Dynamic mode decomposition and short-time prediction of PM2.5 using the graph Neural Koopman network

Abstract

Analyzing and accurately predicting the spatiotemporal dynamics of PM2.5 remain challenging. The existing spatiotemporal prediction approaches are associated with high model complexity and limited interpretability. Conventional methods combining Koopman theory and deep learning often neglect spatial correlations in spatiotemporal data. This study used the hourly PM2.5 dataset of the Beijing-Tianjin-Hebei region to reveal its spatiotemporal hierarchy using Koopman mode decomposition to identify the key dynamic modes. Furthermore, a Spatial Physics Constrained Learning (SPCL) model utilizing a graph representation learning method was proposed to combine the graph topological information of the PM2.5 spatial features with the Koopman feature function. The results showed that PM2.5 has growth, decay, and oscillation modes as well as daily, weekly, monthly, and yearly periods. SPCL achieved mean absolute error, root mean square error (RMSE), correlation r, and index of agreement values of 9.678, 13.922, 0.864, and 0.921, respectively. The average RMSE at 12 h improved by 16.1%, 12.7%, 0.9%, and 3.5% compared with using Long short-term Memory, Graph Convolutional Networks and Long Short-Term Memory Networks, Spatio-Temporal Graph Convolutional Networks, and Dynamic Spatiotemporal Graph Convolution Network, respectively. By discretizing the neural network hidden layers, the explanatory key of PM2.5 modes was elucidated, which demonstrated enhanced stability.