Non-point source pollution prediction and dynamics simulation in urban runoff: a physics-informed neural network approach

Urban non-point source (NPS) pollution poses a significant threat to water environments, yet modeling its complex dynamics remains constrained by the trade-off between the extensive data requirements of process-based models and the limited interpretability of machine learning approaches. This study introduces the physics-informed wash-off network, a hybrid architecture that embeds the differential equations governing pollutant accumulation and wash-off into a recurrent neural network. Leveraging a tabular event dataset, the model generates continuous pollutographs, achieving improved predictive performance with a Nash-Sutcliffe Efficiency of 0.65 and generalization score of 0.94 compared to five state-of-the-art data-driven baselines, where the highest values were 0.33 and 0.89, respectively. Beyond prediction, the model employs interpretability analysis to identify the non-linear drivers of total suspended solids dynamics. Results reveal a distinct divergence: while land use and imperviousness consistently drive both event mean concentration and first flush intensity, precipitation oppositely affects them. Specifically, heavier rainfall dilutes average concentrations but intensifies the first flush. This opposing relationship explains the negative correlation observed between the two metrics and highlights the limitations of uniform stormwater regulations. Consequently, we propose a differentiated management framework: catchments with high first flush potential are strong candidates for rapid diversion and separation technologies, whereas those with low first flush potential are better suited for volume-based retention strategies. These findings advocate for a paradigm shift from static, volume-based controls to dynamic, quality-based management.