Graph Element Networks: adaptive, structured computation and memory

Traditional applications of GNNs assume an a priori We explore the use of graph neural networks notion of entity (such as bodies, links or particles) (GNNs) to model spatial processes in which and match every node in the graph to an entity. We there is no a priori graphical structure. Similar propose to apply GNNs to the problem of modeling to finite element analysis, we assign nodes transformations of functions defined on continuous of a GNN to spatial locations and use a computational spaces, using a structure we call graph element networks process defined on the graph to (GENs). Inspired by finite element methods, we use model the relationship between an initial graph neural networks to mesh a continuous space function defined over a space and a resulting and define an iterative computation that propagates function in the same space. We use GNNs information from some sampled input values in the as a computational substrate, and show that space to an output function defined everywhere in the locations of the nodes in space as well the space. GENs allow us to model systems that have as their connectivity can be optimized to focus spatial structure but lack a clear notion of entity, such on the most complex parts of the space.