A Locally Weighted Neural Network Constrained by Global Training for Remote Sensing Estimation of PM₂.₅

Fine particulate matter (PM
_2.5
) pollution can cause serious public health problems worldwide. A novel geographically and temporally weighted neural network constrained by global training (GC-GTWNN) is proposed in this article for the remote sensing estimation of surface PM
_2.5
. The global neural network (NN) is trained to learn the overall effect of the influencing variables on surface PM
_2.5
, and the local geographically and temporally weighted NN (GTWNN) addresses the spatiotemporal heterogeneity of the relationship between PM
_2.5
and the influencing variables. Specifically, a global NN is trained with all samples collected from the entire study domain and period. Then, initialized with the global NN, the GTWNN models are built for each location and time and fine-tuned via spatiotemporally localized samples. Meanwhile, the geographically weighted loss function is designed for GTWNN. The proposed GC-GTWNN modeling is tested with a case study across China, which integrates satellite aerosol optical depth, surface PM
_2.5
measurements, and auxiliary variables. Cross-validation results indicate that a remarkable improvement is observed from the global NN to GC-GTWNN modeling (
$R^{2}$
value increasing from 0.49 to 0.80), and GC-GTWNN modeling also notably outperforms the conventionally popular PM
_2.5
estimation models.