For exposure estimation of air pollutants, data measurement errors and modeling uncertainty may lead to estimation bias and abnormal predictions and relationships between variables. This paper proposes a method of geospatial constrained optimization and deep learning to reliably simulate and predict spatiotemporal trends of air pollutants. In the proposed method, k-nearest neighbors (k-NN) was first used to retrieve the nearest samples to spatialize regular local temporal basis functions at each target location or subregion; then, a convolutional neural network (CNN) was used to extrapolate temporal basis functions for prediction. Domain and empirical knowledge was embedded in extensive constrained optimization to obtain reasonable simulations and predictions. Bootstrapping was used to estimate the uncertainty of constrained optimized values. The method reduced the bias in the point estimates and obtained robust predictions and their uncertainty estimates of spatiotemporal trend for each spatial target location. In the location-based validations of NO₂, NO${}_{\mathrm{x}}$ and PM${}_{\mathrm{2.5}}$ in California, even with limited noise input, the proposed method captured the primary spatiotemporal variability (correlation with measured values: 0.75–0.91; explaining 55–84% of the variance). In addition, compared with generalized additive spatiotemporal model, kernel smoother and CNN, the proposed method made one-year reliable spatiotemporal forecasts of weekly averages. The proposed method has important implications for reducing the estimation bias and predicting trends in the air pollutant spatiotemporal fields.

对于空气污染物暴露估计，数据测量误差和建模不确定性可能导致估计偏差和异常预测以及变量之间的关系。本文提出了一种地理空间约束优化和深度学习的方法来可靠地模拟和预测空气污染物的时空趋势。在所提出的方法中，k -最近的邻居（k-NN) 首先用于检索最近的样本，以对每个目标位置或子区域的规则局部时间基函数进行空间化；然后，使用卷积神经网络 (CNN) 来推断时间基函数以进行预测。领域和经验知识被嵌入到广泛的约束优化中，以获得合理的模拟和预测。Bootstrapping 用于估计约束优化值的不确定性。该方法减少了点估计中的偏差，并获得了每个空间目标位置的时空趋势的稳健预测及其不确定性估计。在基于位置的 NO ₂验证中，NO${}_{\mathrm{X}}$ 和下午${}_{\mathrm{2.5}}$在加利福尼亚州，即使噪声输入有限，所提出的方法也捕获了主要的时空变异性（与测量值的相关性：0.75-0.91；解释了 55-84% 的方差）。此外，与广义加性时空模型、核平滑器和CNN相比，所提出的方法对每周平均值进行了一年可靠的时空预测。所提出的方法对于减少空气污染物时空场的估计偏差和预测趋势具有重要意义。