A spatiotemporal graph neural network with multi granularity for air quality prediction
Authors: Haibin Liao
Yuan Li
Mou Wu
Hongsheng Chen
Venue: Submitted to ICLR 2023 (2023)
Keywords: Air quality prediction
graph neural network
long short term memory

Abstract: Air quality prediction is a complex system engineering. How to fully consider the impact of meteorological, spatial and temporal factors on air quality is the core problem. To address this central conundrum, in an elaborate encoder-decoder architecture, we propose a new air quality prediction method based on multi-granularity spatiotemporal graph network. At the encoder, firstly, we use multi granularity graph and the well-known HYSPLIT model to build spatial relationship and dynamic edge relationship between nodes, respectively, while meteorological, temporal and topographic characteristics are used to build node features and LSTM (Long Short Term Memory) is used to learn the time-series relationship of pollutant concentration. At the decoder, secondly, we use the attention mechanism LSTM for decoding and forecasting of pollutant concentration. The proposed model is capable of tracking different influences on prediction resulting from the changes of air quality. On a project-based dataset, we validate the effectiveness of the proposed model and examine its abilities of capturing both fine-grained and long-term influences in pollutant process. We also compare the proposed model with the state-of-the-art air quality forecasting methods on the dataset of Yangtze River Delta city group, the experimental results show  the appealing performance of our model over competitive baselines.

Original Manuscript ID: 1215
Original Article Title: "A spatiotemporal graph neural network with multi granularity for air quality prediction"
To: ICLR2023
Re: Response to reviewers
Dear Editors and Reviewers,
We would like to thank you for the time devoted to handling and reviewing our manuscript "A spatiotemporal graph neural network with multi granularity for air quality prediction" submitted to ICLR 2023.
We are particularly grateful for the constructive comments raised by the reviewers for the manuscript, with an opportunity to address the reviewers' comments. We believe that the quality and readability of the revised manuscript have been significantly improved thanks to these valuable comments.
We are uploading (a) our point-by-point response to the comments (below) (response to reviewers) and (b) an updated manuscript.

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Reviewer 1
Reviewer tjqh, Strength And Weaknesses:
Strength:
1. The paper addresses an important problem in air pollutant concentration prediction.
By integrating the mechanical model and machine learning, the work bridges the traditional methods and current trend.
2. The high-level presentation is good which is easy to follow and understand.
3. The experiment solid and comprehensive.
Author response: We are very grateful for your comments and recognition of the
strengths of the manuscript.
Weakness:
1. The paper uses inconsistent terms and symbols, which is confusing at some time For example, R and r are to represent the region in section 3.1, but authors use the same symbol for messages in equation 2, which is a little ambiguous. In figure2, the input data doesn't correspond to the variables in the definition section, would suggest the authors to use consistent symbolic notations for the important features in the both the text and the explanatory figures. Some of the figures need more explanation, e.g., in figurel, the meanings of the axes are unknown. Typo: neighbor node net->neighbor node 2 The novelty is not outstanding. Although integrating the mechanical model and machine lcarning is interesting, most of the techniques are well-established and the authors simply apply them to the new problem. The overall framework is the same as this paper: Jiahui Xu, Ling Chen, Mingqi Lv, Chaoqun Zhan, Sanjian Chen, and Jian Chang. HighAir: A hierarchical graph neural network-based air quality forecasting method. arXiv preprint arXiv: 2101.04264 2021.
Author response:
1. We thank the reviewer for this comment. We have revised the issues of inconsistent terms and symbols, figures explanation, typo and so on. We believe that the quality and readability of the revised manuscript have been significantly improved thanks to these valuable comments.
2. The main contributions of this paper include:
We innovatively propose dynamic spatiotemporal graph model combining
mechanism model and graph neural network. The adjacency matrix and edge weight
vector dynamic graph are constructed based on the simulation results of diffusion,
transport and deposition of polluted air mass by mechanism model, so that the

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architecture learns the spatial influence relationship among multi granularity stations. In order to better learn the temporal patterns and periodicity of pollutants, we propose to add time characteristic attributes of quarter, month, week, hour and holiday to each node in the encoder, use LSTM based attention mechanism for temporal learning in the decoder to enhance MGST-GNN and use new data augmented method to solve the problem of insufficient training data.
As stated in the paper, our model framework refers to HighAir, but our method is very different from Highair:
1. A static graph is built in HighAir, while a dynamic graph is built by HYSPLIT.
Our dynamic graphs are more conducive to learning spatial relationships.
2. In terms of the attributes of graph nodes, we have different geographical
features and add time features.
3. For sequential relationship capture, use the LSTM of the attention mechanism.
Reviewer tjqh, Clarity, Quality, Novelty And Reproducibility: The techniques used in this paper are solid. The overall presentation is good and clear. The originality is average.
Author response: We greatly appreciate your positive comments and
recognition of the paper.
Reviewer tjqh, Summary Of The Review:
This paper is well-written and addresses an important question possibly helping bridge environmental science and machine learning. The work falls short on the technical novelty. However, it's still marginally above the acceptance line.
Author response: We greatly appreciate your positive comments and recognition of the paper.
Reviewer tjqh, Correctness:
3: Some of the paper's claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.
Author response: We are very grateful for your comments on the manuscript.
We have made a lot of endeavors enhance the quality of the manuscript, and revised the manuscript for many times word by word and sorry for that there have

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minor issues that make the paper hard to read. We carried out careful revision which can be seen in the revised manuscript and we hope it reach your standard.
Reviewer tjqh, Technical/ Empirical Novelty And Significance:
2: The contributions are only marginally significant or novel.
Author response: The main contributions of this paper include:
We innovatively propose a dynamic spatiotemporal graph model combining mechanism model and graph neural network. The adjacency matrix and edge weight vector of dynamic graph are constructed based on the simulation results of diffusion, transport and deposition of polluted air mass by mechanism model, so that the architecture learns the spatial influence relationship among multi granularity stations. In order to better learn the temporal patterns and periodicity of pollutants, we propose to add time characteristic attributes of quarter, month, week, hour and holiday to each node in the encoder, use LSTM based on attention mechanism for temporal learning in the decoder to enhance MGST-GNN and use a new data augmented method to solve the problem of insufficient training data.
To our knowledge, no one has yet used the professional air quality model HYSPLIT to dynamically construct the graph structure. Many STGNNs [1, 2, 3] depend on pre-defined graph to indicate the relationship between nodes. However, such a graph is not available or is incomplete in many cases. An intuitive idea is to train adjacency matrix indicates the dependency among nodes. However, since the learning of graph structure and STGNNs are coupled compactly, and there is no supervised loss information for graph structure learning [4]. optimizing such a contiguous matrix usually leads complex bilevel optimization problem [5]. The most important thing is that the adjacency matrix is learned from historical data and cannot adapt smoothly and dynamically according to the change of field conditions.
Fortunately, we can alleviate these problems based on the HYSPLIT. We aim to learn a dynamic graph from field impact factor such as meteorological and topographic conditions, which can be easily extended to other spatiotemporal forecasting tasks. For example, in water quality prediction, professional hydrodynamic model (MIKE) can be used dynamically construct the graph structure, so to better learn the

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influence of water quality in different regions on the prediction points. What is more, in the prediction of traffic flow, professional Traffic Flow Dynamics Model (Traffic Wave Models) can be used to dynamically build the graph structure, so to better learn the influence of different traffic intersections the predicted points.
[1] Yaguang Li, Rose Yu, Cyrus Shahabi, and Yan Liu. 2018. Diffusion Convolutional
Recurrent Neural Network: Data-Driven Traffic Forecasting. In ICLR.
[2]Zonghan Wu, Shirui Pan, Guodong Long, Jing Jiang, and Chengqi Zhang. 2019.
Graph WaveNet for Deep Spatial-Temporal Graph Modeling, In IJCAI.
[3] Chuanpan Zheng, Xiaoliang Fan, Cheng Wang, and Jianzhong Qi. 2020. GMAN: A
Graph Multi-Attention Network for Traffic Prediction. In AAAI.
[4] Haozhe Lin, Yushun Fan, Jia Zhang, and Bing Bai. 2021. REST: Reciprocal
Framework for Spatiotemporal-coupleed Predictions. In The Web Conference.
[5] Luca Franceschi, Mathias Niepert, Massimiliano Pontil, and Xiao He. 2019.
Learning Discrete Structures for Graph Neural Networks. In ICML.
In summary, the main innovations of this paper are the construction of dynamic
graph neural network of spatiotemporal data and the innovative application air quality prediction combining machine learning model and mechanism model. The theme and innovation of this paper are in line with the conference topic and subject areas: applications in audio, speech, robotics, neuroscience, biology, or any other field.
Reviewer 2
Reviewer VRie, Strength And Weaknesses:
Strength:
1. The proposed model is easy to understand and the idea behind partial graph and global graph is explained well.
2. The experimental results contain many ablation study.
Author response: We are very grateful for your comments and recognition of the
strengths of the manuscript.

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Wcaknesses:
The contents of this paper definitely can be organized better.
The experimental results are all in appendixes. The experiments section in main body only have some vague description of the model's performance, c.g. "the MAE decreases about 1.88 and 1.52.... ...", or "MAE decreases about 1.99, 2.09, 0.59...". This is confusing and it's hard for a general reader to understand what these metries mean unless they go to check the tables in the appendix. I'd suggest to make the paper's main body self-contained.
The authors listed many related models in the related work section. However, the differences between existing models and the proposed model were not discussed thoroughly.
2. The experimental results were not presented well. For table 6 in appendix A.6, the first two rows (method MGST GNN) are all bolded. However, it doesn't seem that MGST GNN gets the best metric in each column. For example, under metric=1h, HighAir's MAE is 7.12 while MGST_GGSMM GNN's is 7.16. Under 18t WGGSTGGNNY MAE is 27.92 while HighAir's is 27.49 and ST-UNet's is 27.86. think the tradition is to bold the best metric in the corresponding column.
3. In Appendix A.6 the authors claimed that MGST GNN outperforms the baseline models and provided their explanations. don't think this is very convincing. Even if MGST NGST_GNN gets better results in Table 6, it doesn't imply that, for example, MGST GNN outperforms HighAir model because MGST GNN uses HYSPLIT model. A more promising way is to provide ablation study results on the same dataset.
The proposed model uses HYSPLIT to construct the graphs. Since HYSPLIT is specifically designed for air quality related tasks, how does MGST GNN generalize to other spatiotemporal forecasting tasks? It would be good to see some discussions along this line.
Author response:
1. We have reorganized the paper, and we believe that the quality and readability of the revised manuscript have been significantly improved thanks to these valuable comments. Specifically, the experimental part of the appendix was moved to the paper's main body. At the same time, in order to control the paper's length, the original sections and 2 were merged, and the data enhancement experiment remains in the appendix.
2. Thank you very much for pointing out the error of bold display of the experimental results. We have carefully revised the relevant problems.

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3. In order to further prove the validity of our proposed GNN model (fusion
mechanism model HYSPLIT and machine learning STGNN), an ablation experiment analysis is provided in the appendix.
4. In this paper, we are the first to use the professional model HYSPLIT build the graph dynamically, and we have proved its effectiveness through experiments. This method eliminates the construction process of specially designed auxiliary network to learn the edges of graph and provides a new way for the construction of graph neural network, which can be easily extended to other spatiotemporal forecasting tasks. For example, in water quality prediction, a professional hydrodynamic model (MIKE) can be used to dynamically construct the graph structure, as to better learn the influence of water quality in different regions on the prediction points. What is more, in the prediction of traffic flow, professional Traffic Flow Dynamics Model (Traffic Wave Models) can be used to dynamically build the graph structure, so as to better learn the influence of different traffic intersections on the predicted points.
Reviewer VRie, Clarity, Quality, Novelty And Reproducibility
think in its current form, this paper has quite lot of improvement space for its clarity and quality. seems that both codes and datasets are not open sourced, I'm not confident about its reprodueibility.
Author response: We have made lot of endeavors to enhance the quality of the manuscript, and we believe that the quality and readability of the revised manuscript have been significantly improved thanks to these valuable comments. The code is released on GitHub, which it provides a way to obtain datasets. Because of anonymous review, was not shown in the manuscript.
Reviewer VRie, Summary Of The Review:
There are lot of improvements that can be made in this paper's organizations, experimental results presentations and discussions. think it's not ready yet.
Author response: We have reorganized the paper and made a lot of endeavors
to enhance the quality of the manuscript. we believe that the quality and readability of the revised manuscript have been significantly improved thanks to these valuable comments.

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Reviewer VRie, Correctness:
3: Some of the paper's claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.
Author response: We are very grateful for your comments on the manuscript. We have made a lot of endeavors to enhance the quality of the manuscript, and revised the manuscript for many times word by word and sorry for that there have minor issues that make the paper hard read. We carried out careful revision which can be seen in the revised manuscript and we hope it reach your standard.
Reviewer VRie, Technical/ Empirical Novelty And Significance:
2: The contributions are only marginally significant or novel.
Author response: The main contributions of this paper include:
We innovatively propose a dynamic spatiotemporal graph model combining mechanism model and graph neural network. The adjacency matrix and edge weight vector of dynamic graph are constructed based on the simulation results of diffusion, transport and deposition of polluted air mass by mechanism model, so that the architecture learns the spatial influence relationship among multi granularity stations. In order to better learn the temporal patterns and periodicity of pollutants, we propose to add time characteristic attributes of quarter, month, week, hour and holiday to each node in the encoder, use LSTM based on attention mechanism for temporal learning in the decoder to enhance MGST-GNN and use a new data augmented method to solve the problem of insufficient training data.
To our knowledge, no one has yet used the professional air quality model HYSPLIT to dynamically construct the graph structure. Many STGNNs [1, 2, 3] depend on pre-defined graph to indicate the relationship between nodes. However, such a graph is not available or is incomplete in many cases. An intuitive idea is to train adjacency matrix indicates the dependency among nodes. However, since the learning of graph structure and STGNNs are coupled compactly, and there is no supervised loss information for graph structure learning [4], optimizing such a contiguous matrix usually leads complex bilevel optimization problem [5]. The most important thing is that the adjacency matrix is learned from historical data and cannot adapt smoothly and dynamically according to the change of field conditions.

---

Fortunately, we can alleviate these problems based on the HYSPLIT. We aim to learn dynamic graph from field impact factor such as meteorological and topographic conditions, which can be easily extended to other spatiotemporal forecasting tasks. For example, in water quality prediction, a professional hydrodynamic model (MIKE) can be used dynamically construct the graph structure, so as to better learn the influence water quality different regions on the prediction points. What is more, in the prediction of traffic flow, professional Traffic Flow Dynamics Model (Traffic Wave Models) can be used to dynamically build the graph structure, so as to better learn the influence of different traffic intersections on the predicted points.
[1] Yaguang Li, Rose Yu, Cyrus Shahabi, and Yan Liu. 2018. Diffusion Convolutional
Recurrent Neural Network: Data-Driven Traffic Forecasting. In ICLR.
[2]Zonghan Wu, Shirui Pan, Guodong Long, Jing Jiang, and Chengqi Zhang. 2019.
Graph WaveNet for Deep Spatial-Tempora Graph Modeling. In IJCAI.
[3] Chuanpan Zheng, Xiaoliang Fan, Cheng Wang, and Jianzhong Qi. 2020. GMAN: A
Graph Multi-Attention Network for Traffic Prediction. AAAI.
[4] Haozhe Lin, Yushun Fan, Jia Zhang, and Bing Bai. 2021. REST: Reciprocal
Framework for Spatiotemporal-coulleed Predictions. In The Web Conference.
[5] Luca Franceschi, Mathias Niepert, Massimiliano Pontil, and Xiao He. 2019.
Learning Discrete Structures for Graph Neural Networks. In ICML.
In summary, the main innovations of this paper are the construction of dynamic graph neural network of spatiotemporal data and the innovative application of air quality prediction combining machine learning model and mechanism model. The theme and innovation of this paper are in line with the conference topic and subject areas: applications audio, speech, robotics, neuroscience, biology, or any other field.
Reviewer 3

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Reviewer mQij, Strength And Weaknesses:
Strength:
The topic of air quality prediction is of great social impact.
Author response: We are very grateful for your comments and recognition of the
strengths of the manuscript.
Weaknesses:
The format of the paper is unprofessional. All the experimental results are in the appendix.
2. Figures are in poor resolution. Please use vectorized images for professional academic writing.
The technical contribution is limited. The settings of LSTM, GNN, and attention mechanism are commonly used for air quality prediction. The motivation of multi-granularity also has been studied thoroughly for spatial-temporal forecasting. 4. The experiment cannot fully support the validity of the model. Air quality prediction is inherently a time series prediction task. Time series forecasting models, such as N-BEATS, autoformer, informer, etc, expected to compare.
Author response:
1. We have reorganized the paper, and we believe that the quality and readability of the revised manuscript have been significantly improved thanks to these valuable comments. Specifically, the experimental part of the appendix was moved to the paper's main body. At the same time, in order to control the paper's length, the original sections and 2 were merged, and the data enhancement experiment remains in the appendix.
2. Thank you very much for your reminding. We have provided higher resolution illustrations in the revised manuscript. Once the paper is accepted, we will also provide the original drawing.
3. In this paper, we integrate the mechanism model and the popular machine learning model organically for the first time, and overcome the shortcomings of the mechanism model and machine learning respectively. The main contributions of this paper include:
We innovatively propose a dynamic spatiotemporal graph model combining mechanism model and graph neural network. The adjacency matrix and edge weight vector of dynamic graph are constructed based on the simulation results of diffusion, transport and deposition of polluted air mass by mechanism model, so that the

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architecture learns the spatial influence relationship among multi granularity stations. In order to better learn the temporal patterns and periodicity of pollutants, we propose to add time characteristic attributes of quarter, month, week, hour and holiday to each node in the encoder, use LSTM based attention mechanism for temporal learning in the decoder to enhance MGST-GNN and use new data augmented method to solve the problem of insufficient training data.
To our knowledge, no one has yet used the professional air quality model HYSPLIT to dynamically construct the graph structure. Many STGNNs depend on a pre-defined graph to indicate the relationship between nodes. However, such a graph is not available or is incomplete in many cases. An intuitive idea is to train an adjacency matrix indicates the dependency among nodes. However, since the learning of graph structure and STGNNs are coupled compactly, and there is supervised loss information for graph structure learning, optimizing such a contiguous matrix usually leads to complex bilevel optimization problem. The most important thing is that the adjacency matrix learned from historical data and cannot adapt smoothly and dynamically according to the change of field conditions. Fortunately, we can alleviate these problems based on the HYSPLIT. We aim to learn a dynamic graph from field impact factor such as meteorological and topographic conditions, which can be easily extended to other spatiotemporal forecasting tasks. For example, in water quality prediction, professional hydrodynamic model (MIKE) can be used to dynamically construct the graph structure, so to better learn the influence of water quality in different regions on the prediction points. What is more, in the prediction of traffic flow, professional Traffic Flow Dynamics Model (Traffic Wave Models) can be used to dynamically build the graph structure, so as better learn the influence of different traffic intersections on the predicted points.
4. The method in this paper is based on spatiotemporal graph neural network, and its main innovation point is how to construct dynamic graph. Therefore, in the experimental part, due to the limitation of the length of the conference paper, we only compared with the current advanced graph model.

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Reviewer mQij, Clarity, Quality, Novelty And Reproducibility:
The writing easy to follow. But the novelty is limited. We have concerns about the reproducibility, because the hyperparameter setting is not provided.
Author response: We have made lot of endeavors to enhance the quality of the
manuscript, including innovative statement and experimental super-parameter setting.
The code is released on GitHub. Because of anonymous review, it was not shown in the manuscript.
Reviewer mQij, Summary Of The Review:
The topic is important. But the novelty is limited, the experiment is weak. The paper needs lots of effort to improve.
Author response: We have reorganized the paper and made a lot of endeavors
to enhance the quality of the manuscript. We believe that the quality and readability of the revised manuscript have been significantly improved thanks to these valuable comments.
Reviewer mQij, Correctness:
3: Some of the paper's claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.
Author response: We are very grateful for your comments on the manuscript. We have made a lot of endeavors to enhance the quality of the manuscript, and revised the manuscript for many times word by word and sorry for that there have minor issues that make the paper hard read. We carried out careful revision which can be seen in the revised manuscript and we hope it reach your standard.
Reviewer mQij, Technical/ Empirical Novelty And Significance:
2: The contributions are only marginally significant or novel.
Author response: The main contributions of this paper include:
We innovatively propose a dynamic spatiotemporal graph model combining
mechanism model and graph neural network. The adjacency matrix and edge weight vector of dynamic graph are constructed based on the simulation results of diffusion, transport and deposition of polluted air mass by mechanism model, that the architecture learns the spatial influence relationship among multi granularity stations.
In order to better learn the temporal patterns and periodicity of pollutants, we propose to add time characteristic attributes of quarter, month, week, hour and

---

holiday to each node in the encoder, use LSTM based on attention mechanism for temporal learning in the decoder to enhance MGST-GNN and use new data augmented method to solve the problem of insufficient training data.
To our knowledge, no one has yet used the professional air quality model HYSPLIT to dynamically construct the graph structure. Many STGNNs [1, 2, 3] depend on a pre-defined graph indicate the relationship between nodes. However, such a graph is not available or incomplete many cases. An intuitive idea is to train an adjacency matrix indicates the dependency among nodes. However, since the learning of graph structure and STGNNs are coupled compactly, and there is no supervised loss information for graph structure learning [4], optimizing such a contiguous matrix usually leads to complex bilevel optimization problem [5]. The most important thing is that the adjacency matrix is learned from historical data and cannot adapt smoothly and dynamically according to the change of field conditions. Fortunately, we can alleviate these problems based on the HYSPLIT. We aim to learn a dynamic graph from field impact factor such as meteorological and topographic conditions, which can be easily extended to other spatiotemporal forecasting tasks. For example, in water quality prediction, a professional hydrodynamic model (MIKE) can be used to dynamically construct the graph structure, so as to better learn the influence of water quality in different regions on the prediction points. What is more, in the prediction of traffic flow, professional Traffic Flow Dynamics Model (Traffic Wave Models) can be used to dynamically build the graph structure, so to better learn the influence of different traffic intersections the predicted points.
[1] Yaguang Li, Rose Yu, Cyrus Shahabi, and Yan Liu. 2018. Diffusion Convolutional
Recurrent Neural Network: Data-Driven Traffic Forecasting. In ICLR.
[2]Zonghan Wu, Shirui Pan, Guodong Long, Jing Jiang, and Chengqi Zhang. 2019.
Graph WaveNet for Deep Spatial-Temporal Graph Modeling. In IJCAI.
[3] Chuanpan Zheng, Xiaoliang Fan, Cheng Wang, and Jianzhong Qi. 2020. GMAN: A
Graph Multi-Attention Network for Traffic Prediction. In AAAI.
[4] Haozhe Lin, Yushun Fan, Jia Zhang, and Bing Bai. 2021. REST: Reciprocal
Framework for Spatiotemppral-coupleed Predictions. In The Web Conference.

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[5] Luca Franceschi, Mathias Niepert, Massimiliano Pontil, and Xiao He. 2019.
Learning Discrete Structures for Graph Neural Networks. In ICML.
In summary, the main innovations of this paper are the construction of dynamic graph neural network of spatiotemporal data and the innovative application of air quality prediction combining machine learning model and mechanism model. The theme and innovation of this paper are in line with the conference topic and subject areas: applications audio, speech, robotics, neuroscience, biology, or any other field.
We really appreciate the helpful comments of the referees and hope that we have produced better account of our work now. We believe that the revised manuscript is acceptable for publication.
Sincerely yours, The authors

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Under review conference paper ICLR 2023
A SPATIOTEMPORAL GRAPH NEURAL NETWORK WITH MULTI GRANULARITY FOR AIR QUALITY PREDICTION
Anonymous authors Paper under couble-blind review
ABSTRACT
Air quality prediction is complex system engincering. How to fully consider the impact of meteorological, spatial and temporal factors on air quality is the core problem. To address this central conundrum, in an elaborate encoder-decoder architecture, we propose a new air quality prediction method based on multi- granularity spatiotemporal graph network. At the encoder, firstly, we use multi granularity graph and the well-known HYSPLIT model build spatial relation- ship and dynamic edge relationship between nodes, respectively, while metcoro- logical, temporal and topographic characteristies are used to build node features and L.STM (Long Short Term Memory) is used to learn the time-series relation- ship of pollutant concentration. At the decoder, secondly, we use the attention mechanism LSTM for decoding and forecasting of pollutant concentration. The proposed model is capable of tracking different influences on prediction result- ing from the changes of air quality. On a project-based dataset, we validate the effectiveness of the proposed model and examine its abilities of capturing both fine-grained and long-term influences in pollutant process. We also compare the proposed model with the stateoof-the-an air quality forecasting methods on the dataset of Yangtze River Delta city group, the experimental results show the ap- pealing performance of our model over competitive baselines.
INTRODUCTION
Air quality which is closely related to human public health, has been common research hotspot focused by scholars all over the world. At present, large number of air quality monitoring stations (stations for short) have been built in major cities to monitor the concentration of air pollutants (PM2.5, PMI0, Og, etc.) and meteorological parameters (temperature, pressure, wind speed, wind direction, humidity, etc.). However, these stations only can monitor real-time air quality, and fail to provide air quality prediction (AQP) and auxiliary support for urban intelligent decision makiin or activity planning. How to construct an AQP model using a large amount of historical monitoring data has become hot research topic in the field of environmental engineering. Unfortunately. AQP an extremely complex system engineering. On the one hand, air quality is related to pollutant emission, which is a type of time sequence and has periodicity; On the other hand, there exist physical and chemical changes of pollutants in the air, such diffusion and deposition, which are greatly affected by meteorological and geographical locations; Finally, air quality also certain probability, such as unexpected pollution leakage events will lead to a sharp decline in air quality.
The commonly used types of AQP include mechanism model (MM) and machine learning (ML) methods. The MM method Intira all (20T))) Zhang (Iлл);;; Arystanbekova (ΑIлс);; Stem all (2U15);; Wang et all (20T2)); ei all (M)), also known as numerical model, uses atmospheric physical and chemical reactions to model the emission and diffusion process of air pollutants, and then carries out AQP. For example, Gaussian diffusion models of AERMOD and ADMS, Lagrange models of CALPUFF and HY SPLIT can be applied to small-scale and medium AQP [mira et all (20)): and the third generation air quality models Zhang (2(11)) such as CMAQ, CAMX, WRF. CHEM, NAQPMS, and so on can be applied to predict large-scale air quality. However, most of MM methods require many empirical parameters and assumptions, which are prone to be reliable for a specific environment but not for all urban environments YrAaиl (20T)). For example, AERMOD is empirical model which is mainly applicable to small-scale air diffusion simulation and pollutant

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Under review as conference paper ICLR 2023
forecasting. And the third generation air quality model needs comprehensive and accurate source list and meteorological field data as input to predict, and its application is limited.
With the development of deep learning, AQP methods based on ML have attracted more attention Y ELaI (R(TS); etal (λлда). The AQP method based on MI. takes advantage of large number of
historical observation data for training and testing, finding out the change law pollutant concen- tration, and then predicts the air quality, which include linear statistical models Mossan ci al (20))). fitting optimization techniques al (201)), and deep learning methods Ma all (M Since deep learning has a powerful function to automatically extract nonlinear features, recent literatures about AQP often rely on deep learning models. Zhang et al. Zhang et all (M))) proposed deep learning AQP method combining CNN (Convolutional Neural Network) and LSTM (Long Short Term Memory), which achieved good results and made scholars see the dawn of the application of deep learning in AQP. Subsequently, Du et al. Ductall (2111) used one-dimensional CNN to capture local time trend and bidirectional LSTM to extract long-ten -eem time series features, and then to con- struct hybrid neural network for AQP. Liang et al. [rang et all (AUN) proposed GeoMAN based on LSTM and encoder-decoder architecture for AQP, and took advantage of the attention mecha- nism capture the spatial impact relationship among different stations. Yi et al. Yi (MTT)) proposed the DeepAir model to construct sub-network with multi-source data, and used the fusion network to integrate the results of different sub-networks to obtain the final predicted value. The above methods captured temporal correlation well by LSTM, but their capture of spatial relation- ship was obviously insufficient. Although CNN can he used to establish spatial relationships, it is a static spatial relationship. and the distance among stations is fixed. Due to the influence of weather and terrain, the spatial relationship among stations is not simple static distance relationship, but a dynamic. In addition, the stations in the city are unevenly distributed and sparse, so interpolation is required in the construction of CNN, resulting in a large number of virtual stations, which will affect the forecasting results.
In contrast, graph-based models naturally sidestep the above issue since they shape the concentration values into graph nodes and keep their original distributions in graph structures. Because graph has the ability to construct non Euclidean entity distribution, it can capture spatial relationships well. Thus, in order compensate for the lack of spatial relationship learning in the above methods, the methods based on GNN (Graph Neural Network) are applied to AQP. Qi et al. Qt (2M)) used GNN to learn the spatial relationship among stations, and LSTM to learn the time correlation of stations,
build comprehensive forecasting model GC-LSTM. Lin et al. Lin et all (RUE) used diffusion convolution operation to replace matrix multiplication in GRU (Gate Recurrent Unit) for sequence modeling, and combined with graph convolution operation to build GC-DCRNN for AQP. Xu et al. all (εиz))) proposed ST-MFGCN for AQP, Its main innovation is to obtain the spatiotemporal variation law of vehicle emissions by building a graph structure traffic network, and then predict traffic pollution emissions. Xu et al. Xu all (2/22) proposed HighAir, i.e. hier- archical graph neural network-based AQP method, which adopted an encoder-decoder architecture and considered complex air quality influencing factors, c.g., weather and land usage.
The above methods based on GNN use graph structure to effectively construct the spatial relationship among stations, but they fail to fully construct the edges in the graph structure. For example, litera- ture Ku all (RIZIT simply used distance and wind direction similarity to construct edge weights. In order to better build the edge relationship. Wang et al. WWan et all (λллл)) identified a set of critical domain knowledge for PM2.5 forecasting and developed a novel graph based model, PM2.5- they used domain knowledge (Wind speed and directiondistance, advection coefficient) to construct edge weights. Although they make use of domain knowledge, they simply list some impact fac- tors, which is not enough. The pollution impact relationship among stations is comprehensively determined by meteorological conditions (wind speed, wind direction, pressure, humidity, planetary boundary layer height, etc.) and landform. It is a complex process and needs to be analyzed by using professional models.
According to the existing research status, we can know that machine learning is novel AQP method based on data-driven strategy, which can effectively capture the regularity and time periodicity of pollutant concentration changes and has the characteristics of simplicity, flexibility and rapid deploy- ment. However, these methods unable to timely capture the regional impact and sudden change caused by the pollutant diffusion in the air. On the other hand, the traditional mechanism model based on the principle of atmospheric diffusion can hetter simulate the impact of surrounding areas on the forecasting points. Motivated by the above considerations, use the LSTM (Long Short

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Under review conference paper ICLR 2023
Table 1: Quarter feature representing method
Spring
Summer
Fall
Winter
spring season
0
summertime autumn
0
0
wintertime
0
0
Term Memory) model to learn the timing and periodicity of pollutant concentration, and use the GN- N (Graph Neural Network) model learn the spatial relationship of pollutants among stations, and thus building a multi granularity spatiotemporal graph neural network model, called MGST-GNN. In order to better capture the mutation of pollutant concentration and its impact on air diffusion and deposition, the mechamism model HYSLPLIT is used dynamically construct the adjacency matrix and edge relation of the spatiotemporal graph. The main contributions of this paper include:
We innovatively propose a dynamic spatiotemporal graph model combining mechanism model and graph neural network. The adjacency matrix and edge weight vector of dynamic graph are constructed based the simulation results of diffusion, transport and deposi- tion of polluted air mass by mechanism model, so that the architecture learns the spatial influence relationship among multi granularity stations.
In order better learn the temporal patterns and periodicity of pollutants, we propose add time characteristic attributes quarter, month, week, hour and holiday to each node the encoder, use LSTM based on attention mechanism for temporal learning in the decoder enhance MGST-GNN and use new data augmented method solve the problem of insufficient training data.
2 PRELIMINARY
2.1 RELATED CONCEPTS AND PROBLEM DEFINITION
set R fra, S a N} as set of N regions, L i [S.1] as a set of stations region ra. laa = (la.i, 1 I iis S [Sa]] as a location set of stations in region ra, where la.5 is composed of longitude and latitude of a station, and lo is the mean value of la in la-- Note: According to different application scenarios, the region referred to this paper can be a national region, city region or an administrative region, etc.
Definition 1 Region and Stations:
{La 1 S N} as a location set of N regions, S,
Definition 2 Time Feature (TF): TF includes five features: quarter, month, week, hour and holiday. We represent the quarter by using one-hot encoding adopted for 4-bit binary representation, as shown Table M.
Similarly, the month is represented with 12-bit binary by one-hot encoding; week is represented with 7-bit binary by one-hot encoding; Hour is represented with 24-bit binary code by one-hot coding mode; Holiday represented with 2-bit binary by one-hot coding (0 means non-holidays. means holiday).
Definition Geomorphic Feature (GF): GF contains the topography and land usage information of station, which consider the altitude and five land usage categories: residential area, park, mountain, water (river or pool), and industry. Where, the altitude divided into four categories: very high (more than 1300m), high (1000-1300m), medium (500-1000m) and low (less than 500m), and the corresponding categories are represented by the numbers 1, 2. 3 and 4; The land usage type is determined by the number of major land use types within km around the station. For example, the altitude of 8a.i is 800 meters, and there is one residential area, two park, one mountain, three pool, and two industrial facilities within the perception radius 10 kilometers of Sa,z. Thus, the GF vector gfa, i can be represented as [3, 1, 2, 1, 2].
Definition 4 Weather Data (WD): The WD of region та and stations stations s., at time slot t are represented as the vectors wd", and wa including temperature, humidity, rainfall, wind speed, wind direction, and air pressure.

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Under review conference paper ICLR 2023
NOAA HYSPLIT MODEL May
travectories
01 iInnn Forecast Inttiizzal
Starte al C8SSN 1103/W
Mokes ACL
1000
Figure 1: Trajectory analysis chart (Different colored lines in the figure represent trajectories of dif- ferent heights. The points on each line represent the location of the trajectory, which is represented by latitude and longitude.)
The pollutant concentration data includes the con- centrations of six major pollutants such PM2.5, PMIO, SO2, CO2. CO and O3. Among them, PM2.5 and O3 are the most concerned at present. Therefore, the later experiments focus on the concentration prediction of these two pollutants.
Definition 5 Pollutant Concentration Data:
(DT)) is complete system for computing simple air parcel trajectories, as well complex transport, dispersion, chemical trans- formation, and deposition simulations. HYSPLIT continues to be one the most extensively used atmospheric transport and dispersion models in the atmospheric sciences community. A common application is back trajectory analysis determine the origin of air masses and establish source- receptor relationships. HYSPLIT has also been used in a variety of simulations describing the atmospheric transport, dispersion, and deposition of pollutants and hazardous materials.
Definition 6 HYSPLIT: HYSPLIT Stein ef all (2015)) Warmer
In this paper, HYSPLIT is used to establish the source-receptor relationship among nodes by trajec- tory analysis. When HYSPLIT used for trajectory analysis, it only needs input the meteorolog- ical data of the simulation area and the coordinate information of the initial point of the simulation. The meteorological data can be downloaded from the official website of Air Resources Laboratory (ARL) 0 for free. Fig. M shows an example of trajectory analysis using HYSPLIT. The example takes Beijing Center (116920', 56') as the starting point and 10:00 on May 6, 2022 as the starting time predict the air mass trajectory in the next 48 hours. It can be seen from Fig. M that the location and time of each track can be obtained by HYSPLIT.
2.2 PROBLEM STATEMENT
AQP task: Given region locations L, station locations geomorphic feature data gfa.. Tin hours of pollutant concentration data con, and Tin + Tout hours of weather data re,, the AQP task aims to forecast the pollutant concentrations of stations for the next Tout hours, where Tin denotes the length of historical time window and Tout denotes forecasting horizon.
3 METHODOLOGY
3.1 AQP MODEL FRAMEWORK
Existing AQP methods based on GNN Dulttal (MI)) Cin (20N) mostly simulate the spatial relations among stations by constructing flat static graph. However, due the distance among sta- tions and terrain, it is difficult to transfer information among stations in different regions through flat graph. In addition, the spatial relationship among stations is greatly affected by the dynamic wind

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Under review conference paper ICLR 2023
direction, wind speed and other meteorological parameters, so it is difficult construct edge relationship by means of static graph. Finally, pollutant concentrations at different time in history have different impacts on current air quality. In order to overcome the shortcomings of flat static graphs, we build meoder-decoder architecture based on dynamic multi gulli-granularity spatiotem- poral graph by referring to literature Wang et all (2020), as shown in Figure Q the encoding stage, multi-grandn granularttll graph network is used to learn the spatial relationship among stations and LSTM network is used learn its temporal relationship. In the decoding stage, auxiliary data and attention mechanism are used to enhance LSTM forecasting learning and decade the future pollutant concentration value. This framework fully considers three key factors affecting air quality, name- ly. meteorology, space and time. Among them, the multi- granularity spatiotemporal graph neural network (as shown in Figure + is the focus.
Eaooder
Doonder
Tarel
Murii granaiarity
graph netbaadt
ESTM
LSTM
Tongroa!
Mull-granuarrtty
grophe
AURE Sata
LSTM
FX
Mari Mult-granubrrtt griph networlt
ESTM
ISTM
Mart- Muit-granularity
groph
LITM
LSTM
FOL
Mali gronuaaiity spetotampond gragh network
Tempora attendor mechoniom based ISTM
Figure 2: Framework diagram of AQP model
LSTM
Partia graph
graph
Upper dkliery
updattegg
Figure 3: Multi-gramularity spatiotemporal graph neural network
3.2 SPATIOTEMPORAL GRAPH CONSTRUCTION
We propose a multi-granularig spatiotemporal graph network (MGST GNNN by referring to refer- XX all (ИЛЛл)) Assume that V the set of nodes, E is the of connected edges among nodes, and u is the global attribute of a station-level partial subgraph. Global graph and partial subgraph interact through message passing mechanism. Partial subgraph's information is upper de- livered to the global graph; the global graph's information transmitted downward to the partial subgraph. each time period, MGST GNN will calculate the attribute information of each global node and use to update the corresponding partial node attribute. For each region of the partial sub- graph, calculate the overall air quality information representation of the regions each time slot,

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Under review conference paper ICLR 2023
forming a sequence sent to the LSTM to get the representations of current and historical pollutant concentration.
Taking the AQP of all stations in a city as example, all stations in the city are clustered according their longitude and latitude information to obtain N categories, that is, N regions clustered. Therefore, each region can regarded as node the global graph, while each station in the region can be regarded as node in the partial subgraph. A graph composed of region-level nodes is called a global graph, while graph composed of station-level nodes is called a partial subgraph. From this, graniarrttlrrty graph network can constructed, as shown in Figure EI where the coarse-gan carse-grained graph is region-level global graph and the fine-gratt line-grained graph is a station-level partial subgraph.
3.2.1 ATTRIBUTE DEFINITION OF GRAPH NODE
To the node in the global graph, its attribute is the pollutant concentration value of the node region. To the node in partial subgraph, its attribute is composed of the pollutant concentration value of the node station, GF and TF.
3.2.2 EDGE AND ATTRIBUTE DEFINITIONS OF GRAPHS
Wind speed, wind direction, rainfall and other meteorological data have a decisive influence on the horizontal transmission of pollutants. In order to make use of this domain knowledge, we adopt the air quality model HYSPLIT to learn the relationship among nodes and build dynamic connection edges. Taking the edge calculation of global graph as an example, the city is divided into grids according to the clustered regions, so that each region falls into unique grid. For each region (node va), HYSPLIT is used calculate all trajectories starting from Uo and stepping in hours within the next time f. With HYSPLIT, we can track the time when each trajectories crosses the grid where the node is located, and record the number of pass trajectories and crossing time of the grid from other nodes except lha and dynamically construct the global connection edge and its attribute vector. Repeating these steps until each station is analyzed as starting point, For example, taking as the starting point, using HYSPLIT to calculate that there are trajectories passing through ty in the following 48 hours, and the time interval I hour, 3 hours, 4 hours, 8 hours and 48 hours in the future, then the edge relationship between node 21 and U2 is formed, and its attribute vector is: 0,
= [1, 0, 1, 0, O, 0, 1, O, O, O, O, O, O, O, O, 0, O, 0, O, O, O, 0, 0, O, 0, get the specific impact time of node Y1 to U2. It is dynamic, specific and accurate edge attribute, which is calculated by the mechanism model according to the metcorological conditions and geographical location. Station- level partial subgraph edge and attribute calculation similar.
0, 0, 0. 0,000,000000,,,00000 0, 0, 1]. From e12,
Figure 4: Multi-granularity graph structure
3.3 MODELING OF SPATIAL DEPENDENCIES
MGST GNN can model spatial dependencies with different granularities by message passing mech- anism, which mainly includes message aggregation and description updating. Message aggregation shown as follows:

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Under review conference paper ICLR 2023
Ma = [1 Car (a,e)
(I)
ma (M,)
(2)
where Mr denotes the of all the messages passed to node Vai Fa the attribute of node va 2 the attribute a neighhor node; 6a.s is the edge attribute; ((a) denotes the neighbor node net of node va (dynamically determined by HYSPLIT trajectory); my is the aggregation vector of node Va; (-) denotes aggregate function.
Description updating shown as follows
1/g di(mar Ja. $2 Fa,i, ua), in partial graph
in global graph
(3)
where Φ1 and 62 denote update functions: Ma,s is the aggregation vector of node ta, in the a-th partial subgraph: Ta.; is the attribute of node Ca,5 is the global attribute of a-th partial subgraph: Φ and 2 can be implemented by using different FNNs.
Partial graph
Global graph
1-tnt1
Figure 5: Message aggregation diagram
The specific message aggregation method from the partial subgraph the global graph, as shown in Figure EL The information transmitted from the partial subgraph includes the current and historical pollutant concentration values, and the average method is adopted to aggregate the information transmitted from the partial subgraph:
con mean(con
S i
(4)
where con', denotes the aggregate value at time of node va in the global graph; con',, denotes the pollutant concentration value at time of node Ua,; in the a-th partial subgraph: |Sa is the number of nodes in the a-th partial subgraph.
For nodes in the global graph, message aggregation is used calculate the global repre- sentation pollutant concentration in each time slot, thus forming a series sequences {con F- cont LSTM learn the current and historical representations. The notation à in Figure represents the hidden layer state each slot I.STM, global graph, so the global graph includes current and historical information.
con', < < N}. These sequences are then fed into the global
is taken as the initial attribute nodes in the
The specific updating method is to update the partial subgraph by using the global graph, as shown Figure E The information transmitted from the global graph includes the historical pollutant concentration values all regions. At each time slot, the output of the global graph is fed into the FNN to obtain a downward update vector, which is used to update the global attribute u of the partial subgraph. The includes meteorological parameters and downward update vector, which used

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Under review conference paper ICLR 2023
the partial subgraph by message passing. Therefore, the nodes the station-level partial subgraph can make use of the historical information of neighbor nodes in the region-level global graph.
Partial graph
ENNN
ENNN
FNN
Global graph
Figure 6: Description updating chart
3.4 MODELING OF TEMPORAL DEPENDENCIES
In order to capture the temporal dependence, we adopt an encoder-decoder architecture, shown in Figure M1 In each time slot, node attributes in the partial subgraph form sequence Xa.i [xl_ ----- 1-7xx ..... 2x4 < S N. < < [S.]]. That is, each time slot in the historical a corresponding node attribute. The LSTM state of the LSTM is used as the input of the decoder. The input of the LSTM in the decoder includes not only the output of the encoder, but also the node attribute in the partial subgraph. The output of LSTM in the decoder used the input of FNN, and FNN outputs the predicted pollutant concentration value in the future Tax time slot.
encoder uses Xa.;
input and final
In order to make better use of temporal characteristics, temporal attention mechanism is introduced the decoding stage learn the dynamic temporal correlation between future time and historical
time. Give the hidden state / and cell state - of the LSTM in the decoder time t - 1, then
at time& the attention weight of the hidden state he output by the encoder calculated as follows:
d3 TT tanh(W
11 1: Uh. b)
(5)
exp(pt)
1 EL exp(op)
(6)
where X,, is the attention weight; v. b, W, U are the parameters to be learned. Through the above formulas and R the attention weight of all historical hidden states in encoder can calculated, and then, the hidden state ht is weighted and summed to obtain the time context vector e
h
The output result - of decoder time o' 1. the metcorological data wd,- at time f' the time feature tf., and the time context vector o, are connected as the input for the LSTM the decoder at time and it used to update the hidden state hy:
b46 LSSMM(, To wd (..
(8)

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Under review conference paper ICLR 2023
4 EXPERIMENTS
4.1 EXPERIMENTAL DATASETS
4.1.1 JINAN DATABASE (JN)
Jinan database is a city-level data set collected by us in projects. Jinan is located in the mid- dle of Shandong Province, China. Its geographical position is between 36'01' ~ 37' N and 116 117 44' E. distributed in narrow and long terrain with total area of 7998 square kilometers. There are 130 air monitoring stations in Jinan. Each station outputs the concentration values of pollutants (PM2.5, PM10, SO2, CO2, CO, Og) and meteorological parameters (rainfall, surface pressure, temperature, humidity, wind speed and wind direction) every hour. We collected the historical monitoring data of 30 stations in Jinan from January 1st, 2019, to January 1st, 2022, the training and test set.
We divide the 130 stations into 13 regions, and the global graph consists of 13 regions. Each region is used as a global node in the global graph. The stations in each region form a partial subgraph, and the stations in the region are the nodes of the partial subgraph.
4.1.2 YANGTZE RIVER DELTA CITY GROUP DATABASE(YRD)
The city group contains cities: Shanghai. Hangzhou. Suzhou, Ningbo, Shaoxing, Jiaxing, Wuxi, Zhoushan, Nantong, and Huzhou. We used Air Pollution Prediction system to collect historical pollutant concentration values and meteorological parameters of corresponding stations, and the time span was from January 1th, 2019, to December 3 11th, 2022. Therefore, collected years of historical monitoring data as the training and test set. Each city in the Yangtze River Delta city group is a global graph node, and each station in the city is a node of the corresponding partial subgraph.
Geographic features and weather forecast data are obtained by:
Geographic features are collected from the map engine of AMAP B The perception radius is set to 1000 m.
Weather forecast data are collected from the Air Resources Laboratory (ARL), This web- site can download the meteorological forecast data for the following 26 days at most, with accuracy of 0.25 x 0.25 degrees, which can be updated four times day.
We use min-max normalization normalize the pollutant concentration and meteorological data
into [0, l].
4.2 EXPERIMENTAL SETTINGS
We split the dataset into training data, validation data, and test data by the radio of 0.7:0.1 We choose Adam Kingma & Bi (E() as the optimizer in the training phase. During the training phase, the batch size set 128 and the epoch size set 500, and use RMSprop Knlttal (m2z)) for 50 epochs with learning rate as 5-1, The hidden size of GNNs is set to 32, and the hidden state size of LSTMs is set to 64.
We implement our method by Py Torch Pa (211%) constructing GNNs with PyTorch geo- metrie library Fey & Lenssen (2U)) and implement HYSPLIT trajectory analysis and edge weight construction with PySPLIT Wamne (RUE). The code is released on GitHub. A server with one CPU Intel@Xeon@PPaatnnnn and one GPU (NVIDIA Tesla T4) accomplishes all computing tasks, in- cluding training, validation, and test.
We introduce two metrics: MAE (mean absolute error) and SMAPE (symmetric mean absolute per- centage error), to evaluate the performances of all methods. In the experiments, we utilize previous 48-hour observations and select the results of hour, 6 hours, 12 hours, 18 hours, 24 hours, 36 hours and 48 hours ahead forecasting to report. All experiments are repeated times to avoid contingency.
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Under review conference paper ICLR 2023
UT valuo prodicted valum
250
225
200
125
100
(a)
70
30
32
18
24
30
35
30
(b)
Figure 7: 48-hour predicted value versus true value (a) PM2.5 (b) O₃
Table 2: Results of factor evaluation based on JN database
Method
Metric
6h
12h
18h
36h
48h
MAE
6.15
15.24
20.56
25.62
34.83
43.98
52.06
MGST_GNT
SMAPE
0.07
0.10
0.14
0.19
0.26
0.33
0.46
MAE
7.06
17.17
23.68
29.33
38.56
76.70
53.78
w/o wdf
SMAPE
0.07
0.11
0.16
0.21
0.28
0.35
0.47
MAE
6.76
17.16
23.56
28.45
34.96
45.55
52.01
w/o tf
SMAPE
0.07
0.11
0.16
0.20
0,26
0.34
0,46
MAE
6.71
16.78
22.56
28.64
34.95
46.56
52.11
w/o gs
SMAPE
0.07
0.11
0.15
0.20
0.26
0.35
0.46
Figure depicts the predicted PM2.5 and O3 concentrations and their corresponding real values of a station in Jinan city from 00:00 January 2nd, 2021 23:00 January 3rd, 2021 for consecutive 48 hours. From Figure M. we can see that is easier to predict O₂ concentration than PM2.5, because Oy has more periodic regularity and stability than PM2.5. Therefore, the subsequent experiments were carried out with the forecasting of PM2.5 concentration.
4.3 MULTI-SOURCE FACTOR EVALUATION
To verify the effectiveness of multiple factors, we compare MGST GNN with three variants, each of which removes one kind of factors. Specifically, MGST GNN w/o wdf removes meteorolog- ical forecast data; MGST_ GNN w/o tf removes time feature and MGST GNN w/o gf removes geomorphic feature.
The performances of MGST GNN and its variants given in Table D can be seen from the table:
1. outperforms the other three variants, which indicates that all factors can improve the performance of AQP:
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Under review conference paper ICLR 2023
Table Results model component evaluation based on JN database
Method
Metric
1h
6h
12h
18h
24h
36h
48h
MAE
6.15
15.24
20.56
25.62
34.83
43.98
52.06
MGST- GNN
SMAPE
0.07
0.10
0.14
0.19
0.26
0.33
0.46
MAE
7.12
17.10
23.59
28.02
34.95
48.02
53.58
w/o multi granularity
SMAPE
0.08
0.12
0.16
0.21
0.26
0.36
0.47
MAE
7.16
18.06
23.59
28.16
34.76
48.35
53.02
w/o HYSPLIT
SMAPE
0.08
0.13
0.16
0.21
0.26
0.36
0.47
MAE
6.15
15.85
21.36
28.64
34.96
43.16
52.25
w/o tal STM
SMAPE
0.07
0.10
0.15
0.21
0.26
0.33
0.46
The rank of the effectiveness factors WD>TF>GE. This result shows that air quality is mostly impacted by weather conditions.
4.4 MODEL COMPONENT EVAL NATION
To explore the effectiveness of different components, we compare MGST- GNN with three follow- ing variants:
1. MGST_GNN w/o multi granularity, which removes the global graph and the corresponding interactions, i.e., the region representation removed from the global attributes the partial subgraphs;
MGST w/o HYSPLIT, which removes dynamic edge weight vector by HYSPLIT and use vectors of wind direction and distance instead;
3. MGST-GNY w/o tLL.TM which removes temporal attention mechanism based LSTM at the decoder, and directly use LSTM instead.
The performances of MGST-GNN GNN and the variants mentioned above are given in Table BL as can be seen from the table:
1. MGST GNN outperforms MGST GNN the air quality of adjacent regions beneficial, which can be used model the diffusion processes of air pollutants from adjacent regions;
w/o multi granularity. The result indicates that
2. MGST_ GNN outperforms MGST -GNTT w/o HYSPLIT in all metrics. The result indi- cates that compared with taking wind direction and distance as the edge weight vector, using HYSPLIT to dynamically adjust the weights of edges a more effective strategy, which model the effect patterns of wind direction on air pollutant diffusion with do- main knowledge;
3.
The attention mechanism based LSTM at the decoder is helpful for longer-term prediction, but for short-tent prediction.
4.5 COMPARISON WITH OTHER PREDICTION METHODS
In order to verify the advanced nature of our method, we compare MGST GNN with the following prediction methods:
1. HighAir Xu (ллла):: : GNN network-based air quality prediction method. which adopts an encoder-decoder architecture and considers complex air quality influencing fac- tors, e.g., weather and land usage;
PM2.5-GNN Wang a (ADPL)) graph based model with identify a set of critical domain
knowledge for PM2.5 forecasting;
3. GC-DCRNN cral (20)) GC-DCRNN combines recurrent neural networks with dif- fusion convolution to forecast the air quality. The model describes the spatial relationship by constructing a graph based on the similarity the built environment among the loca-
tions of air quality sensors. To keep the faimess of comparison, we introduce weather data into the input of the decoder;

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Under review conference paper ICLR 2023
Table 4: Model comparison results based on YRD database
Method
Metric
1h
6h
12h
18h
24h
36h
48h
MAE
7.16
17.29
21.25
27.92
36.97
45.28
54.73
MGST_ GNN
SMAPE
0.08
0.12
0.14
0.20
0.27
0.34
0.48
MAE
7.12
17.83
22.65
27.49
38.85
48.36
55.68
HighAir
SMAPE
00.08
0.12
0.15
0.20
0.29
0.36
0.49
MAE
7.15
18.09
23.14
29.57
37.96
48.99
56.12
PM2.5-GNN
SMAPE
0.08
0.13
0.15
0.21
0.28
0.36
0.50
MAE
7.56
18,56
24.88
30.67
43.26
51.84
60.02
GC-DCRNN
SMAPI:
0.08
0.13
0.17
0.22
0.33
0.45
0.53
MAE
8.13
18.97
24.53
31.52
42.51
51.98
58.96
GC-LSTM
SMAPE
0.09
0.13
0.17
0.22
0.33
0.45
0.52
MAE
7.22
18.69
23.36
27.86
40.16
51.97
57.85
ST-UNet
SMAPE
0.08
0.13
0.16
0.20
0.32
0.45
0,51
MAE
8.15
19.21
24.62
31.96
42.87
50.68
60.37
STA-LSTM
SMAPE
0.09
0.14
0.17
0.23
0.33
0.37
0.53
GC-LSTM Qi et al M0 ) GC-LSTM integrates LSTM and Graph Convolutional Net-
works (GCN) to model the temporal and spatial dependency respectively. Differing from our MGST_GNN, GNNN the GCN module in GC-LSTM only applies to undirected graph, and no edges' attributes are used;
5. ST-UNet au (2U1)): ST-UNet is a spatial-temporal prediction method that leverages pooling operation coarsen graph in spatial domain and adopts dilated RNN to capture temporal dependencies;
6. STA-LSTM Zou (μилл]:: STA-LSTM is long short-term memory air quality predic- tion model based on a spatiotemporal attention mechanism.
The performances of MGST- and other prediction methods given in Table EL be seen from the table:
1. MGST GNN outperforms GC-DCRNN, GC-LSTM and UNet, especially in long- term forecasting. It is indicated that multi-gramularity structure can model spatial de- pendencies more effectively than flat structure. The reason is that the multi granularity graph not only considers the local impact of neighboring stations on the prediction station, but also the global impact of different regions on the prediction station, which makes the development of spatial relationships more sufficient;
2. MGST_ GNN outperforms HighAir. This is because in the aspect of spatial relationship learning, MGST GNN uses the professional HYSPLIT model to build edge weight vec- tor. comprehensively uses meteorological and topographical conditions calculate the influence relationship among nodes and the specific influence time, making the construc- tion of spatial relationship more accurate and delicate. HighAir simply uses wind direction and distance to construct rough edge weight vector. In terms temporal relation learn- ing, MGST GNN adds time feature, and uses the attention mechanism based LSTM in decoder. HighAir simply uses LSTM to build temporal relationships;
MGST_GNV outperforms PM2.5-GNN. This is because MGST_GNN uses multi- granularity spatiotemporal graph network and combines meteorological data, topograph- features, time features and professional models to construct node and edge attributes. However. PM2.5-GNN only
spatiotemporal graph network. In the construction of edge attributes, although they make use of domain knowledge, they simply list part of the influencing factors, which is still insufficient, When building node attributes, they only use metcorological data.
5 CONCLUSION
In this paper, the influence of meteorological, spatial and temporal factors on AQP is fully consid- ered, and encodlrrddeoodrr architecture based on multi-granularity spatiotemporal graph network
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proposed to predict pollutant concentration over long period of time. Compared with the ex- isting models, the striking characteristic of this paper is that the meteorological, spatial terrain and time factors are considered comprehensively through the professional air quality model, while other models take the influencing factors as the splitting parameter input. That is, the model in this paper integrates the advantages of mechanism model and machine learning, and namely it a comprehen- sive model. The experimental results show that the proposed model is of progressiveness and has good applicability.
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A APPENDIX
A.I DATA AUGMENTATION AND EXPERIMENTATION
Aiming the difficulty of collecting training samples for air quality prediction, we the method of data augmentation to reconstruct samples. Due to the distribution difference between real weather data and forecast weather data. Gaussian noise is introduced to the meteorological data in the sam- ple to enhance the data and improve the generalization ability of the model. In addition, due to the influence monitoring instruments, environment and other factors, the pollutant concentration val- ues collected may be biased. Therefore, the pollutant concentration values of samples are disturbed up and down by metric to enhance the number of samples and improve the model generalization
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Table List of sample augmentation
Augmentation type
Meteorological data plus noise
Concentration value disturbance
Sample type
original sample sample 1
sample 2
sample 3
Table 6: MAE results data augmentation evaluation based on JN database
Method
Pollutant category
1h
6h
12h
18h
24h
36h
48h
PM2.5
6.15
15.24
20.56
25.62
34.83
43.98
52.06
MGST-GNN
O₂
5.06
13.36
17.14
22.16
29.90
37.93
44.61
PM2.5
6.25
16.97
22.18
28.23
36.96
46.31
54.69
w/o DA
O3
5.11
14.84
18.86
23.72
30.78
39.19
48.07
ability. Therefore, Gaussian noise is introduced into meteorological data and random perturbation for pollutant concentration data to enhance the samples by three times. The specific augmentation methads are shown in Table B. Finally, 26136 samples were obtained from JN and YRD respectively.
order to verify the data augmentation effect, we conduct a comparison experiment between data augmentation and non-data augmentation, as shown in Table E. where w/o DA indicates that data augmentation technology is not used. As seen from Table Et using data augmentation method, the effect effectively improved.
A.2 ABLATION STUDY AND EXPERIMENTATION
In this paper, the first the professional model HYSPLIT build the graph dynam- ically. Therefore, this appendix section will demonstrate the effectiveness of using HYSPLIT to construction graph dynamically through ablation experiments. Specifically, the ablation experiment conducted based on the current advanced spatiotemporal graph neural network HighAir and PM2.5-GNN. In HighAir, it uses the distance among nodes to statically construct the edge of the graph, and uses the wind direction information between nodes to calculate the edge attribute vector. Therefore, use HYSPLIT instead of the graph construction method in HighAir. In PM2.5-GNN, it uses the distance between nodes and the altitude the position to statically construct the edge the graph, and uses the parameter of domain knowledge between nodes to calculate the edge attribute vector. Therefore, experimental results are shown Table W. where HighAir_ HYSPLIT and PM2.5-GNN. HYSPLIT respectively indicate that HYSPLIT is used to replace the original graph construction. As can be seen from the table, HYSPLIT builds dynamic graphs better than static graphs of HighAir and PM2.5-GNN.
HYSPLIT instead of the graph construction method in PM2.5-GNN. The
In order to further verify the effectiveness of using HYSPLIT to dynamically construct graph, e- specially its advantages for air quality prediction in complex scenarios such abrupt change in pollutant concentration. We develop a Dataset-min mini where we focus on heating season (November to February). Dataset-mini is more challenging for two reasons. Firstly, during winters, heating emissions can dramatically increase the frequency of air pollution occurrence. Secondly, the direc- tion of prevailing wind north or northwest, which contributes to pollutant's long-distance transport from North China to South China. The results in Table E show that using HYSPLIT to dynamical- construct graph can significantly improve the accuracy of the model's sudden changes pollution and regional impacts caused by strong winds. This method eliminates the construction process of specially designed auxiliary network to learn the edges of graph and provides new way for the construction of graph neural network, which can be easily extended to other spatiotemporal forecasting tasks. For example, in water quality prediction, professional hy- drodynamic model (MIKE) can be used to dynamically construct the graph structure, so as to better Jeam the influence of water quality in different regions the prediction points.
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Under review conference paper ICLR 2023
Table 7: Ablation experiment result based on
YRD database
Method
Metric
1h
6h
12h
18h
24h
36h
48h
MAE
7.12
17.83
22.65
27.49
38.85
48.36
55.68
HighAir
SMAPE
0.08
0.12
0.15
0.20
0.29
0.36
0.49
MAE
7.12
17.46
22.18
27.50
37.65
47.38
54.75
Bighhir-HYSPLLN
SMAPE
0.08
0.12
0.15
0.20
0.28
0.35
0.48
MAE
7.15
18.09
23.14
29.57
37.96
48.99
56.12
PM2.5-GNN
SMAPE
0.08
0.13
0.15
0.21
0.28
0.36
0.50
MAE
7.14
18.01
22.79
29.05
36.97
47.95
55.52
PM2.5-GNN. HYSPLIT
SMAPE
0.08
0.13
0.15
0.21
0.27
0.35
0.49
Table Ablation experiment result based on Data-mini
Method
Metric
1h
6h
12h
18h
24h
36h
48h
MAE
8.02
20.14
27.55
35.27
44.18
56.46
65.47
HighAir
SMAPI
0.08
0.14
0.20
0.27
0.33
0.50
0.59
MAE
7.86
18.73
25.17
32.94
40.49
50.97
56.
HighLiT_HYSPLIT HYSPLIT
SMAPE
0.08
0.13
0.18
0.25
0.30
0.37
0.51
MAE
8.11
21.30
27.96
34.66
43.88
57.69
67.08
PM2.5-GNN
SMAPE
0.09
0.14
0.20
0.27
0.33
0.51
0.60
MAE
7.95
19.06
26.14 14
32.99
40.85
50.89
55.78
PM2.5-GNN
SMAPE
0.08
0.13
0.19
0.25
0.30
0.37
0.51
16


Reviews:
[{"review_id": "cIAvJ4Dlesh", "reviewer": "Reviewer_mQij", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper provides a method to predict air quality by combining spatial-temporal data and graph neural networks. The contributions of this paper are mainly on integrating HYSPLIT for modeling the dynamic relationships between nodes.", "summary_of_the_review": "The topic is important. But the novelty is limited, the experiment is weak. The paper needs lots of effort to improve.", "strength_and_weaknesses": "Strength:\n1. The topic of air quality prediction is of great social impact.\n\nWeaknesses:\n1. The format of the paper is unprofessional. All the experimental results are in the appendix.\n2. Figures are in poor resolution. Please use vectorized images for professional academic writing.\n3. The technical contribution is limited. The settings of LSTM, GNN, and attention mechanism are commonly used for air quality prediction. The motivation of multi-granularity also has been studied thoroughly for spatial-temporal forecasting.\n4. The experiment cannot fully support the validity of the model. Air quality prediction is inherently a time series prediction task. Time series forecasting models, such as N-BEATS, autoformer, informer, etc, are expected to compare.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "FtEkSe-ycB", "reviewer": "Reviewer_VRie", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper proposes a MGST_GNN model which uses multi-granularity graph neural network and LSTM to do air quality forecasting. In the air quality forecasting task, a region contains multiple air quality stations. The authors define two graphs: The global graph has nodes as regions and the partial graph (within one region) has nodes as the stations in that region. The authors propose a new message passing model that incorporates these two kinds of graphs. The proposed model uses LSTM to learn the temporal dependencies. The authors conducted experiments on two real world datasets and showed the proposed method achieve good results.", "summary_of_the_review": "There are a lot of improvements that can be made in this paper's organizations, experimental results presentations and discussions. I think it's not ready yet.", "strength_and_weaknesses": "Strength:\n1. The proposed model is easy to understand and the idea behind partial graph and global graph is explained well.\n2. The experimental results contain many ablation study.\n\nWeaknesses:\n\n1. The contents of this paper definitely can be organized better. \n* The experimental results are all in appendixes. The experiments section in main body only have some vague description of the model's performance, e.g. \"the MAE ... decreases about 1.88 and 1.52 ...\", or \"MAE decreases about 1.99, 2.09, 0.59...\". This is confusing and it's hard for a general reader to understand what these metrics mean unless they go to check the tables in the appendix. I'd suggest to make the paper's main body self-contained.\n* The authors listed many related models in the related work section. However, the differences between existing models and the proposed model were not discussed thoroughly.\n\n2. The experimental results were not presented well. For table 6 in appendix A.6, the first two rows (method MGST_GNN) are all bolded. However, it doesn't seem that MGST_GNN gets the best metric in each column. For example, under metric=1h, HighAir's MAE is 7.12 while MGST_GNN's is 7.16. Under metric=18h, MGST_GNN's MAE is 27.92 while HighAir's is 27.49 and ST-UNet's is 27.86. I think the tradition is to bold the best metric in the corresponding column.\n\n3. In Appendix A.6 the authors claimed that MGST_GNN outperforms the baseline models and provided their explanations. I don't think this is very convincing. Even if MGST_GNN gets better results in Table 6, it doesn't imply that, for example, MGST_GNN outperforms HighAir model because MGST_GNN uses HYSPLIT model. A more promising way is to provide ablation study results on the same dataset. \n\n4. The proposed model uses HYSPLIT to construct the graphs. Since HYSPLIT is specifically designed for air quality related tasks, how does MGST_GNN generalize to other spatiotemporal forecasting tasks? It would be good to see some discussions along this line.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "E75-BAukkz", "reviewer": "Reviewer_tjqh", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper proposes a comprehensive spatiotemporal graph model to predict air pollution concentration in the future time. The model integrates the advantages of mechanical model and machine learning. The authors compare the model with various SOTAs and the proposed method provides an impressive applicability with competitive prediction ", "summary_of_the_review": "This paper is well-written and addresses an important question possibly helping bridge environmental science and machine learning. The work falls short on the technical novelty. However, it’s still marginally above the acceptance line.", "strength_and_weaknesses": "Strength\n1 The paper addresses an important problem in air pollutant concentration prediction. By integrating the mechanical model and machine learning, the work bridges the traditional methods and current trend.\n2 The high-level presentation is good which is easy to follow and understand.\n3 The experiment is solid and comprehensive.\nWeakness\n1 The paper uses inconsistent terms and symbols, which is confusing at some time\nFor example, R and r_a are to represent the region in section 3.1, but authors use the same symbol for messages in equation 2, which is a little ambiguous. In figure2, the input data doesn’t correspond to the variables in the definition section, I would suggest the authors to use consistent symbolic notations for the important features in the both the text and the explanatory figures. Some of the figures need more explanation, e.g., in figure1, the meanings of the axes are unknown. Typo: neighbor node net->neighbor node set\n2 The novelty is not outstanding. Although integrating the mechanical model and machine learning is interesting, most of the techniques are well-established and the authors simply apply them to the new problem.  The overall framework is the same as this paper:\nJiahui Xu, Ling Chen, Mingqi Lv, Chaoqun Zhan, Sanjian Chen, and Jian Chang. HighAir: A\nhierarchical graph neural network-based air quality forecasting method. arXiv preprint arXiv:\n2101.04264, 2021.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject