## 1 Introduction  
The aggravation of air pollution significantly impacts various fields worldwide, including air-quality-related disasters. According to the World Health Organization, air pollution exposure causes over 6 million premature deaths [1]. As the extent of air-quality-related damage in South Korea increases, studies on the damage caused by air pollution are essential [2; 3]. As the damage caused by highly concentrated air pollution in South Korea has increased, research related to air pollution has also increased. Therefore, an accurate air pollution forecasting system is needed to reduce indirect damage.  
The forecast has been providing air pollution information since 2014. This information is categorized into six types, including fine dust (PM\({}_{10}\)), fine particulate matter (PM\({}_{2.5}\)), ozone (O\({}_{3}\)), sulfurrous acid gas (SO\({}_{2}\)), nitrogen dioxide (NO\({}_{2}\)), and carbon monoxide (CO), which can be used to predict the value of the comprehensive air-quality index (CAI). However, the accuracy of these forecasts is limited [4].  
Recently, with the progress of computing algorithm technology, deep learning models have begun to be used to analyze and forecast nonlinear relationships between data variables. In a similar way, deep learning models have significantly improved data analysis performance because they provide highly reliable results [5]. In addition, deep learning techniques such as deep neural networks (DNNs) and long short-term memory (LSTM) models have been applied for various purposes in the fields of meteorology, hydrology, precipitation, and drought analysis, including for forecasting [6; 7; 8; 9; 10; 11]. Moreover, over the past decades, many researchers have analyzed and predicted the concentrations of air pollutantsto reduce the damage caused by air pollution and enhance prediction accuracy [12; 13; 14; 15]. In most previous studies, all data from all stations around the study area were considered and used as independent variables. However, in using all of the data from the surrounding stations, distorted results are obtained, since data that are unnecessary for model learning are used.  
Network theory studies graphs that represent either symmetric or asymmetric relations between discrete objects. Network theory is a part of graph theory in computer science and network science: a network can be defined as a graph in which nodes and links have attributes. Network theory has applications in many disciplines, including statistics, computer science, and climatology [16; 17; 18; 19; 20].  
In recent years, kriging has been applied in various research fields owing to its excellent predictive performance, and many studies using kriging have been carried out internationally in areas such as hydrology, meteorology, and environmental science [21; 22; 23; 24; 25]. In particular, kriging has been used to understand the spatial distribution of data and predict the spatial distribution of target factors by integrating various remote sensing data in the fields of hydrology and meteorology [26; 27; 28; 29; 30; 31; 32; 33; 34; 35].  
The number of national air-quality warnings issued in South Korea has gradually increased since 2015. Missing data occur for various reasons at each measuring station when they provide incorrect information. In addition, the prediction forecast is only for each administrative unit and significant region. It is necessary to verify correct information and increase the predictive power. Therefore, a need for the spatial distribution of predictive data has emerged. To overcome these limitations, this study aimed to develop CAI prediction models using deep learning models and the network method. We applied network theory, kriging, LSTM, and DNN models in order to predict CAI changes in South Korea.