Spatial Shortcuts in Graph Neural Controlled Differential Equations
This work addresses the challenge of improving prediction accuracy for graph-based dynamical systems, but it is incremental as it builds on existing NCDE frameworks by adding graph information.
The authors tackled the problem of predicting future states of dynamical systems on graphs by incorporating prior graph topology into Neural Controlled Differential Equations (NCDEs), resulting in a model that achieves lower Mean Absolute Error (MAE) with fewer parameters compared to previous methods.
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.