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Networks and network processes have emerged as powerful tools for modelingsocial interactions, disease propagation, and a variety of additional dynamicsdriven by relational structures. Recently, neural networks have beengeneralized to process data on graphs, thus being able to learn from theaforementioned network processes achieving cutting-edge performance intraditional tasks such as node classification and link prediction. However,these methods have all been formulated in a way suited only to data on thenodes of a graph. The application of these techniques to data supported on theedges of a graph, namely flow signals, has not been explored in detail. Tobridge this gap, we propose the use of the so-called Hodge Laplacian combinedwith graph neural network architectures for the analysis of flow data.Specifically, we apply two graph neural network architectures to solve theproblems of flow interpolation and source localization.

HodgeNet: Graph Neural Networks for Edge Data