Urban non-point source pollution modelling: A physics-informed neural network approach

Over the past decades, urban non-point source (NPS) pollution has been the most severe threat to the urban water environment. The sharp increase of impervious surface and the high level of particulate matter from massive human activities exacerbated the water quality of surface runoff, leading to the significant urban NPS pollution globally whereby it is of importance to have a deep knowledge on the accumulation and transport of pollutants. A series of traditional physical models have been developed to simulate the runoff generating as well as the NPS pollution. However, a disadvantage of process-based modelling is its great demand for a large amount of field data which may normally be inaccessible, as well as the demand for the expertise in applying appropriate modelling method on specific study area. Empirical models do not characterize complex physical processes of NPS pollution and thus require fewer data and modelling skills. Nevertheless, the limitation is that these modelling approaches are region-sensitive and spatially untransferable. It is challenging to fill the gap between the requirement of urban water environment management and existing modelling performance on NPS pollution, in the absence of a more effective model with high accuracy, easy employment, and spatial transferability.

Machine learning approach has been utilized in environmental studies for decades, and was originally believed to be a black box that can barely provide any physical insight into environmental processes. However, an approach named physics-informed neural networks (PINN) was proposed lately and then applicated in dynamical system. This approach embeds differential equations of priori knowledge into neural network to make modelling interpretable and generalizable. In this study, a physical process embedded LSTM network was proposed to formulate the cumulation and transport of urban NPS pollution in rainfall runoff, based on the coupling of LSTM and differential equations of classic exponential build-up/wash-off processes. Water quality data of urban runoff from sampling and continuous real-time monitoring campaigns distributed in China, USA and New Zealand were collected and fed into proposed network to model the primary NPS pollutant TSS. The results revealed that the hybrid PINN model excels the vanilla LSTM approach and auto-calibrated SWMM approach in accuracy and convenience. The interpretable model also enhanced the cross-catchment transferability of model for urban water management in data-poor area. In addition, the trained parameters of network units were found consistent with the prior knowledge of accumulation and transport of NPS pollutants, indicating the deep coupling of neural network and physical process. As a very early case of hybrid AI modelling in urban NPS pollution, this study provided a new perspective on water quality modelling and can help in improving the standards of urban environment governance.