Representation Learning with PyTorch Geometric
- Simplifying Graph Convolutional Networks
- Group Equivariant Convolutional Networks
- Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds
- Learning to Simulate Complex Physics with Graph Networks
- Simple and Deep Graph Convolutional Networks
- Graph networks as learnable physics engines for inference and control
- Revisiting Graph Neural Networks: All We Have is Low-Pass Filters
- 3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data
- Spherical CNNs
- Invariant and Equivariant Graph Networks
- Hamiltonian Graph Networks with ODE Integrators
- N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentials