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.