Atmospheric fine particles (${\mathrm{PM}}_{2.5}$) have been found to be harmful to the environment and human health. Recently, remote sensing technology and machine learning models have been used to monitor ${\mathrm{PM}}_{2.5}$ concentrations. Partial dependence plots (PDP) were used to explore the meteorology mechanisms between predictor variables and ${\mathrm{PM}}_{2.5}$ concentration in the “black box” models. However, there are two key shortcomings in the original PDP. (1) it calculates the marginal effect of feature(s) on the predicted outcome of a machine learning model, therefore some local effects might be hidden. (2) it requires that the feature(s) for which the partial dependence is computed are not correlated with other features, otherwise the estimated feature effect has a great bias. In this study, the original PDP’s shortcomings were analyzed. Results show the contradictory correlation between the temperature and the ${\mathrm{PM}}_{2.5}$ concentration that can be given by the original PDP. Furthermore, the spatiotemporal heterogeneity of ${\mathrm{PM}}_{2.5}$-AOD relationship cannot be displayed well by the original PDP. The drawbacks of the original PDP make it unsuitable for exploring large-area feature effects. To resolve the above issue, multi-way PDP is recommended, which can characterize how the ${\mathrm{PM}}_{2.5}$ concentrations changed with the temporal and spatial variations of major meteorological factors in China.

In recent years, deep neural networks (DNN) have been widely used in many fields. Lots of effort has been put into training due to their numerous parameters in a deep network. Some complex optimizers with many hyperparameters have been utilized to accelerate the process of network training and improve its generalization ability. It often is a trial-and-error process to tune these hyperparameters in a complex optimizer. In this paper, we analyze the different roles of training samples on a parameter update, visually, and find that a training sample contributes differently to the parameter update. Furthermore, we present a variant of the batch stochastic gradient decedent for a neural network using the ReLU as the activation function in the hidden layers, which is called adaptive stochastic gradient descent (aSGD). Different from the existing methods, it calculates the adaptive batch size for each parameter in the model and uses the mean effective gradient as the actual gradient for parameter updates. Experimental results over MNIST show that aSGD can speed up the optimization process of DNN and achieve higher accuracy without extra hyperparameters. Experimental results over synthetic datasets show that it can find redundant nodes effectively, which is helpful for model compression.

Accurate and timely short-term forecasting of gridded PM_2.5 concentrations is essential for air-quality management and public health protection, especially for the growing elderly population who are particularly vulnerable to air pollution. Advances in multi-source environmental data and deep learning have substantially improved the spatiotemporal prediction of PM_2.5 concentrations. However, existing studies have mainly focused on developing increasingly sophisticated model architectures and optimization strategies while insufficiently considering the temporal nonstationarity of PM_2.5 pollution and the recurrent characteristics associated with similar seasonal environmental regimes. Changes in natural environmental conditions and anthropogenic emissions can continuously alter the relationships governing PM_2.5 concentrations, challenging the stability of continuous short-term forecasting; meanwhile, historically recurring seasonal pollution characteristics provide potentially valuable prior information for model adaptation. To address this problem, we propose a Seasonal Prior-guided Elastic Weight Consolidation (Seasonal EWC) framework for dynamic forecasting of nonstationary gridded PM_2.5 concentrations in China. The framework derives season-specific parameter anchors and Fisher-based parameter importance from historical seasonal conditions and uses this prior knowledge to guide parameter updates during continuous short-term forecasting. Experiments with four representative spatiotemporal forecasting models showed that Seasonal EWC produced architecture-dependent changes in forecasting performance, reducing the annual mean MAE and RMSE by 30.3% and 31.7% for U-Net and by 10.9% and 7.6% for Earthformer, with only small improvements for IAM4VP and mixed changes for ConvLSTM. Parameter analysis revealed that Seasonal EWC reduced parameter-update magnitudes by approximately 27–32% and substantially limited long-term parameter deviation, indicating more stable adaptation during continuous forecasting. These findings demonstrate that seasonal prior knowledge can effectively guide dynamic model adaptation under evolving PM_2.5 conditions, providing a promising approach for continuous short-term air-quality forecasting.