###### Abstract  
In recent years, deep learning models have gained significant traction and found extensive applications in the realm of PM2.5 concentration prediction. PM2.5 concentration sequences are rich in frequency information; however, existing PM2.5 concentration prediction models lack the ability to capture the frequency information. Therefore, we propose the Time-frequency domain, Bidirectional Long Short-Term Memory (BiLSTM), and attention (TF-BiLSTM-attention) model. First, the model uses Discrete Cosine Transform (DCT) to convert the time domain information into its corresponding frequency domain representation. Second, it joins the time domain information with the frequency domain information, which enables the model to capture the frequency domain information on top of the original. Simultaneously, incorporating the attention mechanism after BiLSTM enhances the importance of critical time steps. Empirical results underscore the superior predictive performance of our proposed univariate model across all sites, outperforming both the univariate BiLSTM, univariate BiLSTM-attention, and univariate TF-BiLSTM. Meanwhile, for the multivariate model that adds PM2.5 concentration from other sites in the study area as input variables, our proposed model outperforms the prediction of some basic models such as BiLSTM and some hybrid models such as CNN-BiLSTM for all sites. air quality prediction; deep learning; BiLSTM; DCT; attention mechanism +
Footnote †: journal: Medical  
between air pollutant concentration and potential predictors by using existing data [7], so this approach effectively circumvents the intricacies and unwarranted complexities inherent in the modeling process, showcasing commendable performance. Among statistical methods, the artificial neural network stands out as a paramount representative. The artificial neural network is not constrained by physical, biological, or chemical processes and is capable of handling non-linear relationships with strong fitting and predictive capabilities. A contemporary advancement in the field of PM2.5 concentration prediction research involves the utilization of deep neural networks, a specialized form of artificial neural network adept at handling extensive data through intricate model architectures. Among these techniques, the prevalent employment of deep learning models revolves around architectures such as Long Short-Term Memory (LSTM) [8], Bidirectional LSTM (BiLSTM) [9], Convolutional Neural Network-LSTM (CNN-LSTM) [10], and CNN-BiLSTM [11]. Moreover, researchers have sought to enhance the predictive prowess of these models by amalgamating diverse techniques, encompassing data decomposition and data/model fusion [12]. One research direction for data fusion is to incorporate the neighboring sites of the target site into the PM2.5 prediction. Air quality data belong to time series data, which are rich in frequency information. Addressing the limitations observed in certain models like the transformer and LSTM, [PERSON] et al. [13] contended that these models exhibited a notable discrepancy between their predicted outcomes and the true values of the datasets due to their inadequate capacity to capture frequency information effectively. As a remedy, they explored the utilization of Discrete Cosine Transform (DCT) instead of the commonly employed Fourier Transform (FT) for time-frequency transformations, thereby mitigating the occurrence of the Gibbs phenomenon during the transformation process. Building on this concept, they introduced the Frequency Enhanced Channel Mechanism (FECAM), enabling proficient feature extraction from time series data. Extensive experiments conducted across diverse time series datasets demonstrated that FECAM, as a versatile approach, substantially enhanced the prediction performance of LSTM models. [PERSON] et al. [14] introduced an innovative approach named the joint time-frequency domain transformer (JJFFT) to facilitate multivariate prediction tasks.