  This paper develops a Deep Graph Operator Network (DeepGraphONet) framework
that learns to approximate the dynamics of a complex system (e.g. the power
grid or traffic) with an underlying sub-graph structure. We build our
DeepGraphONet by fusing the ability of (i) Graph Neural Networks (GNN) to
exploit spatially correlated graph information and (ii) Deep Operator
Networks~(DeepONet) to approximate the solution operator of dynamical systems.
The resulting DeepGraphONet can then predict the dynamics within a given
short/medium-term time horizon by observing a finite history of the graph state
information. Furthermore, we design our DeepGraphONet to be
resolution-independent. That is, we do not require the finite history to be
collected at the exact/same resolution. In addition, to disseminate the results
from a trained DeepGraphONet, we design a zero-shot learning strategy that
enables using it on a different sub-graph. Finally, empirical results on the
(i) transient stability prediction problem of power grids and (ii) traffic flow
forecasting problem of a vehicular system illustrate the effectiveness of the
proposed DeepGraphONet.
