## 1 Introduction  
With continuous advancement of industrialization and urbanization, artificial pollutants such as industrial production and automobile exhaust are increasing. As a consequence, urban air quality has gradually deteriorated, which seriously affects people's living environment. PM2.5, as one of the main pollutants in urban atmosphere has a small particle size, allowing staying in the atmosphere for a long time. It can enter human body through breathing and then deposits in the alveoli, causing great harm to human body [1]. Besides, PM2.5 has a negative impact on atmospheric visibility and climate change [2]. Therefore, accurate PM2.5 concentration prediction is necessary for controlling air pollution and protecting human health.  
Early prediction methods of PM2.5 concentration are mostly simple regression analysis. The regression equation between influencing factors and pollutant is established [3; 4; 5]. Subsequently, back-propagation (BP) neural network [6; 7], support vector machine (SVM) [8; 9], and other machine learning prediction methods are developed for the concentration prediction. However, these traditional machine learning methods are hard to learn the intrinsic relationship between the influencing factors and pollutant due to the shallow learning. In terms of prediction accuracy, it is not satisfactory.  
In 2006, [PERSON] et al. proposed a deep learning model, so-called deep belief network (DBN) [10]. It consists of multiple restricted Boltzmann machines (RBMs) and a back propagation (BP) neural network, allowing processing large amounts of data. In recent decades, the DBN has been successfully applied to fault diagnosis, wind speed forecasting, breast cancer classification, and so on [11; 12; 13; 14; 15]. Due to its advantage in prediction accuracy, in this paper, we introduce the DBN to conduct the PM2.5 concentration prediction. However, how to determine the structure parameters is an important issue when building a DBN network for PM2.5 concentration. The unsatisfactory network structure parameters--which contain number of hidden nodes, learning rate, and momentum coefficient--will reduce the prediction accuracy and increase the calculation time.  
This paper aims to establish a prediction model with high accuracy for PM2.5 concentration. Main contributions are as follows:  
1. An advanced deep learning model, so-called DBN, is introduced to predict the PM2.5 concentration, which establishes the close relationship between the influencing factors and pollutant.
2. A modified grey wolf optimization (MGWO) algorithm is proposed to determine the DBN structure parameters, which improves the prediction accuracy of PM2.5 concentration and reduces the computation time.
3. The proposed model is successfully applied to the PM2.5 concentration prediction of Baoding city in China where air pollution is particularly serious.  
The rest of this paper is organized as follows. Section 2 is devoted to the description of the DBN and the MGWO algorithm, including how to construct their combination. Section 3 presents the data source and the process of model establishment. Besides, several experiments have been done to validate the effectiveness and superiority of the proposed prediction model. In Section 4, the concluding remarks and future work are given.