Using symbolic machine learning to assess and model substance transport and decay in water distribution networks.

Drinking water infrastructures are systems of pipes which are generally networked. They play a crucial role in transporting and delivering clean water to people. The water quality analysis refers to the evaluation of the advective diffusion of any substance in drinking water infrastructures from source nodes. Such substances could be a contamination for the system or planned for the disinfection, e.g., chlorine. The water quality analysis is performed by integrating the differential equation in the pipes network domain using the kinetics of the substance decay and the Lagrangian scheme. The kinetics can be formulated using a specific reaction order depending on the substance characteristics. The basis for the integration is the pipes velocity field calculated by means of hydraulic analysis. The aim of the present work is to discover the intrinsic mechanism of the substance transport in drinking water infrastructures, i.e., their pipes network domain, using the symbolic machine learning, named Evolutionary Polynomial Regression, which provides "synthetic" models (symbolic formulas) from data. We demonstrated, using one real network and two test networks, that the concentration at each node of the network can be predicted using the travel time along the shortest path(s) between the source and each node. Additionally, the formula models provided by symbolic machine learning allowed discovering that a unique formula based on kinetic reaction model structure allows predicting the residual substance concentration at each node, given the source node concentration, surrogating with a good accuracy the integration of the differential equations.

Embedding the intrinsic relevance of vertices in network analysis: the case of centrality metrics.

Complex network theory (CNT) is gaining a lot of attention in the scientific community, due to its capability to model and interpret an impressive number of natural and anthropic phenomena. One of the most active CNT field concerns the evaluation of the centrality of vertices and edges in the network. Several metrics have been proposed, but all of them share a topological point of view, namely centrality descends from the local or global connectivity structure of the network. However, vertices can exhibit their own intrinsic relevance independent from topology; e.g., vertices representing strategic locations (e.g., hospitals, water and energy sources, etc.) or institutional roles (e.g., presidents, agencies, etc.). In these cases, the connectivity network structure and vertex intrinsic relevance mutually concur to define the centrality of vertices and edges. The purpose of this work is to embed the information about the intrinsic relevance of vertices into CNT tools to enhance the network analysis. We focus on the degree, closeness and betweenness metrics, being among the most used. Two examples, concerning a social (the historical Florence family's marriage network) and an infrastructure (a water supply system) network, demonstrate the effectiveness of the proposed relevance-embedding extension of the centrality metrics.