Graph Element Networks: adaptive, structured computation and memory

By Ferran Alet, Adarsh K. Jeewajee, Maria Bauzá, Alberto Rodriguez, Tomas Lozano-Perez, Leslie Pack Kaelbling. 2019

91 citations recorded by the source corpus.

We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational process defined on the graph to model the relationship between an initial function defined over a space and a resulting function in the same space. We use GNNs as a computational substrate, and show that the locations of the nodes in space as well as their connectivity can be optimized to focus on the most complex parts of the space. Moreover, this representational strategy allows the learned input-output relationship to generalize over the size of the underlying space and run the same model at different levels of precision, trading computation for accuracy. We demonstrate this method on a traditional PDE problem, a physical prediction problem from robotics, and learning to predict scene images from novel viewpoints.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

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Citations in the corpus

Isometric Transformation Invariant and Equivariant Graph Convolutional Networks (2020, background): “The studies presented by Baskin et al. (1997); Sperduti & Starita (1997); Gori et al. (2005); Scarselli et al. (2008) were the first research works that discussed the concept of GNNs. Although many variants of GNNs were proposed, including those presented by Hamilton et al. (2017); Veličković et al.”
Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations (2019, background): “Graph neural networks may similarly capture 3D structure [37].”
Neural Operator: Learning Maps Between Function Spaces (2021, background): “The work (Alet et al., 2019) performs an initial study that employs graph networks on the problem of learning solutions to Poisson’s equation, among”
Geometry-Informed Neural Operator for Large-Scale 3D PDEs (2023, methodology): “For ablations, we consider channel dimensions [32, 48, 64, 80], latent space [32, 48, 64, 80], and radius from 0.025 to 0.055 (with the domain size normalized to [-1, 1]).”
Learning Mesh-Based Simulation with Graph Networks (2020, methodology): “But despite mesh-based simulations being the tool of choice in mechanical engineering and related disciplines, adaptive mesh representations have not seen much use in machine learning for physics prediction, with a few notable exceptions [5, 2].”
Choose a Transformer: Fourier or Galerkin (2021, methodology): “In [4, 5], certain kernel forms of the solution operator of parametric PDEs are approximated using graph neural networks.”
GraphCast: Learning skillful medium-range global weather forecasting (2022, methodology): “The encoder and decoder do not require the raw data to be arranged in a regular rectilinear grid, and can also be applied to arbitrary mesh-like state discretizations (Alet et al., 2019).”
Multipole Graph Neural Operator for Parametric Partial Differential Equations (2020, methodology): “The graph convolution network (GCN) method follows [4]’s architecture, with naive nearest neighbor connection.”