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.
Highlights
Graphs are frequently used to describe and study many different phenomena, such as transportation systems, epidemic- or economic-default spread, electrical circuits, and social interactions; the literature typically refers to the use of graph theory to analyze such phenomena with the term “network analysis” [1].Recently, new key contributions to network analyses have been proposed by the neural network (NN) community; in particular, deep learning (DL) approaches can be extended to graph-structured data via the so-called graph neural networks (GNNs)
New key contributions to network analyses have been proposed by the neural network (NN) community; in particular, deep learning (DL) approaches can be extended to graph-structured data via the so-called graph neural networks (GNNs)
If the output feature of vertex v j ∈ {vi1, . . . , vim } through F depends on the input feature of vertex vi, the graph-informed neural network (GINN) needs at least dij = distG (vi, v j ) consecutive GI layers to guarantee that the input feature of vi contributes in making predictions for the output feature of v j
Summary
Graphs are frequently used to describe and study many different phenomena, such as transportation systems, epidemic- or economic-default spread, electrical circuits, and social interactions; the literature typically refers to the use of graph theory to analyze such phenomena with the term “network analysis” [1]. We present a new type of spatial-based graph convolutional layer designed for regression tasks on graph-structured data, a framework for which previous. The output feature of a node is computed by summing up the input features of the node itself and of its neighbors, where each one is multiplied by the corresponding node weights We call this new type of graph layer a graph-informed (GI) layer.
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