Deep learning for predicting the spatiotemporal dynamics of chlorine in water distribution pipes

Residual chlorine is a well-monitored water quality parameter in water distribution networks (WDN) to ensure the microbiological stability of the drinking water supply. To overcome the costs of direct chlorine measurement, predictive models are primarily used to complement water quality monitoring in real-world WDN. Traditional predictive models for chlorine in WDN are process-based and involve numerically solving the advective-reactive (AR) partial differential equation (PDE) governing the transport and decay of chlorine in distribution pipes, arguably the most influential components of water quality due to their extensive spatial coverage. Numerically solving the AR PDE involves spatial and temporal discretisation of the system domain, which is computationally intensive. This makes process-based models impractical for real-time monitoring or digital control of chlorine dosing. To address this limitation, we here compare different deep learning models, including feedforward neural networks (FNNs), convolutional neural networks (CNNs), long short-term memory networks (LSTMs), and convolutional LSTM networks (ConvLSTMs), as computationally efficient surrogates for solving the AR PDE governing chlorine dynamics. The ConvLSTM-based models emerge as the best for approximating the numerical solutions of AR PDE, with greater accuracy and the ability to generalise across different pipe lengths and decay rates. The models based on FNNs, CNNs, and LSTMs exhibit limited generalisation across spatial and temporal domains. These models offer a promising alternative to traditional numerical solvers, advancing the development of hybrid models for predicting chlorine dynamics in WDN.