Graph Element Networks: adaptive, structured computation and memory

TL;DR

This paper introduces Graph Element Networks, a novel GNN-based approach that models spatial processes without predefined graph structures, optimizing node placement and connectivity for better generalization and efficiency across various applications.

Contribution

It proposes a flexible GNN framework that learns spatial node placement and connectivity, enabling adaptive, scalable, and generalizable modeling of spatial functions.

Findings

Successfully applied to PDE problems and robotics predictions.

Demonstrated ability to generalize across different space sizes.

Achieved efficient computation with adjustable precision.

Abstract

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.