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

Author

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  • Stefano Berrone

    (Dipartimento di Scienze Matematiche (DISMA), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
    SmartData@PoliTO Center, Politecnico di Torino, 10129 Turin, Italy
    Member of the INdAM-GNCS Research Group, 00100 Rome, Italy)

  • Francesco Della Santa

    (Dipartimento di Scienze Matematiche (DISMA), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
    SmartData@PoliTO Center, Politecnico di Torino, 10129 Turin, Italy
    Member of the INdAM-GNCS Research Group, 00100 Rome, Italy)

  • Antonio Mastropietro

    (Dipartimento di Scienze Matematiche (DISMA), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
    SmartData@PoliTO Center, Politecnico di Torino, 10129 Turin, Italy
    Addfor Industriale s.r.l., Via Giuseppe Giocosa 36/38, 10125 Turin, Italy)

  • Sandra Pieraccini

    (Member of the INdAM-GNCS Research Group, 00100 Rome, Italy
    Dipartimento di Ingegneria Meccanica e Aerospaziale (DIMEAS), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy)

  • Francesco Vaccarino

    (Dipartimento di Scienze Matematiche (DISMA), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
    SmartData@PoliTO Center, Politecnico di Torino, 10129 Turin, Italy)

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.

Suggested Citation

  • Stefano Berrone & Francesco Della Santa & Antonio Mastropietro & Sandra Pieraccini & Francesco Vaccarino, 2022. "Graph-Informed Neural Networks for Regressions on Graph-Structured Data," Mathematics, MDPI, vol. 10(5), pages 1-29, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:786-:d:761957
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    References listed on IDEAS

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    1. Gert Sabidussi, 1966. "The centrality index of a graph," Psychometrika, Springer;The Psychometric Society, vol. 31(4), pages 581-603, December.
    2. Nedialko B. Dimitrov & David P. Morton, 2013. "Interdiction Models and Applications," International Series in Operations Research & Management Science, in: Jeffrey W. Herrmann (ed.), Handbook of Operations Research for Homeland Security, edition 127, chapter 0, pages 73-103, Springer.
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