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PM 2.5 concentration time series are characterized by obvious chaotic behavior, mutually superimposed multi-period components and notable temporal fluctuations, which pose considerable difficulties to the high-precision prediction of PM 2.5 concentration. To address this issue, this paper proposes a novel hybrid predictive framework, namely IMSTL-FVMD- HLDT-SRAdam. This framework first employs IMSTL decomposition algorithm to separate the original PM 2.5 series into a trend component, multiple seasonal sub-components, and a residual component, and further splits the residual component into multiple residual sub-components via FVMD decomposition strategy for full extraction of its valid information. Subsequently, these three types of components are taken as input features and separately fed into the LSTM, DLinear and TimesNet sub-models to implement independent modeling and prediction for the trend component, total seasonal components and total residual components. During the model training phase, the SRA meta-heuristic optimization strategy is adopted to strengthen the global search ability of the Adam optimizer and reduce the prediction errors of DLinear and TimesNet sub-models via optimizing their output layer parameters. Finally, the PM 2.5 concentration prediction is obtained through additive reconstruction of the predicted results of each component. Experimental results show that the deep learning predictive framework proposed in this paper achieves favorable prediction accuracy and generalization performance for PM 2.5 , and it possesses certain application value in air pollution early warning and governance.
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Zhao et al. (2026) studied this question.
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