Machine Learning-based surrogate modeling of water quality dynamics in a ‘universal’ distribution pipe

<p dir="ltr">Traditional predictive models of water quality in water distribution systems (WDS) are process-based, relying on the numerical solution of the advective-reactive (AR) partial differential equation (PDE), which governs the transport and decay of water quality parameters in distribution pipes. These equations are typically solved through spatial and temporal discretisation, making such models computationally intensive and impractical for real-time monitoring or digital control applications in smart water networks. To address this limitation, this study proposes a hybrid modelling approach that integrates data-driven surrogate models into the process-based framework. Specifically, machine learning (ML) models, including feedforward neural networks (FNNs), convolutional neural networks (CNNs), long short-term memory networks (LSTMs), and convolutional LSTM (ConvLSTM) networks, are evaluated as surrogates for solving the AR PDE at each pipe segment and time step, thereby eliminating the need for traditional spatial discretisation. Among the models tested, FNNs, CNNs, and LSTMs exhibited limited generalisation across spatial and temporal dimensions. FNNs lack any inherent mechanism to model spatial or temporal dependencies. LSTMs are able to capture temporal patterns, whereas CNNs capture spatial features well. These limitations highlighted the need for a model that can simultaneously learn spatial and temporal dependencies. The ConvLSTM model emerged as the most effective solution, as it embeds convolutional operations within LSTM memory cells, allowing it to learn both spatial structures and temporal sequences inherently. These ML-based models eliminate the need for computationally intensive discretisation procedures. The proposed approach, therefore, offers a computationally efficient and accurate alternative for simulating chlorine dynamics in WDSs.</p><p dir="ltr">This paper was presented at the 21st Computing and Control in the Water Industry Conference (CCWI 2025) at the University of Sheffield (1st - 3rd September 2025).</p>