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This paper develops a Deep Graph Operator Network (DeepGraphONet) frameworkthat learns to approximate the dynamics of a complex system (e.g. the powergrid or traffic) with an underlying sub-graph structure. We build ourDeepGraphONet by fusing the ability of (i) Graph Neural Networks (GNN) toexploit spatially correlated graph information and (ii) Deep OperatorNetworks~(DeepONet) to approximate the solution operator of dynamical systems.The resulting DeepGraphONet can then predict the dynamics within a givenshort/medium-term time horizon by observing a finite history of the graph stateinformation. Furthermore, we design our DeepGraphONet to beresolution-independent. That is, we do not require the finite history to becollected at the exact/same resolution. In addition, to disseminate the resultsfrom a trained DeepGraphONet, we design a zero-shot learning strategy thatenables using it on a different sub-graph. Finally, empirical results on the(i) transient stability prediction problem of power grids and (ii) traffic flowforecasting problem of a vehicular system illustrate the effectiveness of theproposed DeepGraphONet.

DeepGraphONet: A Deep Graph Operator Network to Learn and Zero-shot Transfer the Dynamic Response of Networked Systems