# A Hybrid Model for Spatiotemporal Air Quality Prediction Based on Interpretable Neural Networks and a Graph Neural Network

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## Abstract

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## 1. Introduction

- Temporal dependence. Periodicity and trend are the primary ways in which dynamic changes in air quality over time are expressed. Periodicity is the occurrence of similar patterns or regular changes over a certain span of time. As shown in Figure 1a, the air quality index changes periodically over a week (① indicates a period of change). Trend is when a certain data pattern shows a continuous directional development over a certain period of time. Figure 1a shows a downward trend on certain days and for a certain period of time with cyclical changes. As shown in Figure 1b, the air quality index over a day changes with time (② indicates a shift in the trend over a certain amount of time); for instance, air pollutants from a prior or longer period of time have an impact on the current AQI.
- Complex spatiotemporal correlations. In addition to changing dynamically over time, the spatial location also has an impact on air quality. As illustrated in Figure 2, city B’s air quality will be impacted by the atmospheric conditions in city A. Even when taking time into account, the spatial relationship is still challenging.

- An advanced AQP module is constructed, which introduces the extraction of interpretable trends and periodic time series features. In order to thoroughly extract the properties from the data, the interpretation module uses residual connections in conjunction with the trend and periodicity of the time series, to extract the features that are easily missed and are challenging to extract at random moments.
- The INNGNN hybrid model is proposed to perform a spatiotemporal prediction of AQP from time and space dimensions. Graph neural networks (GNN) are used to extract the spatial dependency between different cities, and interpretable neural networks (INN) are used to capture the temporal dependence between the observations made on multiple time scales, and allows for self-attention to acquire the local and global dependence of time. The prediction accuracy of the INNGNN model is enhanced, as shown by its more accurate prediction outcomes in the evaluation we conducted on a Chinese urban air quality dataset.

## 2. Related Work

## 3. Methodology

#### 3.1. Problem Definition

**Definition**

**1:**

**Definition**

**2:**

**Definition**

**3:**

**Definition**

**4:**

#### 3.2. Framework

#### 3.3. Temporal Dependency Modeling

#### 3.3.1. Interpretable Neural Networks

- Trend: The time series of air quality has a certain trend, as shown in Figure 1b. One of the trend characteristics is that it exhibits an upward or downward trend over time. Either a slowly changing function or a monotone function can simulate the trend. A slowly changing function is used here. The formula is described as follows:

- Periodicity: As seen in Figure 1, there is a certain periodicity to the air quality time series (a). Periodic functions can be chosen to mimic the periodicity. Periodicity is defined as recurring or cyclical patterns within a specific time span. The Fourier series is chosen here, and the formula is described as follows:

#### 3.3.2. Time Step Local and Global Dependency Capturing

#### 3.4. Spatial Dependency Modeling

- City grouping: The cities with strong dependencies are assigned to a city group, and each city is mapped onto a city group one by one; this grouping method allows us to identify any potential spatial dependencies between the cities. We use the $\mathsf{\Omega}\in {\mathbb{R}}^{{\mathrm{N}}_{\mathrm{s}}\times {\mathrm{N}}_{\mathrm{u}}}$ matrix to represent the mapping relationship between the cities and city groups. Cities can be assigned to multiple city groups. In order to illustrate the correlation between cities and city groups, $\mathsf{\Omega}$ is randomly initialized during training and optimized at the same time. For the case given, and shown in Figure 7, there are 10 cities divided into 3 city groups, among which the probability of city ${s}_{6}$ being assigned to city group ${u}_{1}$ is 0.1, the probability it of being assigned to city group ${u}_{2}$ is 0.8, and the probability it of being assigned to city group ${u}_{3}$ is 0.1. This shows that city ${s}_{6}$ has a stronger correlation with city group ${u}_{2}$. In order to capture the spatial dependence between the cities, the geographic location $L$ of the city is added, and the process definition for city grouping is as follows:

- Dependencies between city groups: In a city group, the nodes of each city group are fully connected to generate a fully connected undirected graph $\mathrm{g}$, and the dependency relationship between the city groups is modeled through the mechanism of message passing. The modeling process is as follows:

- Dependencies between cities: During city representation, the cities are updated through the process of assigning cities to city groups, and the dependency relationship between the cities is completed through the transmission of messages in city graph $G$, and the message transmission mechanism is similar to that of the city groups. The difference is that the cities incorporate time series features from the temporal dependency module output, geographic location information, and city group information assigned to the city. The specific process is as follows:

## 4. Experiments

#### 4.1. Data Description

- AQI dataset: The data come from the national urban air quality real-time release platform, downloaded from the public platform https://drive.google.com/file/d/1I_vpbLJhOJpNh-TpLdSWsaG3xCpzMVSQ/ (accessed on 15 June 2023.).
- Weather data: Weather data include the humidity, wind direction, rainfall, wind speed, air pressure, temperature, and visibility. The data come from the open platform for environmental big data http://www.envicloud.cn/ (accessed on 15 June 2023).
- Geographic location data: The geographic location of each city is shown in Figure 2. The geographic locations of all the cities are marked on the map with red dots.

#### 4.2. Experimental Settings

#### 4.3. Experimental Results

#### 4.3.1. Comparative Prediction Results

#### 4.3.2. Comparative Analysis: Individual Module vs. Hybrid Model

#### 4.3.3. Ablation Studies

#### 4.3.4. Display and Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Periodicity: air quality changes periodically over a week. (

**b**) Trend: air quality has a tendency to change over a day. The horizontal axis represents time, and the vertical axis represents AQI value.

**Figure 5.**Architecture of interpretable neural networks (INN). : represents the input minus the output of each block; $\oplus $: represents the addition of the output information from each block in every stack with the residual information from the final block, for information aggregation.

**Figure 8.**Comparison of MAE value and RMSE value of prediction results of the INN module, GNN module, and INNGNN model.

**Figure 9.**Correlations between observations and predictions on the test dataset for different components of the model: (

**a**) INNGNN model; (

**b**) INNGNN-INN model; and (

**c**) INNGNN-GNN model. The red dashed line and black solid line are the regression lines, and y = x is the reference line, respectively.

**Figure 10.**Final predictions for city 1 and city 2: (

**a**) city 1 is a city with low-scale fluctuations, and (

**b**) city 2 is a city with high-scale fluctuations. The AQI value was calculated by mapping the concentration values of different pollutants onto indices, calculating the sub-index of each pollutant, and taking the highest value as the AQI value [68].

Model | Metric | 1 h | 2 h | 3 h | 4 h | 5 h | 6 h |
---|---|---|---|---|---|---|---|

INNGNN | MAE | 5.48 | 8.49 | 10.67 | 12.34 | 13.72 | 14.91 |

RMSE | 10.70 | 16.03 | 19.66 | 22.29 | 24.37 | 26.11 | |

DeeperGCN | MAE | 6.54 | 9.74 | 11.77 | 13.40 | 15.29 | 16.41 |

RMSE | 13.67 | 18.93 | 21.14 | 23.83 | 26.25 | 28.02 | |

LSTM | MAE | 6.50 | 10.26 | 13.18 | 15.52 | 17.40 | 18.91 |

RMSE | 13.85 | 19.26 | 23.52 | 26.83 | 29.46 | 31.55 | |

GC-LSTM | MAE | 5.95 | 9.16 | 11.58 | 13.46 | 15.00 | 16.31 |

RMSE | 11.91 | 16.98 | 20.82 | 23.69 | 25.97 | 27.82 | |

GAGNN | MAE | 5.56 | 8.59 | 10.80 | 12.52 | 13.91 | 15.10 |

RMSE | 10.81 | 16.17 | 19.84 | 22.51 | 24.63 | 26.37 | |

SHARE | MAE | 5.84 | 9.07 | 11.49 | 13.35 | 14.74 | 15.79 |

RMSE | 11.27 | 16.84 | 20.77 | 23.60 | 25.80 | 27.38 | |

ST-UNet | MAE | 5.95 | 9.30 | 11.58 | 13.38 | 14.82 | 16.02 |

RMSE | 11.74 | 18.01 | 21.34 | 23.90 | 25.94 | 27.64 | |

XGBoost | MAE | 6.85 | 10.89 | 13.99 | 16.27 | 18.14 | 19.56 |

RMSE | 14.25 | 19.80 | 24.72 | 28.14 | 30.63 | 33.44 | |

HighAir | MAE | 5.50 | 8.52 | 10.81 | 12.50 | 14.00 | 15.09 |

RMSE | 10.80 | 16.10 | 19.85 | 22.70 | 24.91 | 26.40 |

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**MDPI and ACS Style**

Ding, H.; Noh, G.
A Hybrid Model for Spatiotemporal Air Quality Prediction Based on Interpretable Neural Networks and a Graph Neural Network. *Atmosphere* **2023**, *14*, 1807.
https://doi.org/10.3390/atmos14121807

**AMA Style**

Ding H, Noh G.
A Hybrid Model for Spatiotemporal Air Quality Prediction Based on Interpretable Neural Networks and a Graph Neural Network. *Atmosphere*. 2023; 14(12):1807.
https://doi.org/10.3390/atmos14121807

**Chicago/Turabian Style**

Ding, Huijuan, and Giseop Noh.
2023. "A Hybrid Model for Spatiotemporal Air Quality Prediction Based on Interpretable Neural Networks and a Graph Neural Network" *Atmosphere* 14, no. 12: 1807.
https://doi.org/10.3390/atmos14121807