Air Traffic Flow Prediction in Aviation Networks Using a Multi-Dimensional Spatiotemporal Framework

Abstract

A novel, multi-dimensional, spatiotemporal prediction framework is proposed to enhance air traffic flow prediction in increasingly complex aviation networks. This framework incorporates graph convolutional networks (GCNs) with multi-dimensional Long Short-Term Memory (LSTM) networks and multi-scale, temporal convolution, employing an attention mechanism to effectively capture spatiotemporal dependencies. By addressing irregular topologies and dynamic temporal trends, the framework models local air traffic patterns with improved accuracy. The experimental results demonstrate significant predictive accuracy improvements over traditional methods, particularly in accounting for the complex nature of air traffic flows. The model’s scalability and adaptability extend its application to various aviation networks, encompassing all airspace units within three local networks, rather than focusing solely on airport traffic. These findings contribute to the development of more intelligent, accurate, and adaptive air traffic management systems, ultimately enhancing both operational efficiency and safety.

1. Introduction

Air Traffic Flow Management (ATFM) is a crucial component for ensuring the efficient and safe operation of the global aviation system [1]. With the rapid expansion in air travel demand, the volume of flights continues to rise, leading to increased congestion in airspace, particularly around busy airports and along heavily trafficked routes [2]. The primary aim of ATFM is to optimize the allocation of airspace and airport resources to ensure that flights operate safely and efficiently, while minimizing delays and improving punctuality. Effective traffic flow management not only enhances the operational efficiency of the aviation network but also reduces airlines’ operational costs and boosts passengers’ satisfaction.

The operation of air traffic is dependent on the coordinated integration of routes, airspace, and traffic flow [3]. Routes are predefined paths that aircraft follow within the airspace, akin to highways in ground transportation, guiding them from departure to destination via specific waypoints. These routes create a structured network within the airspace, ensuring aircraft adhere to designated paths and avoid conflicts. The planning and adjustment of these routes are influenced by airspace capacity and the volume of air traffic. Airspace refers to the three-dimensional region in which aircraft operate, providing the spatial framework for routes. It is segmented and managed by national or regional aviation authorities, typically based on geographic location, altitude, and usage (e.g., commercial or military operations). Authorities adjust or restrict routes as necessary to ensure safe and efficient flight operations, preventing collisions and other safety incidents. Traffic flow pertains to the number of aircraft within a specific airspace or route section over a given time period [4]. The volume of traffic significantly impacts airspace congestion and management complexity. High traffic volumes lead to congestion, resulting in delays and an increased risk of mid-air conflicts. ATFM’s central task is to optimize the traffic flow within the airspace by adjusting flight speeds and rescheduling departure and arrival times to ensure safe and efficient journeys.

Accurate traffic flow prediction is essential for effective ATFM, particularly as aviation networks become increasingly complex. By predicting air traffic volumes within specific airspaces, air traffic controllers can proactively identify potential congestion areas and develop strategies for optimizing routes and dynamically allocating resources to handle peak traffic periods and unexpected events. Improved prediction enhances air traffic control systems’ intelligence, aiding route planning, airspace capacity distribution, and dynamic adjustments, thereby reducing delays, improving on-time performance, and enhancing economic returns and passenger satisfaction for airlines.

Artificial Intelligence (AI) is playing a key role in advancing air traffic flow prediction, addressing the increasing complexity of air traffic patterns and irregular airspace structures. AI enables aviation networks to manage the spatial and temporal dependencies of air traffic flow more effectively, allowing for more accurate and adaptive predictions. Traditional methods often struggle to capture the complex patterns of traffic in large, interconnected networks, but AI-based approaches can learn from vast data sources and adapt to dynamic conditions, offering intelligent traffic management solutions.

Recent research has explored novel methods and models to enhance air traffic flow prediction accuracy and efficiency. While traditional physical models [5,6] and shallow machine learning techniques such as Support Vector Regression (SVR) [7], neural networks (NN) [8,9,10], clustering algorithms [11], and boosting methods [12] have shown success in predicting traffic at individual airports or specific waypoints [13], these approaches often struggle to capture the complex spatiotemporal correlations associated with traffic fluctuations across broader aviation networks.

Central to AI’s application in this field is the integration of advanced machine learning (ML) and deep learning (DL) techniques. In recent years, temporal dependencies have been modeled using Long Short-Term Memory (LSTM) networks, a class of recurrent neural networks (RNNs) designed to learn from and predict time series data. Studies have applied LSTM networks [14,15], RNNs [16], and causal graphs [17] to capture temporal dependencies in airspace traffic variations. However, predicting air traffic flow remains challenging due to periodic trends (e.g., normal versus peak flight periods, weekdays versus weekends) and random events. These models, while powerful, often face difficulties in managing multi-scale, temporal correlations within the same time series, limiting their ability to provide accurate predictions across varying temporal patterns.

To capture spatial correlations more effectively, some studies have proposed using gridded map methods to encode local air traffic flow conditions into novel two-dimensional [18] or three-dimensional [19] data representations. While this approach theoretically offers richer spatial information, the imposition of fixed-size, regular grid structures onto airspace can conflict with the operational logic of air traffic controllers [20], potentially increasing their workload and failing to reflect the irregularity of airspace structures.

Graph convolutional networks (GCNs) and related models have shown promise in modeling and analyzing traffic changes across the irregular topologies of multiple airspaces. Initial efforts [21,22] have employed GCN domain models to explore interactions between airspace nodes, revealing complex relationships. However, these studies have largely been limited to a small number of airspace nodes, making it challenging for the models to adaptively capture the complexities of non-Euclidean spatial structures in real-world aviation networks [23]. This limitation has hindered the broader application of these models in local aviation networks.

Despite the valuable insights provided by existing methodologies, there remains a need for advanced models that are capable of comprehensively addressing multi-scale, spatiotemporal correlations and irregular structures within the aviation network.

This study addresses existing gaps in air traffic flow prediction by proposing a novel, multi-dimensional, spatiotemporal prediction framework. The primary objectives are as follows:

• To develop an integrated framework that combines GCNs with multi-dimensional, time-dependent modeling and multi-scale, temporal convolution, enhanced by an attention mechanism. This framework aims to capture complex spatiotemporal dependencies within air traffic networks, substantially improving predictive accuracy.
• To incorporate advanced graph convolutional architectures that account for the irregular topologies that are characteristic of local aviation networks. This approach ensures accurate representation and the learning of the intricate spatial relationships among air traffic nodes.
• To utilize the computational power of deep hybrid neural networks for modeling multi-scale, temporal dependencies, enabling the framework to predict air traffic flow with increased precision by capturing both specific periodic trends and short-term fluctuations.
• To our knowledge, this is the first study to perform data collection and traffic flow prediction across all airspace units within three local aviation networks, rather than focusing solely on airport takeoff and landing traffic. This methodology is adaptable to other spatiotemporal data prediction tasks, such as weather prediction and pollution analysis.

By achieving these objectives, this study aims to enhance the accuracy, adaptability, and interpretability of air traffic flow predictions, thereby contributing to more optimized and intelligent air traffic management systems.

2. Materials and Methods

2.1. Multi-Dimensional, Spatiotemporal Prediction Framework

This paper proposes a multi-dimensional, spatiotemporal prediction framework that integrates spatial dependency modeling based on graph convolution, multi-dimensional time-dependent modeling, and multi-scale time domain convolution utilizing the attention mechanism, as demonstrated in Figure 1.

This technology aims to address the complex spatiotemporal correlations within air traffic flow networks. It incorporates airspace configuration and route coupling laws to extract the spatial characteristics inherent in the irregular topology observed in aviation networks. This is achieved through the construction of a graph convolutional network, facilitating a unified and structured characterization of local spatial relationships among nodes. In Figure 1, the number of each local aviation network node represents its ID.

To meet the practical requirements of intelligently predicting multi-dimensional, spatiotemporal states within aviation networks, this approach integrates the spatial and temporal dependencies of each node in the network dynamics. It extracts global components from real-time traffic flow data influenced by long-term spatial and temporal relationships while capturing local components that fluctuate with short-term specific events.

By leveraging the processing capabilities of graph convolutional networks and multi-dimensional recurrent neural networks, a deep hybrid neural network architecture is established. This network analyzes the multi-dimensional, spatiotemporal characteristics of air traffic flow from a hierarchical, multi-perspective standpoint. This enables the accurate prediction of future trends for each node within the aviation network and enhances the interpretability of the prediction methodology.

2.2. Spatial Dependency Modeling Based on Graph Convolution

This technique begins by constructing a topology graph $G$ of the aviation network, based on the spatial structure of the aviation network and the coupling law of airway traffic flow. The vertices of the graph represent the airspace nodes, while the edges are used to describe the nearest neighbors and the distances between them. The relationship between the airspace nodes and the topology graph is represented by the normalized Laplace matrix $L$. This is defined in Equation (1), where $D$ is the degree matrix of the graph $G$, and $A$ is the adjacency matrix with the weighted adjacency matrix.

$$L=I_n-D^{-\frac{1}{2}}A{D}^{-\frac{1}{2}}$$

(1)

Given that the Laplace matrix $L$ is a symmetric positive definite matrix, the eigenvalue decomposition yields $L=U\mathsf{\Lambda }{U}^T$, where the matrix $U$ is the matrix consisting of eigenvectors and the matrix $\mathsf{\Lambda }$ is the diagonal matrix consisting of eigenvalues. With reference to the Fourier transform of Euclidean space, the Fourier transform of the image is denoted as $\widehat{x}=U^{T}x$, and the graph signal $x$ is transformed into the corresponding spectral domain. In this domain, $x$ represents the original feature of the entire graph composition. Consequently, the convolution of the graph signals $x$ and $y$ on the graph $G$ is calculated as ${\ast }_G$, as shown in Equation (2).

$$x{\ast }_{G}y=U\left(\right(U^T x)\odot (U^T y\left)\right)$$

(2)

The aforementioned calculations demonstrate that the current technique establishes graph features that describe local spatial relationships. From graph spectral theory, the convolution of the graph signal $x$ (traffic flow data at a certain moment) is calculated on the graph $G$ using the spectral filter $g_{\theta }$, as shown in Equation (3).

$$g_{\theta }{\ast }_{G}x=g_{\theta }\left(L\right)x=g_{\theta }\left(U\mathsf{\Lambda }{U}^T\right)x=U{g}_{\theta }\left(\mathsf{\Lambda }\right)U^{T}x$$

(3)

To meet the requirements of the spatial relationship analysis, a graph convolution layer was proposed, based on the graph Fourier transform and the polynomial approximation. This extracts graph features embedded in the local spatial structure, as illustrated in Equation (4). In this equation, $\theta$ represents the polynomial coefficients, while $K$ denotes the size of the local perceptual field of the graph filter. This field is defined as the set of nodes whose nearest neighbors are of an order less than $K$.

$$y=U\left(\sum _{k=0}^{K-1}{\theta }_k{\mathsf{\Lambda }}^k\right)U^{T}x=\sum _{k=0}^{K-1}{\theta }_k{L}^{k}x$$

(4)

The objective of this technique is to characterize the spatial relationships of aviation networks through the application of a cluster analysis to the graphical features of local spatial relationships of aviation network nodes.

2.3. Multi-Dimensional, Time-Dependent Modeling

• Multi-Dimensional LSTM.

The state of aviation network traffic flow is influenced not only by recent specific events but also by strong, long-term cyclical patterns, such as daily and weekly cycles. This technique leverages the historical cyclical fluctuations in the aviation network state and the impact of random events by employing a temporal attention mechanism, as illustrated in Figure 2. The method combines the advantages of convolutional neural networks and recurrent neural networks in handling irregular spatiotemporal data to establish a dynamic spatiotemporal network based on deep hybrid neural networks. This network is designed to predict the operational state of each node in the aviation network under complex scenarios.

The implicit layer structure of the Long Short-Term Memory network unit is enhanced in order to construct the dynamic spatiotemporal network unit, as illustrated in Equation (5). This includes the input gate $i$, the forgetting gate $f$, the output gate $o$, and the memory unit $c$, which is used for storing and forgetting information. $X$ represents the input data, ${\ast }_G$ represents the dynamic graph convolution operation, $H$ represents the output of the unit, $t$ represents the current moment, $T$ represents the time interval, and $j$ represents the time–attention selection parameter, which is used to select periods such as days, weeks, years, etc. $W$ and $b$ represent the corresponding control weights and deviations, while $\odot$ denotes the matrix dot product.

$$\left\{\begin{array}{l}\hspace{1em}{i}_t=\sigma \left(W_{xi}{\ast }_G{X}_t+W_{hi}\odot H_{t-1}+{\displaystyle \sum _j}{W}_{hi}^j\odot H_{t-jT}+b_i\right)\\ \hspace{1em}{f}_t=\sigma \left(W_{xf}{\ast }_G{X}_t+W_{hf}\odot H_{t-1}+{\displaystyle \sum _j}{W}_{hf}^j\odot H_{t-jT}+b_f\right)\\ c_t=f_t\odot c_{t-1}+i_t\odot \mathit{tanh}\left(W_{xc}{\ast }_G{X}_t+W_{hc}\odot H_{t-1}+{\displaystyle \sum _j}{W}_{hc}^j\odot H_{t-jT}+b_c\right)\\ \hspace{1em}{o}_t=\sigma \left(W_{xo}{\ast }_G{X}_t+W_{ho}\odot H_{t-1}+{\displaystyle \sum _j}{W}_{ho}^j\odot H_{t-jT}+b_o\right)\\ \hspace{1em}\hspace{1em}{h}_t=o_t\odot \mathit{tanh}\left(c_t\right)\end{array}\right.$$

(5)

This model proposes stacking multiple layers of dynamic spatiotemporal network units and utilizing the temporal attention mechanism to focus on historical cyclical information. This facilitates the automatic learning of the state fluctuation patterns of the aviation network and enables the accurate prediction of future trends. An objective function incorporating a regularization term was constructed to guide the training of the model.

• Multi-Scale Time Domain Convolution Based on the Attention Mechanism

The proposed technique converts the sequence of graphical features into one-dimensional lattice data that are formed by regular sampling on the time axis. This ensures that predictions made at previous moments do not leak future information, utilizing full convolution and causal convolution operations. The causal convolution of the filter $f$ at moment $t$ in the time series $x$ is calculated as shown in Equation (6), where $K$ is the filter size.

$$\left(f\ast x\right)\left(x_t\right)=\sum _{k=1}^{K}f\left(k\right)\cdot x_{t-K+k}$$

(6)

Causal convolution necessitates additional layers or larger filters to augment the receptive field, making it ineffective for processing extensive historical data. To address this limitation, the proposed approach employs dilation convolution to increase the receptive field of the convolution. For a one-dimensional input sequence, $x$, and a convolution kernel, $f:\{0,1,\dots ,k-1\}$, the dilation convolution operation, $F$, is illustrated in Equation (7).

$$F\left(s\right)=\left(x{\ast }_{d}f\right)\left(s\right)=\sum _{i=0}^{k-1}f\left(i\right)\cdot x_{s-d\cdot i}$$

(7)

where $d$ is the dilation factor, $k$ is the convolution kernel size, and $s-d\cdot i$ denotes the position of adopting the previous layer of input data; the dilation factor controls the number of zeros to be inserted between each of the two inputs to achieve an increase in the length of the observed sequences, with essentially no change in the computational effort.

In traffic flow predicting, researchers have shown that traffic time series are influenced by key temporal characteristics in both recent and long-term historical data, such as daily cycles and weekdays versus weekends. However, canonical RNNs and existing models struggle with very long input sequences. For instance, peak hour traffic flows may be similar across consecutive weekdays, while weekday and holiday traffic patterns can differ significantly.

The value $Z^i\left(t\right)$ of the dilation causal convolution at the moment $t$ of layer $i$ is determined by the input value at the moment $t$ of layer $i-1$ and the moments before that, as shown in Equation (8). Here, $Z\left(t\right)$ represents the time series data arranged in one dimension, and $d$, $k$, and $f$ are the corresponding dilation rate, the size of the filter, and the parameters. In order to avoid information loss and information redundancy, the present technique sets $d_i=d_{i-1}{k}_{i-1} \left(i>1\right)$. According to the derivation, the receptive field (RF) of $Z^i\left(t\right)$ for the historical time series $Z\left(t\right)$ is calculated as shown in Equation (9).

$$Z^i\left(t\right)=\left\{\begin{array}{cc}{\displaystyle \sum _{j=0}^{k_{i-1}-1}}{f}^{i-1}\left(j\right)\cdot Z^{i-1}\left(t-d_{i-1}\cdot j\right),& i>1\\ {\displaystyle \sum _{j=0}^{k_0-1}}{f}^0\left(j\right)\cdot Z\left(t-j\right),& i=1\end{array}\right.$$

(8)

$$RF\left(i\right)=d_{i-1}{k}_{i-1}=\prod _{j=0}^{i-1}{k}_j$$

(9)

2.4. Dynamic Analysis of Prediction

In the aforementioned process, the model learns static spatial dependencies. However, the occurrence of uncertainty events causes the spatial dependencies of the posture of some nodes in the aviation network to change over time. Consequently, the use of a fixed Laplace matrix is unable to capture such changes. In order to track the spatial dependencies of the nodes’ posture changes under stochastic events, this technique introduces tensor decomposition into the deep learning framework. It was proposed that the global component ${\mathcal{X}}_Q$, which is determined by the structure of the whole network, and the local component ${\mathcal{X}}_S$, which is determined by a specific time period or event, should be extracted from the aviation network traffic data samples $\mathcal{X}$. This is shown in Equation (10), where $\mathcal{G}$ is the low-rank kernel tensor and ${\times }_i$ is denoted as the multiplication with each one-dimensional matrix $U_i$.

$$\mathcal{X}=\mathcal{G}{\times }_1{U}_1{\times }_2{U}_2\times \cdots {\times }_N{U}_N={\mathcal{X}}_Q+{\mathcal{X}}_S$$

(10)

Combined with the event knowledge, this technique led us to propose a deep learning-based Laplace matrix estimator, which dynamically learns the Laplace matrix under the influence of a specific event based on the global and local components, i.e., the local Laplace matrix $L_S$. Through the above calculation, the spatiotemporal dependency of the aviation network under random events is represented by a new Laplace matrix, $L$, as shown in Equation (11), and the real-time estimated Laplace matrix is input to the graph convolution layer for feature extraction and prediction, where $L_Q$ is the global Laplace matrix determined by the spatial structure of the aviation network, and F is the learned estimation function.

$$L=L_Q+L_S=L_Q+F\left({\mathcal{X}}_Q,{\mathcal{X}}_S\right)$$

(11)

2.5. Objective Function

This technique employs a three-pronged approach to construct the objective function. Firstly, it incorporates regular terms to guide the model training. Secondly, it employs back propagation to guide the network parameter learning. Thirdly, it incorporates representation by minimizing the prediction error generated from the sample prediction results and the true values. Furthermore, it incorporates regular terms to constrain the model complexity and prevent the model from overfitting, as shown in Equation (12).

$$\underset{W,\Theta ,\mathcal{F}}{min}\sum _p{‖X\left(t+p\right)-\hspace{0.33em}\widehat{Z}\left(t+p\right)‖}_2^2+\alpha {‖W‖}_2^2+\beta {‖\Theta ‖}_2^2+\gamma {‖F‖}_2^2$$

(12)

where $W$, $\mathsf{\Theta }$, and F are network parameters, the latter three are L2 paradigm regularization terms, and $\alpha$, $\beta$, and $\gamma$ are the corresponding regularisation parameters used to balance the objectives of fitting the training and keeping the parameter values small.

3. Results

3.1. Datasets

• Spatial Structure of Three Local Aviation Networks

This study collected traffic flow data from three local aviation networks, referred to as Aviation Networks NS, NG, and NC, containing 36, 24, and 21 airspace units, respectively. The spatial relationships among the airspace units within these networks are depicted in Figure 3, Figure 4 and Figure 5. Each polygon’s center number corresponds to an airspace unit ID, with the horizontal and vertical axes representing latitude and longitude. As observed in Figure 3, Figure 4 and Figure 5, the size of the airspace units is non-uniform, and their boundaries are irregular, significantly complicating spatial relationship modeling.

• Time Domain Characteristics of Traffic Flow in Each Airspace Unit

This study preprocesses ADS-B raw data for all aircraft within the aviation network, aggregating aircraft numbers within each airspace unit according to their real-time spatial location. Traffic data for each unit are aggregated every 15 min, spanning from 00:00 on 1 February 2021, to 19:00 on 18 May 2021, yielding 10,252 time intervals.

The daily traffic flow data (within 15 min) of typical airspace units of the three local aviation networks are presented in Figure 6, Figure 7 and Figure 8. The traffic flow data for each airspace unit vary significantly, influenced not only by daily airspace traffic planning but also by other dynamic factors. Substantial differences are observed both between airspace units within the same aviation network and across different aviation networks.

Similarly, Figure 9, Figure 10 and Figure 11 display the weekly traffic flow data (within 15 min) for typical airspace units. These figures highlight the presence of cyclical patterns in the weekly time series, albeit with a high degree of stochasticity.

3.2. Evaluation Indicators

The following three metrics were employed in this paper to assess the predictive accuracy of the prediction model:

• Root Mean Squared Error (RMSE).

$$RMSE=\sqrt{\frac{1}{MN}\sum _{j=1}^M \sum _{i=1}^N {\left(y_i^j-{\widehat{y}}_i^j\right)}^2}$$

(13)

2.

Mean Absolute Error (MAE).

$$MAE=\frac{1}{MN}\sum _{j=1}^M \sum _{i=1}^N \left|y_i^j-{\widehat{y}}_i^j\right|$$

(14)

3.

Weighted Mean Absolute Percentage Error (WMAPE).

$$WMAPE=\frac{\sum _{j=1}^M \sum _{i=1}^N \left|y_i^j-{\widehat{y}}_i^j\right|}{\sum _{j=1}^M \sum _{i=1}^N \left|y_i^j\right|}$$

(15)

where $y_i^j$ and ${\widehat{y}}_i^j$ denote the real and predicted traffic flow information, respectively. $M$ is the number of samples in the time series, and $N$ is the number of airports. Three key indicators were used to evaluate prediction accuracy, with smaller values indicating higher accuracy.

To address instances where traffic flow data were minimal or zero, WMAPE was employed in place of the more commonly used Mean Absolute Percentage Error (MAPE) in these experimental evaluations. This choice is crucial for maintaining the accuracy and reliability of the performance metrics, particularly in datasets with significant variability in traffic volume, including periods of extremely low or zero traffic.

Although MAPE is widely utilized for error measurement, it has well-documented limitations when dealing with small denominators, often leading to inflated and misleading error values—particularly in scenarios with sparse traffic. This issue is of particular concern in air traffic flow prediction, where certain airspace units may experience low or zero traffic flow at specific times. Under such conditions, the standard MAPE can distort the overall error metrics, as it inadequately reflects the influence of these low traffic values.

In contrast, WMAPE offers a more stable and representative measure of prediction accuracy by adjusting for the relative magnitude of the data. By assigning weights to absolute errors based on the actual values of the data points, WMAPE mitigates the disproportionate influence of low or zero traffic values on the overall error calculation. Consequently, this approach provides a more balanced assessment of the model’s performance across varying traffic conditions, from low-density traffic zones to high-volume airspace corridors.

3.3. Spatial Dependency Modeling

To model the spatial characteristics of the irregular topology in aviation networks, the spatial relationships between the airspace units of the three networks are represented using a graph structure as described in Section 2.2, shown in the left panels of Figure 12, Figure 13 and Figure 14. Each node represents each airspace unit, and the line between two nodes represents whether there is a flight route connection. Each node’s center number corresponds to an airspace unit ID. Importantly, spatial adjacency between airspace units does not necessarily imply a high correlation in traffic flow between them. For example, two adjacent airspaces may lack direct route connections.

Graph convolution was employed to model the spatial dependencies based on these topological relationships. The right panels of Figure 12, Figure 13 and Figure 14 depict normalized spatial dependencies, where the axes represent airspace units, and each square indicates the dependency between two units. Darker colors represent stronger correlations.

3.4. Model Training

The dataset is divided into three sets, with a ratio of 7:1:2. The first 70% of the data serve as the training set, the middle 10% as the validation set, and the last 20% as the test set. The training processes for predicting the next 15 min, 1 h, and 3 h for Aviation Network NS are illustrated in Figure 15, Figure 16 and Figure 17.

3.5. Comparative Analysis of Test Results

In this experiment, a multi-dimensional, spatiotemporal framework (MDSTF) model for network traffic prediction was constructed.

Table 1. Comparison of Aviation Network NS model prediction results.

Model	15 min			1 h			3 h
	RMSE	MAE	WMAPE	RMSE	MAE	WMAPE	RMSE	MAE	WMAPE
ARIMA	2.92	3.87	19.66%	4.62	6.25	29.91%	7.19	9.85	43.13%
SVR	2.95	3.87	19.83%	4.53	6.13	29.86%	7.23	10.06	44.86%
BPNN	2.84	3.76	19.50%	4.14	5.58	27.65%	6.18	8.53	38.36%
MDSTF	2.78	3.76	18.97%	3.87	5.35	25.92%	4.87	6.87	30.59%

,

Table 2. Comparison of Aviation Network NG model prediction results.

Model	15 min			1 h			3 h
	RMSE	MAE	WMAPE	RMSE	MAE	WMAPE	RMSE	MAE	WMAPE
ARIMA	3.34	4.49	18.99%	5.67	7.88	30.54%	9.14	13.07	45.74%
SVR	3.40	4.54	19.18%	5.54	7.67	30.15%	9.20	13.37	46.59%
BPNN	3.30	4.46	19.10%	4.99	6.95	27.77%	7.84	11.39	39.56%
MDSTF	3.34	4.65	19.05%	4.88	6.80	26.15%	6.49	9.17	34.49%

and

Table 3. Comparison of Aviation Network NC model prediction results.

Model	15 min			1 h			3 h
	RMSE	MAE	WMAPE	RMSE	MAE	WMAPE	RMSE	MAE	WMAPE
ARIMA	2.90	3.94	20.26%	4.77	6.53	32.44%	7.14	9.93	44.48%
SVR	2.90	3.93	20.20%	4.65	6.42	32.46%	7.23	10.30	46.29%
BPNN	2.77	3.79	19.72%	4.13	5.81	29.45%	6.02	8.55	39.48%
MDSTF	2.69	3.74	18.77%	3.85	5.43	27.55%	4.51	6.58	31.77%

present the results of predictions for the next 15 min, 1 h, and 3 h across the three aviation networks, comparing classical methods such as ARIMA, SVR, and BPNN. These methods are well-established and widely used across various domains due to their robustness and broad applicability, making them valuable benchmarks for this study. The results indicate that the proposed method demonstrates a significant advantage, especially in prediction accuracy, for the next 1 h (improved by approximately 1.6% to 4.9%) and for the next 3 h (improved by approximately 5.1% to 14.5%).

The analysis revealed that the traffic data values for numerous airspace units were insufficiently detailed, negatively impacting the prediction efficacy. This is demonstrated in Figure 18, Figure 19 and Figure 20 and

Table 4. Correlation analysis between airspace unit traffic flow and prediction error.

WMAPE (%)	15 min			1 h			3 h
	f ≥ Median	f < Median	Average	f ≥ Median	f < Median	Average	f ≥ Median	f < Median	Average
Network NS	16.79%	23.33%	18.97%	23.98%	29.80%	25.92%	29.60%	32.58%	30.59%
Network NG	15.91%	22.75%	19.05%	22.95%	29.93%	26.15%	35.33%	33.50%	34.49%
Network NC	16.53%	23.24%	18.77%	24.34%	33.98%	27.55%	28.56%	38.21%	31.77%

, which compare the relationship between the traffic flow of airspace units and the prediction accuracy. It was observed that when the average traffic flow of an airspace unit was greater than or equal to the median value of the corresponding aviation network, the prediction accuracy was relatively high. Specifically, for 15 min prediction, the accuracy exceeded the average by 2.2% to 3.1% and surpassed that of low-traffic prediction by 6.5% to 6.8%. For one-hour prediction, the accuracy was 1.9% to 3.2% higher than the average and 5.8% to 9.6% higher than that for low-flow airspace units.

4. Discussion

The results of the proposed multi-dimensional, spatiotemporal prediction framework demonstrate substantial improvements over baseline models, highlighting the effectiveness of integrating GCNs, multi-dimensional LSTM networks, and attention mechanisms for air traffic flow prediction.

• Superior Predictive Performance.

The most notable outcome is the significant enhancement in prediction accuracy across all the evaluated metrics, particularly Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Weighted Mean Absolute Percentage Error (WMAPE). These improvements suggest that the proposed model is better equipped to capture the complexities of air traffic flow compared to traditional methods. Specifically, the incorporation of GCNs enables the model to capture the irregular, non-Euclidean spatial relationships between nodes in the aviation network—an area in which conventional Euclidean-based models often struggle.

Furthermore, the integration of multi-scale, temporal convolution enhances the model’s capacity to capture temporal dependencies across varying scales, from short-term fluctuations to long-term trends. This is crucial for air traffic flow prediction, where interactions between different time scales (e.g., hourly, daily, weekly) can be highly complex.

• Scalability and Generalization.

The consistent performance of the proposed framework across diverse local aviation networks with varying characteristics highlights its scalability and generalization capabilities. Unlike models that require extensive design adjustments for specific datasets or environments, this framework demonstrates broad applicability across diverse network configurations, making it highly suitable for global air traffic management systems. Scalability is a critical feature, enabling deployment across a wide range of operational contexts, from smaller regional airspaces to large, complex international networks.

The robustness of the framework is further evidenced by its stable performance metrics across different network sizes and structures, indicating its ability to handle varying levels of complexity within aviation networks. This adaptability is a crucial advantage in real-world applications, where network structures can vary significantly across regions and countries.

5. Conclusions

In summary, the results of the proposed multi-dimensional, spatiotemporal prediction framework confirm its superiority over traditional models in predicting air traffic flow. By leveraging the strengths of GCNs, multi-dimensional LSTM networks, and attention mechanisms, the model is able to accurately capture the complex spatiotemporal dependencies that characterize air traffic networks.

5.1. Limitations

Despite the significant improvements achieved by the proposed multi-dimensional, spatiotemporal prediction framework, several limitations remain, highlighting potential areas for future research and enhancement.

• Handling Extreme Outlier Events.

While the model performs well across various scenarios, its ability to handle extreme outlier events, such as rare but impactful weather disruptions or large-scale airspace interference, is limited. These events often introduce abrupt, unpredictable changes in air traffic patterns that may not be fully captured by the current model’s architecture. In particular, these outliers often lead to the formation of bottlenecks in the airspace, further complicating prediction efforts. The current model’s ability to predict these bottlenecks, while functional, could be further improved to account for their often sporadic and complex nature.

• Computational Complexity.

The model’s reliance on GCNs and LSTM networks introduces considerable computational demands, particularly in large-scale networks, which can hinder real-time applications. The high processing power and memory requirements pose challenges in environments where rapid inference is critical, such as in high-frequency air traffic control operations, where even minor delays in prediction could have operational consequences. This computational overhead also affects the model’s ability to react quickly to emerging bottlenecks in the airspace.

• Data Availability and Quality.

The model’s performance is highly dependent on the availability and quality of data. Inconsistent or sparse data across certain air traffic networks may result in reduced prediction accuracy. Furthermore, the model may struggle to generalize effectively in regions where historical data are either scarce or of low quality, due to missing records, sensor failures, or incomplete datasets. This limitation could restrict the model’s applicability in less-developed regions with limited data infrastructures. Moreover, these data limitations make it challenging to accurately predict and address bottlenecks, particularly in regions with limited real-time monitoring capabilities.

5.2. Future Work

• Predicting Multiple Time Horizons.

Future research should explore the model’s capacity for predicting air traffic flow over medium- and long-term horizons, contingent on the availability of such data. While some commercial companies offer these datasets, their high costs currently place them beyond the reach of this research. Medium-term predictions (weeks to months) and long-term predictions (months to years) are essential for strategic air traffic management, infrastructure planning, and policy development. Enhancing the model to incorporate broader seasonal trends, airport expansions, and shifting air traffic patterns will be key to developing more adaptive and future-oriented air traffic systems.

• Medium-Term Prediction: By incorporating techniques such as seasonal decomposition of time series (e.g., SARIMA models) alongside deep neural networks, the model can better capture medium-term periodicities in air traffic, such as fluctuations due to holidays, vacation seasons, or major events like the Olympics or trade conferences. Understanding these patterns can support more efficient scheduling, staffing, and resource allocation at airports.
• Long-Term Prediction: Long-term prediction can consider broader trends, such as global air travel demand shifts, fleet modernization, regulatory changes, and the rise of urban air mobility (e.g., drones or air taxis). Techniques such as multi-dimensional RNNs with extended time horizon capabilities, combined with macroeconomic and policy-based inputs, could be employed to predict long-term air traffic growth and flow changes, which are crucial for infrastructure investments and regulatory planning. This long-term prediction will also include an analysis of airspace bottlenecks caused by systemic issues such as increased air traffic demand and infrastructure constraints.
• Incorporating Anomaly Detection Mechanisms.

To address the limitations in handling extreme events, future work could integrate advanced anomaly detection algorithms into the prediction framework. These algorithms could identify and mitigate unusual events more effectively by flagging anomalous patterns before they propagate through the network. Unsupervised learning techniques, such as autoencoders or more sophisticated probabilistic models, could enhance the model’s ability to detect and adjust for outlier events. Anomaly detection will also play a key role in the early identification of airspace bottlenecks, allowing for quicker interventions and more accurate traffic flow management.

• Model Optimization for Real-Time Applications.

Given the model’s computational intensity, future research should focus on optimizing its architecture for faster inference times while maintaining accuracy. Techniques such as model pruning, which reduces the number of parameters, or knowledge distillation, which trains a smaller model to mimic the larger one, could make the framework more suitable for real-time air traffic management. These optimizations will improve the model’s responsiveness, enabling it to predict and manage bottlenecks more effectively in real-time scenarios.

• Improved Data Fusion and Augmentation Techniques.

To overcome the limitations posed by inconsistent or sparse data, future work could focus on advanced data fusion and augmentation techniques. Incorporating external data sources such as weather prediction, satellite data, or even social media insights could provide additional context that improves the model’s robustness. Synthetic data generation techniques, such as GANs (Generative Adversarial Networks), could also be employed to augment the training dataset in regions with limited historical data, thus enhancing the model’s ability to generalize. These data enhancements will help refine bottleneck detection and prediction, particularly in regions with less-developed monitoring infrastructure.