Accurate reporting and prediction of PM_2.5 concentration is very important for improving public health. In this article, we use spectral clustering algorithm to cluster 15 cities in the Pearl River Delta. On this basis, we propose a special difference equation model, especially the use of nonlinear diffusion equations to characterize the temporal and spatial dynamic characteristics of PM_2.5 propagation between and within clusters for real-time prediction. For example, through the analysis of PM_2.5 concentration data for 91 consecutive days in the Pearl River Delta, and according to different accuracy definitions, the average prediction accuracy of the difference equation model in all city clusters is 97% or 88%. The mean absolute error (MAE) of the forecast data for each urban agglomeration is within 7 units ( μ). Experimental results show that the difference equation model can effectively reduce the prediction time and improve the prediction accuracy. Therefore, based on the spectral clustering algorithm and the difference equation model, the fastest prediction speed and the best prediction result can be obtained, and the problem of PM_2.5 concentration prediction can be effectively solved. The research can provide decision support for local air pollution early warning and urban integrated management.

中文翻译：

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基于差分方程模型和细颗粒物（PM2.5）浓度数据的区域级预测模型

准确报告和预测 PM _2.5浓度对于改善公众健康非常重要。在本文中，我们使用谱聚类算法对珠三角15个城市进行聚类。在此基础上，我们提出了一种特殊的差分方程模型，特别是利用非线性扩散方程来表征PM _2.5在簇间和簇内传播的时空动态特征，以进行实时预测。例如，通过对珠三角地区连续91天的PM _{2.5浓度数据分析，根据不同的精度定义，差分方程模型在各城市群的平均预测精度为97} %或88 %。各城市群预测数据的平均绝对误差（MAE）在7个单位以内（ μ）。实验结果表明，差分方程模型可以有效减少预测时间，提高预测精度。因此，基于谱聚类算法和差分方程模型，可以获得最快的预测速度和最好的预测结果，有效解决PM _{2.5浓度预测问题。}研究可为当地空气污染预警和城市综合管理提供决策支持。