An interpretable physics-informed deep learning model for estimating multiple air pollutants

Accurate and effective monitoring of atmospheric components is urgently needed due to the compound air pollution in China. Despite numerous efforts to estimate various air pollutant concentrations, the focus on individual pollutants has overlooked their interactions, thereby limiting estimation accuracy. In addition, the use of shared data and model structures in these studies has led to inefficiencies due to duplicated efforts. Moreover, widely applied machine learning models have demonstrated a lack of interpretability and a weak physical basis. To address these issues, this study developed an interpretable physics-informed deep neural network to estimate multiple air pollutants simultaneously (IPMDNN). The model inputs were initially categorized based on prior atmospheric knowledge. To account for the varying impact of each input on different pollutants, a tanh-based self-attention mechanism was followed to dynamically adjust their contributions. A deep interaction module was then introduced to capture the complex physicochemical interactions among pollutants. To ensure consistency with physical laws, a physics-constrained loss function was incorporated. Finally, layer-wise relevance propagation was employed to interpret the model results. Experiments conducted in China in 2019 and 2020 demonstrated that the proposed model effectively estimated ozone (O3) and particulate matter (PM2.5 and PM10) concentrations simultaneously. Compared with separate estimation models, the proposed model achieved higher sample-based cross-validation R2 values of 0.92, 0.90, and 0.87 for O3, PM2.5, and PM10, respectively, and demonstrated more than twice the efficiency. Furthermore, the model interpretation identified formaldehyde, carbon monoxide, hydroxyl radical, and temperature as key contributors in the joint estimation. Mapping results derived from the model highlighted severe O3 and PM pollution in East, Central, and North China. In terms of seasonal trends, severe O3 pollution was observed in the summer, whereas high levels of PM pollution occurred in the winter. These findings suggested that the proposed model, with its high accuracy and efficiency, could provide valuable insights for the coordinated control of air pollution in China.