Graph-Informed Neural Networks for Regressions on Graph-Structured Data

Stefano Berrone, Francesco Della Santa, Antonio Mastropietro, Sandra Pieraccini and Francesco Vaccarino
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Stefano Berrone: Dipartimento di Scienze Matematiche (DISMA), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
Francesco Della Santa: Dipartimento di Scienze Matematiche (DISMA), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
Antonio Mastropietro: Dipartimento di Scienze Matematiche (DISMA), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
Sandra Pieraccini: Member of the INdAM-GNCS Research Group, 00100 Rome, Italy
Francesco Vaccarino: Dipartimento di Scienze Matematiche (DISMA), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy

Mathematics, 2022, vol. 10, issue 5, 1-29

Abstract: In this work, we extend the formulation of the spatial-based graph convolutional networks with a new architecture, called the graph-informed neural network (GINN). This new architecture is specifically designed for regression tasks on graph-structured data that are not suitable for the well-known graph neural networks, such as the regression of functions with the domain and codomain defined on two sets of values for the vertices of a graph. In particular, we formulate a new graph-informed (GI) layer that exploits the adjacent matrix of a given graph to define the unit connections in the neural network architecture, describing a new convolution operation for inputs associated with the vertices of the graph. We study the new GINN models with respect to two maximum-flow test problems of stochastic flow networks. GINNs show very good regression abilities and interesting potentialities. Moreover, we conclude by describing a real-world application of the GINNs to a flux regression problem in underground networks of fractures.

Keywords: graph neural networks; deep learning; regression on graphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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