Spatial Shortcuts in Graph Neural Controlled Differential Equations

TL;DR

This paper introduces an informed Neural Controlled Differential Equation model that leverages prior graph topology to improve dynamical system predictions on graphs, achieving better accuracy with fewer parameters.

Contribution

It proposes a novel way to incorporate graph topology into NCDEs, identifying an optimal model position for this information and demonstrating improved performance.

Findings

Informed NCDEs outperform previous methods in MAE.

The outer position for graph information in the model is most effective.

Fewer parameters are needed for comparable or better accuracy.

Abstract

We incorporate prior graph topology information into a Neural Controlled Differential Equation (NCDE) to predict the future states of a dynamical system defined on a graph. The informed NCDE infers the future dynamics at the vertices of simulated advection data on graph edges with a known causal graph, observed only at vertices during training. We investigate different positions in the model architecture to inform the NCDE with graph information and identify an outer position between hidden state and control as theoretically and empirically favorable. Our such informed NCDE requires fewer parameters to reach a lower Mean Absolute Error (MAE) compared to previous methods that do not incorporate additional graph topology information.