Digital water solutions are emerging as a viable alternative for improving the resilience of urban water systems to extreme weather events. The advances in deep learning enabled the creation of time series forecasting models that assimilate measurements and rainfall forecasts to predict the future state and optimize the operation of urban water systems. Despite its promise, developing and using deep learning-based digital water solutions for operational decision-making has been challenging. The existing deep learning research in urban water systems treats these methodologies as a “black box” that directly learns the mapping between input and output data. The deep learning model’s ability to determine the relationship between data is one of the primary reasons for its widespread adoption, but it requires significant computational resources to discover these relationships. Furthermore, developing deep learning-based time series forecasting models that are interpretable and generalizable across diverse scenarios in urban water systems adds additional complexity. In this work, we present a novel approach for embedding hydrological-hydraulic phenomena into deep learning model architectures to reduce computational requirements and create explainable and generalizable time series forecasting models. Rather than rediscovering the physical processes in the watershed (e.g., rainfall-runoff conversion, hydraulics) through data, embedding them in the deep-learning model architecture reduces the computational resources required for training the forecasting models. We demonstrate the efficacy of this approach through two real-world case studies. In the first case study, we use the proposed methodology for predicting inflows to the treatment plant based on NOAA rainfall forecasts and demonstrate the approach’s computational efficiency. In the second case study, we show the approach’s generalizability by training one deep-learning model to predict river levels across space and time. We also discuss how embedding physical processes into deep learning models can turn these black-box models into glass-box models and improve their explainability.
