A Dynamic Multi-Graph Convolutional Spatial-Temporal Network for Airport Arrival Flow Prediction

Abstract

In air traffic systems, aircraft trajectories between airports are monitored by the radar networking system forming dynamic air traffic flow. Accurate airport arrival flow prediction is significant in implementing large-scale intelligent air traffic flow management. Despite years of studies to improve prediction precision, most existing methods only focus on a single airport or simplify the traffic network as a static and simple graph. To mitigate this shortage, we propose a hybrid neural network method, called Dynamic Multi-graph Convolutional Spatial-Temporal Network (DMCSTN), to predict network-level airport arrival flow considering the multiple operation constraints and flight interactions among airport nodes. Specifically, in the spatial dimension, a novel dynamic multi-graph convolutional network is designed to adaptively model the heterogeneous and dynamic airport networks. It enables the proposed model to dynamically capture informative spatial correlations according to the input traffic features. In the temporal dimension, an enhanced self-attention mechanism is utilized to mine the arrival flow evolution patterns. Experiments on a real-world dataset from an ATFM system validate the effectiveness of DMCSTN for arrival flow forecasting tasks.

1. Introduction

As the demand for air transportation continues to increase, there is a growing need for larger airport infrastructure in many parts of the world. According to the International Civil Aviation Organization (ICAO), global air passenger traffic is projected to double by 2037, with the Asia-Pacific region expected to account for over 40% of this growth due to rapid urbanization and economic development [1,2]. Investigated by the Civil Aviation Administration of China (CAAC), China has 248 civil airports in 2021 and is expected to have around 450 airports by 2035 to sustain the coming increase in passenger numbers and flights. EUROCONTROL also forecasts that 20 of the largest airports in Europe will be completely saturated by 2030, with 11% of flights not being accommodated on the ground [3]. Globally, many hub airports are already operating at or near capacity, with significant constraints in Asia and Europe due to land scarcity, regulatory barriers, and environmental concerns. These global capacity challenges underscore the urgency of enhancing air traffic flow management (ATFM) systems. As a critical component of ATFM, accurate airport arrival flow prediction (AAFP) is essential for optimizing traffic management initiatives (TMIs) and mitigating the capacity crunch. However, air transportation is highly susceptible to external factors beyond capacity constraints. Weather conditions, such as storms or strong winds, frequently cause flight delays, cancellations, or rerouting, significantly impacting arrival flow patterns [4]. Similarly, space weather events, such as solar storms, can disrupt navigation and communication systems, posing challenges to ATFM [5]. To meet this challenge, enhancing air traffic flow management (ATFM) is an optimal alternative solution in short term [6]. As the precondition of ATFM, airport arrival flow prediction (AAFP) is critical to assist air traffic controllers in timely identifying the airport traffic situation for better traffic management initiatives (TMIs).

Past decades have witnessed a growing interest in understanding the flow forecasting of air traffic. In terms of methods, previously published works can generally be classified into three categories: classical simulation, conventional data-driven, and deep learning (DL) methods. Among the classical simulation approaches, flight plan- and traffic flow model-based are two representatives. These methods tend to model air traffic systems from the perspective of individual flight [7,8,9] and flight flow [10,11,12], respectively. However, the classical simulation methods are usually dependent on simplified assumptions of the flight operation process, which makes it difficult to fully illustrate the real and complicated air traffic situation.

To relax these assumptions, the traffic flow prediction task is defined as a branch of the time series prediction problems. Numerous conventional data-driven models for time were applied to forecast air traffic states, including Linear Regression (LR) [13], Auto-Regressive Integrated Moving Average (ARIMA) [14], K-Nearest Neighbor (KNN) [15], Support Vector Regression (SVR) [16], and Bayesian Network (BN) [17]. Although progress has been made with these conventional methods, their weak generalization ability in capturing nonlinear features is still obvious due to the over-dependence on handcrafted features.

Recently, deep learning methods enable intelligence to the air traffic domain. Specifically, through the global search ability of the genetic algorithm, an improved wavelet neural network is proposed to mine the airport traffic flow patterns [18]. Employing the parameter-sharing mechanism across continuous timesteps, Recurrent Neural Networks (RNNs) are extensively applied to explore AAFP tasks [19,20]. In reality, many real scenarios are graph in nature, such as sensor networks [21,22], road networks, and airport networks. Unfortunately, previous works mostly focus on single-airport scenarios but ignore the effects of flight interactions among airports in the spatial dimension. Consequently, the dynamic airport network is not reflected in the forecasting tasks, which consequently results in limited prediction performance.

Considering the problem of spatial-temporal data modeling on graphs, a series of Spatial-temporal Graph Neural Networks (STGNNs) are proposed for traffic state prediction tasks. The typical frame of STGNNs combines graph convolutional network (GCN) [23] over the spatial dimension with a forward computation function modeling the dynamics across the temporal dimension [24], including DCRNN [25], T-GCN [26], ST-GCN [27], and Graph WaveNet [28]. Due to the specific graph-oriented model architectures, these STGNNs obtain the expected prediction results and show superiority on traffic state forecasting tasks.

Motivated by the success of STGNNs in various prediction tasks for transportation, this paper terms the AAFP problem as a multivariate time-series prediction task considering airport network architectures. Since the dynamic and heterogeneous nature of airport networks, two intractable problems need to be addressed:

• In general, the hourly airport arrival flow prediction highly depends on the flight schedule and observed flight duration. These factors impose different constraints (relationships) on airport pairs forming multiple airport networks (graphs). However, the conventional GCN is designed for a single graph and fails to handle multiple graph structures simultaneously.
• The topology of the airport network is dynamic due to the requirement of real-time ATFM and ever-changing flight interactions among airports. Thus, the airport arrival flow data demonstrate complex and dynamic correlations in spatial and temporal dimensions. However, most existing STGNNs are designed for the static (predetermined) spatial topology of traffic networks. Therefore, these methods fails to explicitly consider the time-evolving property of network structures. How to model the dynamic spatial-temporal dependencies jointly is still challenging.

To solve these challenges in the AAFP task, we propose a Dynamic Multi-Graph Convolutional Spatial-Temporal Network (DMCSTN) to integrate the prior spatial dependencies and dynamic traffic situations simultaneously. Specifically, two major prior factors that influence the airport arrival flow are identified as flight schedule and duration. These factors are further encoded into two graphs indicating the geographical and semantic spatial dependencies among airports. To fully utilize this knowledge, a learnable fusion function is designed to merge multiple graphs into a fused one to enhance the high-level representation of prior information. For the dynamic properties of the airport network, a dynamic gating graph generation mechanism is constructed to manipulate the time-varying throughput among airports. Based on these mechanisms, we propose a Dynamic Multi-Graph Convolutional Network (DMGCN) to extract informative spatial topology to support AAFP tasks. Along the temporal dimension, temporal attention with a position embedding layer is introduced to mine the evolution patterns of airport arrival flow. In summary, the contributions of this paper are as follows:

• To capture the prior operation knowledge and the time-varying airport network, DMGCN is proposed to adaptively merge the graphs into a fused one for obtaining informative spatial representation.
• By combining temporal attention with DMGCN, a novel deep neural network is designed to mine spatial-temporal dependencies of airport arrival flow, considering heterogeneous and dynamic airport networks jointly.
• A real-world dataset is built to evaluate the performance of the proposed approach, covering major airports in China. Compared with other baselines, the experimental results demonstrate that our proposed framework is superior in the multiple-step situational (network-level) AAFP task.

The rest of this paper is organized as follows. The related works are reviewed in Section 2. Preliminaries of airport networks and the definition of airport arrival flow prediction problem are introduced in Section 3. Section 4 details the proposed framework. Section 5 lists experimental configurations. The experimental results are reported and discussed in Section 6. We conclude the paper and introduce the future research direction in Section 7.

2. Related Work

2.1. Classical Simulation Methods

The plan-based method derives the air traffic flow of concerned airspaces by evaluating the 4-D aircraft trajectories [7,8,9] depending on flight plans. However, the trajectory prediction method is susceptible to uncertainties of real-time traffic states, such as weather conditions. As a result, this approach fails to offer sufficient insights into the dynamics of the traffic flow. The model-based method means that the evolution patterns of the traffic states are represented by some handcrafted traffic models. Prior knowledge is required to design the traffic model to forecast traffic flow, including the aggregate flow model [10,11], and the cell transmission model [12], etc. However, the air traffic state can be influenced by many factors in practice. Over dependence on prior knowledge may lead to weak generalisability in the case of unseen environments.

2.2. Conventional Data-Driven Methods

With a deep understanding of studies in air traffic forecasting, conventional data-driven approaches can be subdivided into parametric and non-parametric methods. The parametric method means the regression function and parameters are determined by the process of fiting the observed data, and then the traffic forecasting task is realized based on the learned function.

The parametric methods for mining temporal dependencies include the LR, the ARIMA, etc. Specifically, an LR model was used for air traffic demand predictions with a combination of the focused time interval as well as adjacent preceding and following intervals [13]. To mine the underlying patterns of monthly air traffic, a sparse seasonal ARIMA was employed to analyze the relationships between the air traffic and the related seasonal pattern, economic situation, and social environment of HongKong by decomposing the air traffic into three parts (trend, seasonal pattern, and random noise). In the calculation manner, the parametric model is simple and convenient. However, these models depend on the assumption of stationary and cannot reflect the nonlinearity and uncertainty characteristics of traffic data [26].

By contrast, non-parametric methods can relax these assumptions, and only require historical data to mine the transition patterns among different time slices, containing the KNN [15], the SVR [16], the BN model [17], etc. In detail, referring to the KNN, a regression method was constructed to predict the future flow values based on real air traffic flow data collected from the terminal corridors [15]. By taking advantage of SVR and fuzzy sets, an improved SVR model was designed to enhance the prediction accuracy of freight volumes [16]. To obtain the impacts of TBO uncertainties to the precision of the complexity prediction in terms of air traffic demand, several BN models were developed for two demand capacity balance solutions by SESAR [17]. Recent studies have further advanced these methods by incorporating domain-specific factors. For instance, short-term multi-step predictions have been improved using attention-enhanced graph convolutional LSTM networks, which combine temporal modeling with spatial dependencies for sector-based traffic flow forecasting [29]. However, these approaches often focus on temporal patterns or local spatial features, limiting their ability to capture dynamic network-level interactions, a gap addressed by our DMCSTN through adaptive multi-graph modeling.

2.3. Deep Learning Methods

With the exponential increase in traffic data and computational capability, numerous neural network architectures were constructed to extract features automatically, including the Artificial Neural Network (ANN), Long Short-term Memory (LSTM), CNN, etc. Specifically, With the statistical information of historical data, multiple regression methods were embedded into the ANN to predict air traffic flow [30]. For better modeling sequential traffic data, the LSTM model was utilized to mine the continuity and trend of airport traffic flow [19]. In light of the meteorological factors, a hybrid LSTM-XGBoost [20] method was introduced to the forecast arrival flow at the Nanjing Lukou international airport. Recent advances have integrated external factors like weather into deep learning frameworks. For example, a multimodal spatial-temporal network with a weather-aware model (MST-WA) enhances terminal area flow predictions by incorporating meteorological data [31]. Similarly, multi-view attention-based networks leverage diverse data perspectives to improve arrival flow forecasting [32].

Considering the importance of spatial features, CNN was usually applied to extract local spatial correlations in a gridded traffic system. In [33], a ConvLSTM is proposed to make full use of spatial-temporal dependencies to support prediction tasks. However, CNN is designed for Euclidean space with a regular spatial structure. Hence, it is difficult to manipulate non-Euclidean dependencies among nodes on traffic networks directly.

Recently, the progress of the CNN study has been made by GCN, which crossed over its original limitation and generalize the CNNs into non-Euclidean space. Since air traffic is an extension of the ground transportation system, these works are of great significance to the study of air transportation system. Thus, a series of related STGNN methods [25,26,27,28,34] developed for network-level traffic state forecasting are introduced. The DCRNN [25] was a pioneering work to mine spatial-temporal dependencies of traffic features simultaneously on the road network, which was developed by integrating the bidirectional random walks with the encoder-decoder architecture. As for the multistep prediction task, the T-GCN [26] was built upon the combination of the GCN and GRU and showed obvious superiority by related experiment results. To explore more efficient model components in STGNN models, ST-GCN [27] was proposed with complete convolutional structures. More recent STGNN approaches have addressed dynamic and heterogeneous networks. For instance, causality graphs have been used to model multi-airport traffic flow, capturing complex interaction patterns [35]. Similarly, methods considering heterogeneous and dynamic network dependencies improve arrival flow predictions by adapting to real-time operational changes [36]. Despite these advances, most STGNNs rely on static or partially dynamic graphs, which may not fully capture the evolving operational constraints like varying flight schedules and durations. In contrast, our DMCSTN introduces a dynamic multi-graph convolutional mechanism to jointly model geographical and semantic dependencies with adaptive graph structures, enhancing network-level AAFP performance.

As to this problem, an adaptive matrix was proposed in Graph WaveNet [28] to augment the spatial representation ability for superior prediction performance. Inspired by this research line, we further extend the adaptive matrix to multiple graph scenarios.

3. Preliminaries and Problem Definition

3.1. Airport Network Definition

In air transportation, flights commute among airports under constraints imposed by flight duration and schedule factors. From the perspective of air traffic flow management (ATFM), flight schedules and durations are the primary drivers of airport arrival flows due to their direct influence on traffic distribution and arrival timing [10]. Flight schedules, as predefined operational plans, dictate the macroscopic distribution of flights across the airport network. For instance, high-frequency schedules on busy routes (e.g., Beijing Capital to Shanghai Hongqiao) significantly increase arrival flow at destination airports, shaping hourly traffic patterns. Conversely, flight duration governs the micro-level timing of arrivals, as it determines when a flight, departing at a scheduled time, will arrive. Duration is influenced by geographical distance and real-time factors such as wind conditions, air traffic control restrictions, or weather disruptions, which are critical for accurate hourly flow predictions. Other factors, such as runway capacity or meteorological conditions, often manifest indirectly through their impact on schedules (e.g., cancellations) or durations (e.g., delays due to headwinds). Thus, modeling these two factors captures the core dynamics of arrival flows.

To represent these constraints, two directed graphs are defined based on operational data:

(1) Airport Duration Graph (ADG): The flight duration reflects the result of multiple factors acting on a flight operation and is often proportional to the distance among airports. A directed airport duration graph ${\mathcal{G}}_{adg}=(V,A_{adg},E)$ is defined to represent the geographical spatial dependencies among airports based on the average flight duration. Here, each node $v_i\in V$ corresponds to an airport (e.g., ZBAA for Beijing Capital), and the node set V includes all airports in the dataset. A directed edge $e_{ij}\in E$ exists from airports $v_i$ to $v_j$ if there are historical flights between them, with the edge weight defined as the average flight duration (in hours) computed from historical records. The weighted adjacency matrix $A_{adg}\in R^{N\times N}$ is constructed from historical flight records, by computing the average duration for each airport pair (e.g., 2 h for ZBAA-ZSHC). These durations are normalized to [0, 1] to serve as edge weights, where $a_{adg\_ij}=0$ if no flights exist between airports i and j. This encoding captures spatial proximity and operational constraints, such as longer durations due to weather or airspace restrictions.

(2) Airport Schedule Graph (ASG): As a predefined arrangement of flight operations, flight schedules provide macroscopic flight demands among airports. A directed airport schedule graph ${\mathcal{G}}_{asg}=(V,A_{asg},E)$ is defined to represent the semantic spatial dependencies among airports based on scheduled flights. The weighted adjacency matrix $A_{asg}\in R^{N\times N}$ is derived from flight schedule data, by counting the number of scheduled flights per hour between airport pairs (e.g., 10 flights from ZBAA to ZULU). These counts are normalized to form edge weights, where $a_{adg\_ij}=0$ if no scheduled flights exist. This encoding reflects the planned traffic demand and operational connectivity between airports.

Here, V is a finite set of nodes ($N=\left|V\right|$) representing airports, and E is a set of edges indicating scheduled flight connections. The matrices $A_{adg}$ and $A_{asg}$ enable the proposed DMCSTN model to capture both geographical and semantic dependencies for accurate arrival flow prediction.

3.2. Problem Definition

In this work, network-level airport arrival flow prediction is termed as a multivariate time-series forecasting instance in air transportation, which can be characterized as learning the mapping function on the premise of given complex airport networks $\mathcal{G}$ and feature X:

$$\begin{array}{c}\hfill ([X_t,X_{t+1},\dots ,X_{t+n}];\mathcal{G}])\stackrel{f(·)}{⟶}[X_{t+n+1}^{\prime },X_{t+n+2}^{\prime },\dots ,X_{t+n+m}^{\prime }],\end{array}$$

(1)

where $X_t\in R^{N\times D}$ demonstrates traffic flow features of N airports at the time t including scheduled departure, scheduled arrival, observed departure, and observed arrival flights, where D denotes the dimensions of the traffic flow feature. n is the length of input traffic sequence. $X_{t+n+m}^{\prime }\in R^{N\times 1}$ is the predicted airport arrival flow at the timestamp $t+n+m$, and m denotes the length of prediction timesteps. $f(·)$ is a traffic flow prediction model that is usually optimized by data-driven methods.

4. Methodologies

4.1. Overview of the DMCSTN

In this work, the high-level idea of our proposed method is to model the complex spatial-temporal characteristics of airport traffic flow considering the multiple prior flight operation factors and dynamic airport networks. The framework of the DMCSTN is visualized in Figure 1. Specifically, the DMCSTN follows four sequential procedures: (1) Preparing the adjacency matrices of airport networks (ADG and ASG) and traffic time-series data as input. (2) Modeling the network-level airport traffic situation at each time step by the DMGCN. (3) Extracting the evolution patterns of airport traffic situation along the temporal dimension and outputting the prediction results with temporal attention. (4) Utilizing a fully connected neural network to transform the raw output of TA into the desired numerical space. The second and third steps are the critical modules in the DMCSTN.

4.2. Dynamic Multi-Graph Convolutional Network

To capture the prior operation information and dynamic airport network along the spatial dimension, a variation of GCN, DMGCN is designed, which requires two steps: dynamic multi-graph fusion and graph convolution operation. The components of DMGCN are visualized in Figure 1b.

4.2.1. Dynamic Multi-Graph Fusion

To model the spatial dependencies of airport arrival flows, the proposed DMCSTN leverages two prior graphs: the Airport Duration Graph (ADG) and the Airport Schedule Graph (ASG), as defined before. These graphs are encoded from operational data to reflect the scientific principles of air traffic flow management. Specifically, the ADG’s adjacency matrix $A_{adg}$ is constructed by averaging flight durations from historical records, capturing geographical and real-time operational constraints such as distance and weather-induced delays. The ASG’s matrix $A_{asg}$ is derived by aggregating scheduled flights per hour, representing the planned demand and connectivity between airports. These encodings ensure that both static (schedules, distances) and dynamic (duration variations) factors are integrated into the model’s spatial representation.

First, a linear fusion method is designed to fuse multiple prior graphs into an adjacency matrix based on a learnable parametric matrix, which can be expressed as Equation (2):

$$\begin{array}{c}\hfill A_{fused}=W_{asg}^{\prime }\odot A_{asg}+W_{adg}^{\prime }\odot A_{adg},\end{array}$$

(2)

where ⊙ is an element-wise product operation, $A_{asg}\in N\times N$ and $A_{adg}\in N\times N$ are adjacency matrices of ASG and ADG, respectively. $W_{asg}^{\prime }$ and $W_{adg}^{\prime }$ are the normalized matrices of learnable parameter matrices $W_{asg}\in N\times N$ and $W_{adg}\in N\times N$ by $Softmax$.

In air traffic systems, real-time traffic situations may perturb normal flight operations. For example, when congestion or massive arrival flow occurs at a certain airport, it may derive a series of TMIs to delay or cancel related flights on the ground for ensuring operational safety. Motivated by this phenomenon, a dynamic gating graph generation strategy is created to automatically complete the topology of the traffic network. Specifically, a dot product operation ⊗ is used to generate a gating matrix to model the dynamic airport network according to the input traffic features, which is shown in Equation (3):

$$A_{gating}=Softmax(\left(W_{1}X\right)\otimes W_2{X}^T),$$

(3)

where $X\in N\times D$ is the raw airport traffic flow features, $W_{*}$ is the weight matrix. By the gating matrix $A_{gating}$, the informative spatial topology of the airport network $A\in N\times N$ can be adjusted as follows:

$$A=A_{gating}\odot A_{fused}$$

(4)

4.2.2. Graph Convolution Operation

A bidirectional GCN is designed to extract the traffic situation H on the airport network as Equation (5):

$$H={\mathrm{\Theta }}_F\star \mathcal{G}\left(X\right)=\sigma \left(\widehat{A}X{W}_0+\widehat{A^{\mathrm{T}}}X{W}_1\right),$$

(5)

where $\star \mathcal{G}$ denotes a bidirectional convolution operation on a graph, ${\mathrm{\Theta }}_F$ is the parameter set used in a graph, X represents the traffic features, and A is the context matrix learned from the dynamic multi-graph fusion operation. $\widehat{A}={\tilde{D}}^{-1}A$, where $\tilde{D}=diag\left(A\right)$ is an out-degree diagonal matrix. $A^T$ is the transpose of A, $W_0\in D\times$$d_{model}$ and $W_1\in D\times d_{model}$ represent the weighted matrices referring to $\widehat{A}$ and $\widehat{A^{\mathrm{T}}}$, respectively. $d_{model}$ is the model dimension shared between different modules and $\sigma$ is the $Sigmoid$ activation function.

4.2.3. Temporal Attention

Along the temporal dimension, traffic situations change dynamically. To mine non-linear evolution patterns, Temporal Attention (TA) is introduced and visualized in Figure 1c. This attention-based module can automatically assign different importance to input features. The weights are calculated as the dot-product between queries and values. Formally, holistic temporal attention is defined as follows:

$$Att\left(H\right)=Attention(\mathrm{Q},\mathrm{K},\mathrm{V})=softmax\left({\displaystyle \frac{{\mathrm{QK}}^{\mathrm{T}}}{\sqrt{d}}}\right)V,$$

(6)

where $Q=W_q\widehat{H}$, $K=W_k\widehat{H}$, $V=W_v\widehat{H}$, and d are queries, keys, values, and their dimensions, respectively. $W_{*}\in N\times N$ are the related coefficient matrices. Considering the periodicity in arrival flow data, we concatenate the historical average value at the same time interval covering the last three weeks as the global traffic feature $G\in N\times 3$ with the learned spatial representation H. For example, the historical average arrival flow covering 9:00 am–10:00 am on Tuesday means the average arrival flow of the last three Tuesdays span from 9:00 am to 10:00 am. Therefore, $\widehat{H}=Enc\left(t\right)+(H\oplus G)W_l$, where $W_l\in (d_{model}+3)\times d_{model}$. $Enc\left(t\right)$ is a fixed position embedding operation [37] to enhance the order recognizability of input order, as shown in Equation (7):

$$\begin{array}{c}{E}_{nc}(t,2d)=sin\left(t/{10000}^{2d/d_{\mathrm{model}}}\right)\\ E_{nc}(t,2d+1)=cos\left(t/{10000}^{2d/d_{\mathrm{model}}}\right),\end{array}$$

(7)

where t is the relative position of each element in the sequence, and each vector-dimension $1\le d\le$$d_{model}$. Once the attention score is calculated, the hidden representation of the traffic situation in the future is updated as follows:

$$F_o\left(X\right)=Relu\left(Att\left(H\right)W_o\right),$$

(8)

where $W_o\in d_{model}\times 1$ is the projection matrix to output the final prediction results.

In summary, prior operation factors can provide informative instruction for airport arrival flow forecasting. To mine this knowledge, a parametric fusion matrix is designed in DMGCN to merge prior static graphs into an adjacency matrix indicating the learned spatial topology of the airport network. Considering the effects of real-time traffic situations, a dynamic gating matrix generation strategy is imposed on the learned fusion matrix to model the throughput among airports. By integrating these operations with GCN, dynamic high-level spatial representation at each time step can be captured. Compared to the former studies about multi-graph machine learning methods [38], an explicit dynamic multi-graph modeling pattern is proposed in this work to capture the dynamic and heterogeneous airport networks. Along the temporal dimensions, the evolution patterns of airport traffic flow change non-linearly. To extract complex correlations across different time slices, the TA block is introduced to model the relevance between the input and target arrival flow sequences. It is believed that the complex dynamics of airport arrival flow along both temporal and spatial dimensions can be captured by the DMCSTN.

5. Experiments Preparation

5.1. Data Preparation

The airport traffic dataset is collected from an industrial ATFM system, which contains hub airports in China including ZBAA (Beijing Capital International Airport), ZUUU (Chengdu Shuangliu International Airport), etc. The raw dataset is stored as flight records including departure airport, arrival airport, scheduled departure time, scheduled arrival time, actual departure time, actual arrival time, etc. By aggregating all flights for each airport pair, an available airport traffic dataset is constructed. The sample interval is set to one hour ranging from 1 January 2016 to 30 December 2016.

To describe the fundamental flight operation regulations, two graphs are defined in Section 3.1. In these graphs, an ADG is constructed based on flight duration, measuring the geographical proximity among airports. In the ADG, airports are abstracted as nodes, flight conditions as edges, and the average flight duration for each airport pair as the weight of edges. Meanwhile, for speeding up model training, the Max–Min normalization operation is performed on the ADG.

The airport schedule graph is an important tool to describe the pre-defined arrangement of long-term traffic flow in an air traffic system. A raw flight schedule example is listed in

Table 1. A flight schedule example from the Civil Aviation Administration of China (CAAC) in 2016.

Flight Number	Aircraft Type	Day of Week	Departure	Departure Time	Arrival Time	Arrival
8L9938	737	246	ZBAA	0740	1200	ZPMS
3U8896	320	1234567	ZBAA	0625	0935	ZUUU
CA1592	320	346	ZSYN	1245	1440	ZBAA
CA1593	738	14567	ZBAA	2015	2145	ZSYT

, which describes the weekly arrangement of flights for each origin and destination (O-D) airport pair. Focusing on the first row, the ‘Day of Week’value is [246]. This means that there are flights from ZBAA to ZPMS (departure at 07:40 and arrival at 12:00) every Tuesday, Thursday, and Saturday. By aggregating all flights for each O-D pair in one week, a statistical table is calculated to record the macro-temporal flight arrangement, describing the periodicity of network-level airport traffic flow in week granularity. As shown in the first row of the statistical example

Table 2. A statistical tabular example calculated from the flight schedule.

Serial Number	DEP	DES	Number
1	ZBAA	ZUUU	220
2	ZGGG	ZSSS	223
3	ZBAA	ZSHC	154

, the ‘Number’ value is 220, indicating 220 flights from ZBAA to ZUUU each week. Thus, similar to the ADG, we use the number of scheduled flights for each airport pair as weights of edges and normalized by the Max-min normalization function.

In addition, the airport traffic flow dataset is also normalized to [0,1] by the Max-min normalization function and further chronologically divided into three parts: training set (70% of data), validation set (20% of data), and test set (10% of data). Meanwhile, the training dataset is shuffled in the training phase in case of over-fitting. In the validation and test phases, unshuffled data are used to investigate the model performance.

5.2. Evaluation Metrics

Three metrics are applied to evaluate the performance of the proposed DMCSTN by measuring the difference between the actual traffic flow $Y_i$ and the prediction flow ${\widehat{Y}}_i$. The equations are shown as follows:

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n{\left(Y_i-{\widehat{Y}}_i\right)}^2};$$

(9)

$$MAE={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left|Y_i-{\widehat{Y}}_i\right|;$$

(10)

$$MAPE={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left|{\displaystyle \frac{Y_i-{\widehat{Y}}_i}{Y_i}}\right|,$$

(11)

where n is the sample size in the test set, MAE (Mean Absolute Error) represents the average of the absolute values of the prediction errors of airport traffic flow for all test samples, and RMSE (Root Mean Squared Error) represents the square root of the average of the squared prediction errors for all test samples. MAPE (Mean Absolute Percentage Error) is the average of the absolute percentage values of the prediction errors. For these three metrics, generally speaking, the smaller their values are, the better the performance of the prediction model is.

5.2.1. Experiment Hyperparameters

In the experiment, the batch size is set to 64, and the training epoch to 500. The length of input windows is set to eight. Because the purpose of this work is to forecast short-term airport flow, the timespan of the output sequence is set to four hours (i.e., the output length is four). The output dimension of DMCSTN is set to 35, which equals the number of airports in the dataset. For the deep learning model, the model dimension and the hops of the DMGCN block may have great effects on the prediction precision. The model configuration studies are designed to determine the optimal model architecture in Section 6.4.

The DMCSTN is constructed based on the PyTorch 1.7.1 framework. The Adam optimizer is employed during the training with ${10}^{-3}$ initial learning rate. Our experimental platform is on the server with one CPU (AMD Ryzen 2990WX @3.00 Ghz, 32 cores), 128-GB RAM, and two GPUs (GEFORCE RTX 2080 Ti, 11-GB memory).

5.2.2. Baselines

To further prove the superiority of the proposed approach, several baselines are applied to conduct the comparative experiments, which are illustrated below:

•

SAF: Scheduled arrival flow (SAF) is the statistical data from a flight schedule table, which describes the expected arrival flight flow at a given interval.

•

HA: It takes the average value of each airport arrival flow by the week as prediction results.

•

RF [39]: Random forest (RF) is an ensemble learning method, which combines multiple classifiers to form an effective model.

•

GBRT [40]: Gradient boosted regression trees (GBRT) is a flexible non-parametric statistical learning technique for regression.

•

VAR [41]: The number of temporal lags is set to four. The input feature is the actual airport arrival flow in the training dataset.

•

ARIMA [42]: It fits the historical time series into a parametric model to predict future traffic data.

•

SVR [43]: It uses historical data to fit the relationship between the input and output, which is then used to predict future traffic data. Here, we use the linear kernel.

•

GAT [44]: It leverages an attention mechanism to capture the useful representation from graph-structured data for downstream prediction tasks without depending on knowing the entire graph structure.

•

GRU [45]: It is configured with one layer and 64 hidden units. The initial learning rate is ${10}^{-3}$. The model is trained with batch size 32 and loss function MAE.

•

ST-GCN [27]: it is utilized to model the spatial-temporal dependencies of traffic flow with a fully convolutional framework.

•

Graph WaveNet [28]: Based on a full convolutional architecture, a self-adaptive graph generation method is embedded into Graph WaveNet to complete unknown or incomplete spatial structures for enhancing prediction performance.

To underline the fair comparison of the network-level AAFP, the GCN-based baselines and GAT are equipped with the ASG as spatial topology except for the DMCSTN. For evaluation, the predicted values are retransformed back to the normal numerical space and compared with the ground truth.

6. Experimental Results and Discussion

6.1. Experimental Results

The performance of our proposed approach and other baselines are summarized in

Table 3. The performance comparison on the airport traffic flow dataset.

Methods	1st Hour			2nd Hour			3rd Hour			4th Hour
	MAE	MAPE (%)	RMSE	MAE	MAPE (%)	RMSE	MAE	MAPE (%)	RMSE	MAE	MAPE (%)	RMSE
SAF	2.431	34.4	3.516	2.431	34.4	3.516	2.431	34.4	3.516	2.431	34.4	3.516
HA	1.922	26.9	2.532	1.922	26.9	2.532	1.922	26.9	2.532	1.922	26.9	2.532
VAR	1.836	25.7	2.523	1.970	27.6	2.705	2.034	28.5	2.784	2.084	29.2	2.852
SVR	2.862	39.4	3.887	3.082	44.5	4.362	3.158	44.0	4.474	3.192	46.4	4.418
ARIMA	3.202	43.2	4.717	3.982	56.8	6.142	4.021	56.8	6.113	4.775	65.4	6.639
GBRT	5.421	76.9	7.782	5.423	76.9	7.785	5.521	77.9	8.081	5.905	78.1	8.447
RF	2.420	33.7	3.243	2.504	34.8	3.453	2.571	35.8	3.611	2.889	39.5	3.891
GRU	1.748	24.2	2.427	1.767	24.4	2.461	1.826	25.3	2.525	1.861	25.7	2.575
GAT	2.136	29.6	3.016	2.150	29.9	3.044	2.193	30.4	3.108	2.459	35.1	3.527
ST-GCN	1.767	24.5	2.499	1.768	24.5	2.501	1.990	27.6	2.767	2.007	27.9	2.774
Graph waveNet	1.731	24.2	2.467	1.756	24.3	2.494	1.784	24.7	2.548	1.795	24.9	2.577
DMCSTN	1.680	23.3	2.441	1.702	23.6	2.469	1.727	23.9	2.509	1.742	24.1	2.522

with three measurements, which shows that the DMCSTN achieves the highest performance for all metrics and prediction horizons. In Table 3, MAE, MAPE, and RMSE are computed as the average prediction errors across all airport nodes in the network for each prediction horizon. Specifically, DMCSTN outputs arrival flow predictions for each node (airport) based on its dynamic multi-graph structure, and these node-level predictions are aggregated by averaging the absolute errors (MAE), relative errors (MAPE), and squared errors (RMSE) across all nodes to evaluate network-level performance. The mean square error (MSE) of DMCSTN during the training procedure are shown in Figure 2. To be specific, the following conclusions can be drawn from the experimental results:

(1) Generally, the neural network models with temporal modeling components show better prediction performance than that of the traditional methods (HA, ARIMA, SVR, GBRT RF, VAR). For example, compared with the HA, DMCSTN obtains relative improvement on RMSE, MAE, and MAPE by 3.6%, 12.6%, and 13.4% at the 1st hour prediction horizon. This phenomenon can be mainly attributed to the complex spatial-temporal dependencies of traffic time series that are difficult for conventional data-driven methods to handle. In addition, it can be found that the RF outperforms the GBRT obtaining a comparable performance with the VAR. Meanwhile, among conventional methods, HA utilizes the weekly-periodic average of observed airport arrival flow as the prediction results, so that it is independent of prediction horizons.

(2) ST-GCN shows better prediction precision than GAT, which demonstrates that the temporal modeling is significant in AAFP due to the robust plannability in air traffic. However, ST-GCN performs worse than GRU. Especially, at the relatively long time slices (3–4 h), the prediction performance declines sharply. This phenomenon is mainly caused by the complicated air traffic context. Increasing prediction horizons implies higher uncertainties in dynamic airport networks. It makes conventional GCN difficult to handle the time-varying graph structure and fails to provide desired performance. In addition, although GRU can models the short-term correlations among multiple time series, its representation ability to capture spatial-temporal dependencies is weak resulting in the severe fluctuation of prediction stability. Therefore, only focusing on the temporal or spatial-temporal modeling without considering the dynamic network structure is not enough for accurate AAFP tasks.

(3) Among STGNNs, the DMCSTN and Graph WaveNet with dynamic graph generation mechanisms surpass GRU and ST-GCN. This mechanism effectively completes the agnostic and dynamic spatial topology of the traffic network. Compared to Graph WaveNet, the average MAE, MAPE, and RMSE of DMCSTN are improved by 3%, 3.2%, and 1.4%, respectively. It reveals that the DMCSTN has better prediction ability by elaborately modeling the dynamics of the airport network. In detail, the gating graph generation strategy is different from the self-adaptive graph in the Graph WaveNet which is invariant to the input after being learned. The gating graph of DMCSTN is generated as a gate unit to determine the throughput for each airport pair according to the input airport traffic flow. Furthermore, the temporal component is built upon the self-attention mechanism, together with the position embedding layer, which can obtain the information covering all time steps for data at every time step. Thus, DMCSTN achieves the best prediction performance and stability.

(4) SAF plays a key role to master the daily traffic situation of the airport network in advance, which means an acceptable level of air traffic controllers’ situation awareness. As the prior information, it is independent of prediction horizons. At the 1st hour horizon, the MAE, MAPE, and RMSE of SAF are 2.431, 34.4%, and 3.516 respectively, which indicates more than 2 aircraft averagely deviate from reality in one hour. By contrast with the SAF, the MAE of the proposed DMCSTN is improved by 30% at the 1st hour horizon. It reveals that more than 6570 flights will be accurately predicted by extending the time scale to one year. This improvement can efficiently enhance traffic situation awareness ability and prompt the airspace user experience.

6.2. Effects of Different Spatial Configurations

In a bid to validate the effectiveness of our proposed approaches in modeling spatial dependencies, the dedicated experiments are constructed on DMCSTN with three different spatial configurations as the following designs:

• DMCSTN_Sem: DMCSTN is configured with only ASG as the spatial topology.
• DMCSTN_Geo: DMCSTN is configured with only ADG as the spatial topology.
• DMCSTN_MGCN: It is a variant of DMCSTN, which is constructed by replacing DMGCN with the Multi-Graph Convolutional Network (MGCN) [38].

All the variants have the same settings as DMCSTN except for the aforementioned differences. The prediction results are measured by MAE, MAPE, and RMSE covering four horizons, which are shown in Figure 3. Among the variants of DMCSTN with a unique graph as spatial topology, DMCSTN_Sem performs better than DMCSTN_Geo. This phenomenon verified that the ASG contributes more than ADG in AAFP tasks, which agrees with the fact that flight schedule plans the global traffic flow distribution in the air traffic system. By contrast, DMCSTN_MGCN outperforms the above methods. This improvement proves the advantages of fusing multiple prior factors in forecasting tasks. Meanwhile, with expanding the prediction horizon, there is a growing performance gap between DMCSTN and suboptimal DMCSTN_MGCN. This performance advantage demonstrates the usefulness of capturing dynamic airport network structures in AAFP. More importantly, it further reveals that jointly modeling heterogeneous and dynamic spatial dependencies by the DMGCN contributes to extracting the informative spatial representations, which can enhance the model forecasting performance.

6.3. Effects of Different Temporal Configurations

To further understand the temporal components in DMCSTN, three variants of DMCSTN in specific comparison experiments are shown as follows:

• DMCSTN_GRU: A variant of DMCSTN is constructed by embedding DMGCN into GRU.
• DMCSTN_TCN: A variant of DMCSTN is built by combing DMGCN with TCN.
• DMCSTN_noPos: A variant of DMCSTN is built by removing the position embedding layer from DMCSTN.

All the variant models have the same settings as DMCSTN except for the aforementioned differences. The experiment results were shown in Figure 4. It can be found that DMCSTN_GRU performs worse than DMCSTN_TCN. It reveals that the parallel convolutions regard the input sequence as a whole, which is useful in capturing the sequential correlations. Moreover, the attention-based DMCSTN and DMCSTN_noPos show better performance than DMCSTN_TCN. These results can be mainly attributed to that stacking multiple convolutional layers is required in TCN to connect any two positions in the sequence. However, it fails to efficiently extract internal correlation information of input. In contrast, the utilization of attention mechanisms can obtain the whole sequence information at each time slice. Hence, variants of DMCSTN are superior in capturing long-term correlations and could yield more interpretable models [37]. Furthermore, it was observed that DMCSTN outperforms DMCSTN_noPos, which verified that the position embedding layer is significant in sequential data mining.

6.4. Effects of Different Model Configurations

To investigate the effects of hyperparameters, two experiments are designed to validate the proper model dimensions ($d_{\mathrm{model}}$) of the proposed model and hops of DMGCN. The MAE metric is utilized to measure the experiments. A smaller measurement indicates higher performance. For convenient observation, curves of specific experiments covering four prediction steps are illustrated in one figure. As shown in Figure 5, the prediction performance gradually decreases with expanding the prediction horizon. In addition, the model performance covering four prediction steps demonstrates a similar trend with the increasing of the model configurations, i.e., decreases to an inflection point and then returns. While the $d_{\mathrm{model}}$ is configured with 64, the proposed DMCSTN obtained the best performance. Meanwhile, stacking hops of DMGCN can enhance receptive fields which contribute to AAFP tasks. When the number of hops is increased to three, the proposed model yields the best metrics for overall prediction horizons. Therefore, 64 $d_{\mathrm{model}}$ and three hops are the best model configurations in the airport traffic flow prediction task.

6.5. Case Study

To intuitively know the real prediction ability of DMCSTN, the prediction results of four representative airports are shown in Figure 6, which can derive three observations as follows:

(1)

Although the transition patterns of the arrival traffic flow vary among the four airports, the proposed DMCSTN is still capable of capturing the flow trend, especially at the inflection points. It is hypothesized that the capability of extracting prior operation information improves the distinguishability of different airport traffic time-series data.

(2)

Focusing on the first 23:00 horizon, the observed arrival flights of ZBAA deviated from the normal level and declined sharply to 15. By tracing the weather calendar, it is found that the thunderstorm disturbed the regular flight operation. However, the predicted results of DMCSTN remain closer to the ground truth. This is because the dynamic gating graph mechanism is capable of learning the throughput which is bound by severe weather.

(3)

In summary, the experimental results show that the proposed DMCSTN is more suitable for the AAFP tasks. The performance improvements can be mainly attributed to the combination of DMGCN and TA blocks, which provide superior ability in jointly modeling the complex dynamic dependencies in both spatial and temporal dimensions. These capabilities are particularly valuable in addressing the global airport capacity crunch, where accurate network-level predictions can enhance operational efficiency and mitigate delays in congested regions.

6.6. Discussion

Accurate airport arrival flow prediction (AAFP) plays a critical role in advancing air traffic management, offering significant benefits in operational efficiency and environmental sustainability. The DMCSTN model, by leveraging dynamic multi-graph convolutional structures, enhances the precision of network-level AAFP, contributing to several practical applications.

First, AAFP supports sustainable aviation by enabling more efficient flight operations. Precise arrival flow predictions allow air traffic controllers to optimize descent trajectories and reduce holding patterns, which are fuel-intensive and contribute to carbon emissions. For instance, continuous descent operations, which rely on accurate arrival scheduling, have been shown to reduce fuel consumption and CO₂ emissions significantly [46]. By improving prediction accuracy, DMCSTN facilitates the adoption of such eco-friendly practices, aligning with global efforts toward low-carbon aviation.

Second, AAFP enhances airspace capacity by optimizing traffic flow allocation. In high-density airspaces, such as those over major hub airports, inaccurate predictions can lead to congestion and delays. DMCSTN’s ability to model dynamic spatial-temporal dependencies across multiple airports enables strategic traffic management, ensuring balanced utilization of airspace resources. This capability supports airport capacity planning and flow management, as seen in studies addressing strategic allocation at busy international airports [47], ultimately reducing bottlenecks and improving throughput.

Third, AAFP improves flight efficiency by minimizing delays and enhancing schedule reliability. Accurate predictions of arrival flows allow airlines and airports to better coordinate ground operations and gate assignments, reducing turnaround times. Moreover, by capturing real-time operational constraints, such as flight schedules and durations, DMCSTN helps mitigate the cascading effects of delays across the network. Research on integrated arrival time prediction highlights the importance of precise forecasting for operational efficiency [48], and DMCSTN’s robust performance strengthens these outcomes.

While these benefits underscore the value of AAFP, challenges remain, such as integrating external factors like weather or geopolitical events into predictions. Nonetheless, the advancements offered by DMCSTN pave the way for more resilient and efficient air traffic systems, supporting sustainable and high-capacity aviation networks.

7. Conclusions

In conclusion, this work provides a deep learning-based neural network DMCSTN for network-level AAFP, considering the multiple prior operation factors and dynamic network structure. The proposed DMCSTN includes DMGCN and TA two critical modules. The baseline experiment results on a real-world airport traffic dataset demonstrate the DMCSTN achieves the best prediction performance. In detail, compared to suboptimal Graph WaveNet, the average MAE, MAPE, and RMSE of DMCSTN are improved by 3%, 3.2%, and 1.4%, respectively. In addition, the experiments on the effects of different modules confirm that the DMGCN can adaptively capture the time-varying traffic situations on the airport network. Meanwhile, the TA is able to efficiently mine the evolutional patterns of the airport arrival flow. Furthermore, more than 6570 flights will be accurately predicted by extending the time scale to one year compared to prior SAF information. This performance improvement reveals that the proposed DMCSTN is superior for network-level AAFP tasks, which can efficiently enhance situation awareness of the airport traffic and prompt the airspace user experience.

In the future, we plan to further explore the effects of more flight operation principles on airport arrival flow prediction tasks. Meanwhile, expanding the application of the dynamic multi-graph convolutional mechanism to the other spatial-temporal prediction task in ATFM is also our interest. Moreover, the generalization ability in spatial-temporal prediction tasks would be tested and further investigated.