Using Symbolic Machine Learning to Assess and Model Substance Transport and Decay in Water Distribution Networks

Abstract

Abstract The evaluation of the substance concentration at each node of a water distribution network can be performed by integrating the advective diffusion in the network domain using a decay formulation and a Lagrangian scheme for differential equations. The kinetics of the substance decay can be formulated using a specific reaction order. The first order corresponds to a decay rate with a constant reaction rate, while higher order captures the reaction rate’s dependency on substance concentration. The aim of the present work was to discover the intrinsic mechanism of the substance transport in water distribution networks using the symbolic machine learning. We used the strategy named Evolutionary Polynomial Regression. To this purpose, we consider the chlorine transport, without imparing the generality of the procedure, assuming the first or second order for kinetic model. We demonstrated, using one real network and two test networks, that the concentration at each node of the network mainly depends on the substance decay along the shortest path(s) between the source and each node. Additionally, the symbolic machine learning allowed discovering the relationship between the source concentration and the residual one at each node of the network with a unique formula based on kinetic reaction model structure and its water age, possibly surrogated by travel time in the shortest path(s) to make the prediction faster.