A Graph Neural Networks approach to the state estimation of water distribution systems

Traditional Machine Learning cannot deal with graph data in a satisfactory way, in fact they are designed to work with simpler data types like images, which can be represented as grids. Graphs are more complex and they are used to model a set of objects (nodes) and the relationships between them (edges). Graphs do not have a fixed shape and each node can have a different number of neigh- bors; moreover the nodes inside a graph are interconnected and hence they are not independent. These are some of the reasons traditional machine learning algorithms struggle to work with this data. As a consequence Graph Neural networks were developed, with the goal of learning not only from the informa- tion encoded in the main elements of a graph, which are the nodes, but also from the connectivity among them, represented by the edges. Graph Neural networks can be applied to different tasks, such as semi supervised classifica- tion or regression, where the model learns to label or predict the target values of all nodes, given only a subset of them as training data. The problem presented in this thesis falls under this category. A Graph Neural network is applied to a water distribution system (WDS) in an attempt to esti- mate the missing values of the pressures at those junctions where sensors are not present. In fact, these systems are often quite large and sensors too expen- sive to be installed at all locations; however, it is very important to estimate the pressures everywhere in the WDS, in order to monitor the state of the system and plan the appropriate control actions.