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Article

A Traffic Flow Prediction Model Based on Dynamic Graph Convolution and Adaptive Spatial Feature Extraction

by
Weijun Li
*,
Guoliang Yang
,
Zhangyou Xiong
,
Xiaojuan Zhu
and
Xinyu Ma
School of Computer Science and Engineering, North Minzu University, Yinchuan 750021, China
*
Author to whom correspondence should be addressed.
Symmetry 2025, 17(7), 1007; https://doi.org/10.3390/sym17071007
Submission received: 20 May 2025 / Revised: 19 June 2025 / Accepted: 24 June 2025 / Published: 26 June 2025
(This article belongs to the Section Computer)

Abstract

The inherent symmetry in traffic flow patterns plays a fundamental role in urban transportation systems. This study proposes a Dynamic Graph Convolutional Recurrent Adaptive Network (DGCRAN) for traffic flow prediction, leveraging symmetry principles in spatial–temporal dependencies. Unlike conventional models relying on static graph structures that often break real-world symmetry relationships, our approach introduces two key innovations respecting the dynamic symmetry of traffic networks: First, a Dynamic Graph Convolutional Recurrent Network (DGCRN) is proposed that preserves and adapts to the time-varying symmetry in node associations, and an Adaptive Graph Convolutional Network (AGCN) that captures the symmetric and asymmetric patterns between nodes. The experimental results on PEMS03, PEMS04, and PEMS08 datasets demonstrate that DGCRAN maintains superior performance symmetry across metrics: reducing MAE, RMSE, and MAPE by average margins of 12.7%, 10.3%, and 14.2%, respectively, compared to 15 benchmarks. Notably, the model achieves maximum MAE reduction of 21.33% on PEMS08, verifying its ability to model the symmetric and asymmetric characteristics in traffic flow dependencies while significantly improving prediction accuracy and generalization capability.

1. Introduction

With the acceleration of urbanization and the surge of population, this not only triggers large-scale population movement, but also severely puts the sustainable development of cities to test. Among the many problems, intelligent transportation systems (ITS) have become a hot research topic nowadays due to their great potential in improving system efficiency and optimizing decision-making [1]. As a key part of ITS, traffic flow prediction aims to predict the future traffic flow, operating speed, and passenger demand of urban transportation systems with the help of past traffic data. Since traffic flow prediction plays an important role in traffic scheduling and management, it has successfully attracted the attention of many experts and scholars in the field of machine learning in recent years [2].
Over the past decades, thousands of data-driven traffic prediction models have been proposed in the field of scientific research. These methods mainly cover three major categories based on statistical theory, deep learning, and graph convolutional networks. In early research, traditional statistical models and machine learning techniques [3], such as the autoregressive integral sliding average model (ARIMA) and the random forest regression algorithm [4], were applied to predict future traffic conditions. Some researchers have proposed algorithms for improving prediction performance, such as the Kalman filter [5] and its variants. However, statistical theoretical models often rely on the researcher’s a priori knowledge and have difficulties in effectively capturing the dynamics of traffic flows. The lag problem and other related issues have resulted in the poor practical effectiveness of these methods. With the continuous development of technology, deep learning methods have been widely used in the field of traffic flow prediction by virtue of the advantage of being able to capture nonlinear dependencies.
In the early stages of deep learning model development, most models used CNNs to analyze spatial correlations contained in grid-based traffic data, while RNNs were used to simulate temporal dynamics [6]. Methods such as convolutional neural networks, long short-term memory networks (LSTMs) [7] and gated recurrent units (GRUs) have been widely used, but these methods are mainly applicable to Euclidean spatial scenarios, which do not clearly reflect the topological connections between nodes in the traffic network, and make it difficult to comprehensively characterize correlations between road segments. As research advances, graph neural networks (GNN) are found to be more suitable for modeling the underlying graph structure of traffic data, and GNN-based spatio-temporal graphical models [8] have triggered extensive explorations in the field of traffic prediction, which allows the efficiency of extracting structured spatio-temporal features from non-Euclidean spatial data and temporal features to be significantly improved.
Today, many predictive models based on graph convolution tend to build complex graph neural network architectures. These models rely on a predefined graph structure, which is generally based on the Euclidean distance between nodes, to capture the spatial dependencies between nodes. However, when applying these models to traffic flow data, it is often difficult to fully consider the dynamic node associations latent in the data. Traffic flow data will show extremely significant spatio-temporal dynamic characteristics, so building a dynamic graph structure that reflects the spatio-temporal dynamic connections between nodes is of great significance for improving the model prediction performance. In order to effectively solve the above difficulties and at the same time deeply explore the spatio-temporal characteristics of traffic flow data, in this paper, we innovatively propose a spatio-temporal traffic flow prediction method, i.e., the DGCRAN model. Specifically, the main contributions of this paper include the following:
(1)
A convolution algorithm based on dynamic graph structure is designed for mining the implicit spatial characteristics in traffic flow data. The algorithm first constructs a similarity matrix through node embedding initialization, so that the graph convolution operation can effectively identify the unique features of each node when performing feature fusion. The whole training process adopts an end-to-end parameter optimization strategy to ensure that the model can adapt to the dynamic changes in traffic data. In order to further improve the model performance, a dynamic graph convolution recurrent neural network (DGCRN) is constructed by innovatively combining GRU with graph convolution, which realizes the automatic learning and extraction of complex spatio-temporal correlation features in traffic time-series data.
(2)
A graph convolutional neural network architecture based on an adaptive mechanism is proposed, and its innovation is mainly reflected in the design of the spatial feature extraction component, which consists of two key parts: an adaptive neighbor matrix and adaptive node parameters. Among them, the adaptive adjacency matrix is able to autonomously discover and establish potential associations between vertices through a trainable matrix structure, effectively mining the implicit spatial topological information in the data; while the adaptive node parameters utilize the embedded representation of vertices to derive targeted weight coefficients and offsets from the common parameter space, thus realizing the accurate modeling of personalized features for each vertex.
(3)
On the three publicly available datasets, PEMS03, PEMS04, and PEMS08, the DGCRAN model demonstrates significant performance advantages, and its prediction efficiency significantly outperforms that of the 15 currently available traffic flow prediction methods. In addition, various experiments are conducted to demonstrate the effectiveness of our proposed model.
In this paper, the DGCRAN model is proposed to solve the existing problems, and the specific contributions cover the design of a new convolutional algorithm, the proposal of a new network architecture, and the demonstration of excellent performance in experiments. The subsequent parts of the paper are structured as follows: Section 2 elaborates on the related work, introducing the development of the traffic prediction field from traditional statistical methods to deep learning methods to graph neural network applications, as well as the research progress of graph neural networks in traffic prediction, which lays the theoretical foundation for understanding the model in this paper; Section 3 explains the model structure design in depth, including the problem definition, the overall model architecture, and the specific construction methods of dynamic graphical recurrent network and adaptive graphical convolutional network, which clearly presents the design ideas and implementation details of the model; Section 4 carries out a comprehensive experimental validation and analysis, introduces the datasets, evaluation indexes, and the baseline model used, and verifies the effectiveness of the model from multiple perspectives through the comparative experiments, the comparison of the prediction time steps, and the ablation experiments, etc. The embedding dimensions and the cost of the computation are analyzed in Section 5. Section 5 summarizes the study, outlines the advantages of the model, points out the limitations of the study, and proposes the direction of future research; Section 6 lists the references cited during the study to facilitate readers’ further review of related materials.

2. Related Work

2.1. Traffic Prediction

Traffic forecasting is a key research focus in the field of transportation engineering, which has attracted many scholars’ in-depth research as a typical case of multivariate time-series forecasting. In the initial stage of traffic forecasting, researchers generally adopt classical statistical methods such as historical average (HA), vector autoregressive model (VAR), and autoregressive integrated moving average model (ARIMA) [9] to forecast traffic indicators. However, these traditional methods are based on linear assumptions and are difficult to capture the nonlinear features in traffic data, which leads to their ineffectiveness in dealing with traffic data with significant nonlinear relationships.
In recent years, scholars have been working on using deep learning techniques to address the challenges of traffic prediction. In early studies, CNN and RNN-based prediction methods, including LSTM [7], TCN [10], and Transformer [11], mainly model the time-series data collected by a single sensor. Although such methods can effectively capture the time-dimensional features, they fail to fully consider the spatial correlation characteristics among different monitoring points in the traffic road network, such as the influence of environmental factors on the sensor traffic flow records. It is worth noting that, similar to traditional methods, CNN architectures have the ability to extract spatio-temporal features simultaneously. Take the Fully Connected Long Short-Term Memory Network (FC-LSTM) [10] as an example, which innovatively integrates the advantages of CNN and LSTM to achieve comprehensive modeling of traffic data. In addition, Spatio-Temporal Residual Network (ST-ResNet) [12] has been successfully applied to the task of urban pedestrian flow prediction by introducing a deep residual CNN architecture, which fully demonstrates the strong potential of residual networks in this field. In addition, CNNs have been widely used to process grid-based traffic information to effectively obtain spatially locally dependent features. Nevertheless, CNNs excel in processing regular grid data, but the correlations in traffic data are often more suitable to be characterized by graph structures. In this graph structure, traffic data may present low correlation with neighboring nodes but maintain strong correlation with more distant nodes. This intrinsic characteristic of traffic data restricts the effectiveness of CNN in processing graph-structured information. In contrast, GNN shows significant advantages in processing graph-structured traffic data by virtue of its flexible topological expression, global information integration capability, and adaptive sensory range. For example, STGCN [13] and AGCRN [14] use GCN to screen and extract features from traffic signals, so as to establish spatial correlation. STGCN [13] constructs skeleton sequences into spatio-temporal graphs, introduces graph convolution based on division rules, and is able to automatically learn action spatio-temporal patterns, which is used for skeleton action recognition. DCRNN [15] combines diffusion convolution with bi-directionally gated cyclic units. It can capture the spatial diffusion and temporal evolution of traffic data, and use the diffusion convolution model to portray the flow characteristics of traffic signals and then capture spatio-temporal features for traffic flow prediction. ASTGCN combines spatio-temporal modeling with graph convolutional networks and introduces the attention mechanism, which is able to handle complex spatio-temporal data and is used for prediction in multiple domains, such as air quality. In contrast, STFGNN [16] is able to effectively integrate the semantic a priori information of road network structure and historical traffic data through spatio-temporal fusion maps. On this basis, STGODE [17] introduced tensor-based neural differential equations to solve the over-smoothing phenomenon in deep GCN [18].
With the significant advantages of attention mechanisms in modeling capabilities, their applications in traffic data analysis have become increasingly widespread. For example, the GMAN [19] model introduces three different attentional mechanisms used to capture spatio-temporal correlations, while ST-GAT [20] constructs an IST individual spatio-temporal graph by combining the attentional mechanisms with time and road segments as spatio-temporal nodes to capture the overall correlation of traffic speed. In addition, many innovative approaches have been widely applied, such as ST-SSL [21] which employs a novel self-supervised learning framework for capturing spatio-temporal heterogeneity in traffic flow prediction, and PMMemNet [22] which utilizes the key-value memory structure to match the input data with representative patterns. Although these models propose generalized prediction methods such as plug-in networks [23] and loss of covariance [24] to enhance the performance of GCN-based models, they are still limited to relying only on historical data for prediction without considering the use of information related to the prediction target to aid in prediction.

2.2. Graph Neural Network

The research of GNN began with Gori et al. [25], who pioneered the application of neural network techniques to graph-structured data. With the continuous development of the field, graph neural networks have made significant breakthroughs in directions such as dynamic graph information processing. Taking a graph convolutional network as an example, this improved model of convolutional neural network based on graph structure has been widely used in tasks such as node classification, graph classification, and link prediction [26]. The relevant research focuses on the learning of node representations by fusing the node’s own features and its neighboring node information.
In the field of traffic prediction, CNNs have been widely used due to their excellent spatio-temporal pattern-capturing ability [27]. These networks can model complex relationships in sequences without relying on cyclic architectures, especially by introducing the self-attention mechanism, which significantly improves the effectiveness of capturing long-distance spatio-temporal dependencies, thus showing good adaptability in traffic prediction [28,29]. Aiming at the dynamic spatial correlation characteristics in traffic networks, GNN has become an important research method in this field by virtue of its powerful dependency modeling capability [30]. Some scholars have integrated the self-attention mechanism with GNN to further strengthen the ability to characterize the spatial relationships in transportation networks [31]. Currently, GCN-based prediction methods are in the leading position, with models such as DCRNN [15] and STGCN [32] being the most representative. These models use predefined graph structures to extract spatial features between nodes, while combining with CNN or RNN to obtain temporal features. However, it should be noted that the prediction effect of such methods depends largely on the quality of the artificial predefined graph structure. To address this issue, researchers have proposed models such as Graph Wavenet, MTGNN [33], and AGCRN [14]. These architectures adopt a data-driven approach and are able to generate graph structures autonomously, which has led to significant results.
Recently, the application of dynamic graph convolution in traffic prediction has been gradually deepened; for example, EvolveGCN evolves the static graph weights through RNN, but its adaptability to sudden traffic changes is limited; DGCRN evolves the static graph weights through RNN, and its adaptation to sudden traffic changes is limited. is limited; DGCRN is more attuned to the instantaneous nonlinear nature of traffic data through an end-to-end dynamic adjacency matrix generation mechanism. STG-NDCE [30] further improved the prediction performance by fusing adaptive graphs with neural control differential equations. In general, traffic data have significant spatio-temporal dynamic correlation properties. Therefore, the establishment of dynamic nonlinear spatio-temporal correlation models plays a key role in realizing accurate traffic prediction. The generation mechanism of dynamic maps has gradually become a research hotspot. Based on the multi-scale traffic transformation information and the local–global dependence between regions, the spatio-temporal graph diffusion network (ST-GDN) proposed in the literature [34] achieves effective prediction. In terms of spatio-temporal feature extraction, the Dynamic Sensor Graph Neural Network (DSTAGNN) [35] realized the capture of spatial correlation dynamic characteristics between nodes through the deep mining of historical traffic flow data. In addition, Peng et al. [36] constructed a probabilistic graph model of traffic flow, combined with reinforcement learning techniques to construct a dynamic graph structure, and realized the deep extraction of spatio-temporal features.
In recent years, the application of graph convolutional networks in traffic prediction has been deepening. For example, ref. [37] proposed a multi-task learning network based on a collision-aware graph transformer, which significantly improves the accuracy of trajectory prediction by dynamically modeling the interactions of traffic agents, while [38] designed an action–interaction two-branch network focusing on the real-time prediction of pedestrian crossing behavior. These works provide new ideas for the design of Dynamic Graph Convolutional Networks through task-driven graph structure learning. In contrast, the DGCRAN model in this paper focuses more on the global spatio-temporal dependency modeling of traffic flow, and achieves the efficient capture of complex traffic patterns through an end-to-end dynamic graph generation mechanism and adaptive parameter learning.

3. Model Structure Introduction

3.1. Problem Definition

In traffic flow prediction research, sensor devices are typically treated as vertices in a network, with spatial distances or directional relationships between them serving as connecting edges. This allows the entire traffic network to be modeled as an undirected graph G = ( V , E , A ) , where the node set V = v 1 , v 2 , , v n represents traffic sensor locations, the edge set E denotes connections between nodes, and A R N × N is the graph’s adjacency matrix. At time t , the traffic state of the N -th node can be expressed as X t R N × D , where D represents the number of features. Thus, the traffic prediction task aims to use the road network structure G and historical data from T time steps to estimate future traffic conditions at time τ through a mapping function f ( · ) , mathematically expressed as:
[ X t + 1 , X t + 2 , , X t + τ ] = f ( G , [ X t T + 1 , X t T , , X t ] )
in the equation, f ( · ) denotes the mapping function for traffic flow prediction. Thus, the objective is to estimate future traffic flow sequences X t T + 1 , , X t 1 , X t based on historical observations X t + 1 , X t + 2 , , X t + τ using the predictive function. As shown in Figure 1, the overall prediction process of the model is shown below.

3.2. General Model Architecture

The overall architecture of the DGCRAN model is shown in Figure 2. The combined model takes the time series of historical road network-wide nodes as inputs and uses the dynamic graph convolution module to initialize the node embedding, which in turn generates a similarity matrix for assessing the spatial correlation among nodes. In traffic and other road network related application scenarios, different colors in Figure 2 represent nodes denoting historical traffic nodes with different attributes or functions, for example, they may be different types of road network nodes distinguishing between traffic hubs, common intersections, etc. In the traditional GRU framework, dynamic graph convolution operations are introduced to capture time-series features and spatial dependencies simultaneously. In addition, by constructing an adaptive graph convolution network, it is able to focus on different regions of the graph structure to extract complex associations in the graph more effectively. The model consists of the following two main components:
The Dynamic Graph Convolutional Recurrent Network (DGCRN) introduces a dynamic graph convolution mechanism for capturing potential hidden spatial dependencies. The network combines dynamic graph convolution with GRU to capture spatio-temporal correlation features of traffic flow more effectively.
Adaptive spatial feature extraction: spatial features are extracted to capture complex relationships in the graph structure more efficiently through the constructed adaptive graph convolutional network. This improves the model’s representational capability and enhances its predictive performance in complex scenarios.

3.3. Construction of Dynamic Graph Convolutional Recurrent Networks

In recent years, numerous researchers have focused on extracting spatially dependent features of spatio-temporal data using graph convolution techniques. However, these studies tend to construct predefined adjacency matrices through distance functions, which is a limitation of this approach and cannot adequately reflect the nodes’ own characteristics (e.g., POI, road structure and type) [31]. Although traditional GCN simulates the spatial distribution of real traffic networks with the help of a predefined graph structure, its performance is limited by this fixed pattern. Although this structure can capture explicit similarity relationships between nodes, it is difficult to fully characterize the complex implicit associations prevalent in traffic data. This limitation results in the lack of spatial node association information, which reduces the accuracy of prediction. More importantly, the graph structures based on these methods are usually static, which makes it difficult to cope with the complexity and dynamically changing characteristics of spatial dependencies among nodes in real transportation networks.
To address the above problems, a Dynamic Graph Convolutional Recurrent Network (DGCRN) is proposed for mining potential spatial features of traffic data, as shown in Figure 3. The network incorporates GRU to efficiently capture spatio-temporal features. The DGCRN generates similarity matrix by initializing node embeddings and utilizes GCN to consider the unique patterns of nodes during feature aggregation. A DGCRN is constructed by integrating GRUs to automatically capture fine-grained spatio-temporal correlations in traffic sequences and dynamically update the parameters during training to adapt to traffic data in an end-to-end manner. In DGCRN, a supernetwork is designed to extract dynamic features using node attributes. The parameters of the dynamic filter are generated at each time step and the node embeddings are filtered to generate a dynamic graph. The two are very different in nature.
Traffic prediction involves complex temporal and spatial correlation features, and the DGCRN module is constructed by introducing GCN into the fully connected layer of GRU. Given the excellent performance of GRU in temporal tasks, graph convolution operations are integrated into its original architecture to capture temporal dynamic features and spatial dependencies simultaneously. In the model architecture, each time step receives not only the current input data, but also the hidden state of the previous moment, in order to regulate the store-and-forget mechanism of information. In this framework, GRU operations are applied in parallel to all nodes in the graph structure and the nodes share the same parameter settings.
Specifically, based on the input data X t at time step t and the previous hidden state h t i , this paper formulates the single-step computation process of the gated recurrent unit as:
r t = σ Θ r [ X t , h t i ] G + b r
u t = σ Θ u [ X t , h t i ] G + b u
h ^ t = tanh Θ h [ X t , r t h t i ] G + b h
h t = u t h t i + 1 u t h ^ t
in the equation, X t and h t represent the input and output at time step, respectively, b r , b u , and b h denote trainable parameters of the recurrent neural network, σ indicates the sigmoid activation function, and Θ is used for dynamic graph generation.
The fusion of dynamic graph convolution with GRU enhances the model’s ability to capture fine spatio-temporal features. By adaptively constructing associations between nodes through the training data, this dynamically generated graph structure can break through the limitations of predefined graphs, resulting in more flexible handling of complex spatio-temporal patterns.
The application of dynamic graph convolution in traffic prediction has been gradually deepened, for example, EvolveGCN [38] evolves the static graph weights through RNN, but its adaptability to sudden traffic changes is limited; DGCRN evolves the static graph weights through RNN, and its adaptation to sudden traffic changes is limited; DGCRN is more attuned to the instantaneous nonlinear nature of traffic data through an end-to-end dynamic adjacency matrix generation mechanism.

3.4. Adaptive Graph Convolutional Networks

In a traffic network, the traffic state of each road is affected by a variety of factors, and it is difficult to achieve accurate prediction only by obtaining the shared patterns among nodes. For this reason, adaptive neighbor matrix and node parameters are introduced to extract spatial features. The adaptive adjacency matrix captures potential spatial correlations in traffic data by automatically learning the dependencies between nodes; adaptive node parameters are generated from a shared pool of weights and biases to capture the unique patterns of specific nodes. Combining these two mechanisms, adaptive graph convolutional networks can extract spatial features of the data more comprehensively.

3.4.1. Adaptive Neighborhood Matrix

Adaptive Adjacency Matrix (AAM) is a dynamic adjacency matrix applied to graph neural networks. It continuously adjusts the matrix structure during stochastic gradient optimization by introducing an adaptive mechanism. Specifically, each row of the matrix represents a set of neighboring nodes of a node, and the row length corresponds to the degree of the node. The method not only effectively alleviates the sparsity problem, but also adapts to the dynamic changes in the number of nodes and edges in the graph. Through the data-driven approach, the adaptive adjacency matrix can learn the potential intrinsic associations between nodes and thus construct a more accurate representation of adjacencies. Predefined graph structures may not fully reflect spatial dependencies, which may lead to biased prediction results. In contrast, adaptive adjacency matrices do not rely on a priori knowledge and can learn the underlying spatial dependency patterns directly from the input data. The method described in reference [14] captures the complete spatial correlation of traffic flow data by extracting spatial features, which can effectively improve the prediction accuracy. The specific implementation steps are as follows: First, a learnable embedding vector E A R N × f is randomly generated for each node. Then, the spatial dependencies between nodes are derived using E A and its transpose E A T . Finally, the normalized adaptive adjacency matrix can be expressed as:
D 1 2 A D 1 2 = s o f t max ( Re L u ( E A · E A T ) )
in the equation, each row of E A represents a node embedding. The total number of nodes is denoted as N , with the degree matrix D R N × N being a diagonal matrix. The adjacency matrix is represented as A R N × N . The Re L u activation function is employed, while the adaptive adjacency matrix undergoes normalization via the softmax function. During training, E A automatically adjusts to capture latent dependencies among different traffic flow sequences while simultaneously acquiring adjacency information required for graph convolution.
The phenomenon of gradient vanishing or gradient explosion can be effectively mitigated by constructing an adaptive adjacency matrix to capture the spatial dynamic dependencies among road networks more comprehensively. The graph convolution module is able to automatically learn the dynamically changing spatial dependencies in transportation networks without a priori information. The matrix is sparsified using Re L u and normalized by s o f t max to directly obtain 3. The adaptive graph convolution in this model can be expressed as:
Z = θ ( I N + s o f t max ( Re L u ( E A · E A T ) ) ) x

3.4.2. Adaptive Node Parameter

In transportation networks, the dynamic nature of time-series data and the various factors that nodes may be affected by lead to diverse patterns among different traffic sequences. Therefore, it is difficult to achieve accurate traffic prediction by capturing only the common patterns among nodes. Since the characteristics of neighboring nodes in the road network structure may exhibit different traffic conditions at a certain time due to specific attributes (e.g., weather, accidents), even the characteristics of non-neighboring nodes may show opposite trends. Therefore, relying only on the shared patterns among all nodes cannot ensure the accuracy of prediction, and it is especially important to allocate an independent parameter space for each node to learn its unique patterns. Typically, graph convolutional networks are computed as:
Z = ( I N + D 1 2 A D 1 2 ) X Θ + b
in the equation, A R N × N represents the adjacency matrix of the graph, while X R N × C and Z R N × F denote the input and output matrices, respectively. The trainable weight matrix Θ R C × F and bias vector b R F complete the parameter set.
To address the issue where assigning independent parameters to each node leads to an excessively large Θ R N × C × F that is difficult to optimize, we enhance traditional GCN through a node-adaptive parameter learning module. For the adaptive node parameters, we define a node-embedding matrix E G R N × d and a weight pool E G R d × C × F , where d is the embedding dimension with d N , yielding Θ = E G · W G . From a node’s perspective, this process extracts candidate patterns from all traffic sequences while learning node-specific patterns—specifically, node embedding E G i retrieves parameters Θ i for node i from the shared weight pool W G , with analogous operations for b . The GCN formulation incorporating adaptive node parameters is as follows:
Z = ( I N + D 1 2 A D 1 2 ) X E G W G + E G b G

4. Experimental Design and Analysis

4.1. Dataset Description

To validate the accuracy of the model, experiments were conducted on the publicly available PEMS03, PEMS04, and PEMS08 datasets. The PEMS database integrates traffic data collected by the California Department of Transportation on highways and includes informational data from other California transportation agencies and partners. The database provides users with a comprehensive assessment of highway performance. By monitoring the real-time status of the highway network, users can make more informed operational decisions, analyze congestion bottlenecks, and identify potential improvements. In addition, the data helps to develop more effective overall traffic management strategies, thereby improving the efficiency and sustainability of the transportation system. The PEMS03 dataset contains freeway information recorded by 358 traffic detection sensors in the Los Angeles freeway region between 1 September and 30 November 2018. The PEMS04 dataset covers freeway data collected by 307 sensors in San Francisco between 1 January and 28 February 2018. The PEMS08 dataset is from the San Bernardino region and records freeway information collected between 1 July and 31 August 2016 by 170 sensors. Traffic flow data from these datasets are summarized every 5 min, with more details shown in Table 1. The following is a link to download the dataset: https://gitcode.com/open-source-toolkit/06a2f (accessed on 25 June 2025)
The missing values in the dataset are linearly interpolated and normalized to ensure the stability of the training process. In the dataset, all the historical data of 12 time steps are used to predict the traffic flow for the next 12 time steps. The dataset was divided into training, validation, and test sets in the ratio of 6:2:2. The optimization process was performed using the Adam optimizer, which is well suited for handling large-scale data and parameters due to its high computational efficiency and low memory requirements. The training setup consists of 200 iterations with a bit size of 64, an initial learning rate of 0.001, and the application of an early stopping method with a patience of 15.

4.2. Evaluation Metrics and Baselines

To evaluate the effectiveness of DGCRAN, we used three performance metrics that are widely used in traffic prediction tasks to compare the performance of different models.
  • Mean Absolute Error (MAE):
M A E = 1 M i = 1 M | y i y ^ i |
2.
Root Mean Square Error (RMSE):
R M S E = 1 M i = 1 M y i y ^ i 2
3.
Mean Absolute Percentage Error (MAPE):
M A P E = 1 M i = 1 M | y i y ^ i y ^ i | × 100 %
in the equation, M denotes the total number of samples, y i represents the ground truth value of the i -th sample, and y ^ i indicates the predicted value for the i -th sample. The prediction error is evaluated using MAE, RMSE, and MAPE metrics, where lower values correspond to better prediction performance.
In order to verify the prediction effect of DGCRAN model, 15 prediction models were selected as benchmark comparison models in this paper as follows:
HA [9]: modeling traffic as a seasonal process and traffic flow based on the average of previous seasons as historical data.
VAR [9]: time-series modeling that captures the spatial correlation between all traffic sequences.
DSANet [39]: a correlated time-series prediction model that captures the temporal correlation between time series and spatial correlation using a CNN network and a self-attention mechanism.
DCRNN [15]: diffusion convolution recurrent neural network which formulates the graph convolution and diffusion process and combines the GCN with a recurrent model in an encoder–decoder fashion for multi-step prediction.
ASTGCN [14]: an attention-based spatio-temporal graph convolutional network that further integrates spatio-temporal attention mechanisms into STGCN to capture dynamic spatio-temporal patterns for modeling traffic data.
LSGCN [40]: using gated graph blocks to satisfy the spatial dependence of long and short distances, which contains a graph convolutional network and a new cosine graph attention network.
STSGCN [32]: spatio-temporally synchronized graph convolutional network captures spatio-temporal correlations by superimposing multiple local GCN layers and adjacency matrices on the time axis.
AGCRN [14]: integrating the adaptive GCN of graphs into a recurrent network based on codec architecture for modeling.
STFGNN [16]: designing a dynamic time-warping-based temporal graph to mine spatial relationships in function perception.
STGODE [17]: solved the GCN over-smoothing problem using CGNN to extract spatio-temporal dependencies.
Z-GCNETs [41]: introduces the concept of sawtooth persistence for time-series prediction;
STG-NCDE [30]: predicting traffic volumes using two neural control differential equations.
DSTAGNN [35]: simulates dynamic spatial relationships between nodes by designing a spatio-temporal perceptual graph and mines historical traffic flow data of nodes using an attention mechanism.
DDGCRN [8]: extracts dynamic spatio-temporal features of traffic data using spatio-temporal embedding and dynamic signals to capture the spatio-temporal correlation of traffic data.
PDG2Seq [42]: extracts dynamic real-time traffic spatio-temporal features using the Periodic Feature Selection Module (PFSM) and Periodic Dynamic Graph Convolutional Gated Recurrent Unit (PDCGRU) to accurately predict traffic flow.

4.3. Forecasting Performance Comparison

The results of the comparison experiments between the DGCRAN model and the benchmark model on the PEMS03, PEMS04, and PEMS08 datasets are shown in Table 2. First, traditional time-series analysis methods (e.g., HA and VAR) tend to have poor prediction performance, indicating limitations in handling nonlinear and complex traffic data. HA performs the worst of all models, setting the minimum standard for traffic prediction. In addition, VAR and DSANet yielded much worse results than neural network-based models because they cannot effectively capture nonlinear dependencies and require manual design of features. Second, in graph-based models, DCRNN relies on predefined graph structures to capture spatial correlations. However, the quality of the predefined graph structure has a significant impact on the final performance of the model. ASTGCN and LSGCN perform well in extracting dynamic relationships in traffic time series, proving their effectiveness. STFGNN and STGODE extend the spatial sensory field by introducing temporal graphs and GODE, outperforming other graph-based methods. However, they are deficient in mining global spatial correlation and thus inferior to the AGCRN model. Models such as AGCRN, STFGNN, and DSTAGNN achieve significant results by generating graph structures to extract spatial features in a data-driven manner. However, these models do not fully consider the periodic characteristics and dynamic signals of the traffic system, resulting in inferior performance to DGCRAN. Although DDGCRN utilizes dynamic graphs to extract spatial features, it only focuses on the temporal information of the input data and ignores the temporal information of the prediction target. In contrast, DGCRAN makes full use of the temporal information of the predicted target and thus outperforms DDGCRN.PDG2Seq predicts by capturing the spatio-temporal characteristics of dynamic real-time traffic, but it still does not perform as well as DGCRAN.
In conclusion, DGCRAN demonstrates lower MAE, RMSE, and MAPE metrics on the three datasets compared to other traffic flow prediction models, proving its superiority in prediction accuracy and capability. Compared with the traditional HA and VAR models, the MAE of DGCRAN on the PEMS08 dataset is reduced by 21.33% and 5.66%, respectively; the RMSE is reduced by 46.02% and 6.59%, respectively; and the MAPE is reduced by 19.02% and 4.24%, respectively. This indicates that the deep learning-based prediction method significantly improves the accuracy compared to the traditional statistical model. Compared with other models, DGCRAN introduces graph convolution operation into the original GRU structure to capture the time-series information and constructs an adaptive graph convolution network. This not only makes the model closer to the actual situation when extracting spatial features, but also gives different weights to the spatio-temporal features for different time periods, better reflecting the changing pattern of daily traffic flow, thus further improving the accuracy of prediction.

4.4. Comparison of Prediction Time Steps

In order to assess the prediction accuracy of the models and their trends at different time steps, we performed a comparative analysis of the prediction results of DGCRAN, DSTAGNN, AGCRN, and STGODE on the PEMS04 and PEMS08 datasets. As shown in Figure 4, the MAE, RMSE, and MAPE of all models show an increasing trend as the prediction time horizon is extended, which is consistent with the expectation that the prediction difficulty increases with the expansion of the horizon. It is worth noting that although STGODE performs poorly in short-term prediction, its error grows significantly faster than the other models, resulting in the highest average error. DSTAGNN performs similarly to AGCRN in long-term prediction, but outperforms the latter in short-term prediction, showing its advantage in short-term prediction. In contrast, DGCRAN is able to automatically capture fine-grained spatio-temporal correlations in traffic sequences by freeing itself from the constraints of predefined graphs, thus demonstrating a significant performance advantage. Overall, DGCRAN outperforms the other models at different time steps, demonstrating its higher accuracy, stability and reliability in the prediction task.

4.5. Ablation Study

In order to validate the effect of dynamic graph convolution and AGCN in the proposed model, multiple variants of the model were constructed by removing or replacing some of the modules and tested on the PEMS04 and PEMS08 datasets. The ablation experiments cover the following variants:
(1)
GCGRU: As a benchmark model for ablation experiments, the graph-convolution gated recurrent unit (GCGRU) combines classical GCN and GRU to capture spatio-temporal dependencies.
(2)
DGCRN: This model uses Dynamic Graph Convolutional Network (DGCN) instead of the traditional GCN to construct Dynamic Graph Convolutional Recurrent Network. By initializing node embeddings to generate similarity matrices, DGCN takes into account the unique characteristics of nodes in the feature aggregation process, thus escaping from the limitation of predefined graphs. The combination of GRU further enhances the model’s ability to model fine-grained spatio-temporal patterns.
(3)
No adaptive graph convolution (w/o adaptive DGCRAN): In this variant, the adaptive graph convolution module is removed and a simple graph convolution is used instead.
The results of the ablation experiments on the PEMS04 and PEMS08 datasets are shown in Table 3. First, DGCRN outperforms GCGRU as a whole, indicating that dynamic graph convolution is able to break through the limitation of predefined graphs and effectively capture spatial dependencies. DGCRN dynamically generates the adjacency matrix through the hypernetwork, and accurately reflects the real-time correlation strength between nodes by utilizing the multidimensional information of the input data such as the features at the current moment, the temporal data, and the hidden state of the previous moment, to achieve a Dynamic Capture. Secondly, the prediction performance of the model is not as good as that of DGCRAN when using an ordinary graph convolution neural network instead of adaptive graph convolution, which indicates that ordinary graph convolution is limited by the fixed graph structure, and it is difficult to adapt to the complex spatial relationship of traffic network. On the other hand, DGCRAN generates adaptive neighbor matrix in real time during the training process through the node-embedding technology, which can keenly capture the correlation changes between road sections in different time periods and fully explore the spatial dynamic correlation, proving the effectiveness of the adaptive graph convolution module. Overall, the DGCRAN model outperforms GCGRU and DGCRN, indicating that the synergistic effect of DGCRN and AGCN is crucial to the model prediction results. The graph structure is optimized by AGCN to effectively extract features and accurately capture key information of the graph data, which improves the accuracy and robustness of the prediction.

4.6. Embedding Dimensional Analysis

In DGCRAN, the embedding dimension of a model node is a crucial parameter, the size of which directly determines the model’s ability to extract spatio-temporal information. The PeMSD4 and PeMSD8 datasets are used as test subjects, and the embedding dimensions are set to 3, 6, 9, 12, 15 and 4, 6, 8, 10, 12, respectively. The MAE and MAPE values of DGCRAN in the 12-step prediction interval are shown in Figure 5. The following experimental data are the average values of each evaluation metric in the 12-step prediction interval. As can be seen from Figure 5, there is a significant difference in the performance of the model at different embedding dimensions. Excessive or insufficient embedding dimensions can adversely affect the performance of the model. Although a larger embedding dimension can contain more data information, it also leads to an increase in model parameters, which increases the difficulty of model optimization.
In summary, for the PeMSD4 dataset, when the embedding dimension is set to 12, the MAE and MAPE values are closest to the real evaluation values, at which time DGCRAN is able to achieve the best performance; while for the PeMSD8 dataset, when the embedding dimension is set to 8, the MAE and MAPE values are closest to the real evaluation values, at which time DGCRAN is also able to achieve the best performance.

4.7. Calculation Cost Analysis

In order to evaluate the computational cost, the number of parameters and training time of DGCRAN are compared with four models, DCRNN, STGCN, ASTGCN, and AGCRN, on the PEMS04 dataset, as shown in Table 4. In terms of the number of parameters, DGCRAN exceeds DCRNN and STGCN when the node embedding dimension of DGCRAN is set to 12. This is due to the fact that the node-embedding dimension is added as a cost of learning node-specific patterns in order to better capture specific node patterns; ASTGCN introduces a spatio-temporal attention mechanism to obtain more accurate spatio-temporal features, but it also increases the number of parameters and training time. AGCRN uses an adaptive convolutional recursive algorithm that increases the number of model parameters. In terms of training time, AGCRN runs slightly faster than DCRNN because the model generates all predictions directly instead of using the iterative approach in DCRNN. STGCN is the fastest due to the temporal convolution structure that accelerates model training; ASTGCN has a higher number of parameters and training time due to the fact that it requires a higher number of parameters and training time to introduce spatial and temporal attention mechanisms to learn more accurate spatio-temporal patterns.
When the embedding dimension of DGCRAN is 6, the number of modeled parameters is less than DCRNN, STGCN, ASTGCN, and AGCRN, and the training time and RMSE values are also lower. When the embedding dimension is 12, DGCRAN has less number of parameters than ASTGCN and AGCRN and the smallest RMSE value, but the training time is slightly longer, which is due to the fact that the model contains a stack of three DGCN modules, which enhances the extraction of temporal information but also increases the computational complexity. Overall, considering the number of parameters and prediction accuracy together, the prediction effect of DGCRAN is better when the embedding dimension is 12, and the computational cost is more reasonable.

5. Discussion

The DGCRAN model proposed in this study achieves significant performance improvement in the traffic flow prediction task through the co-design of dynamic graph convolution and adaptive spatial feature extraction. From a broader perspective, this study has three implications for the development of intelligent transportation systems: first, the dynamic graph generation mechanism provides a generalized framework for dealing with non-smooth spatio-temporal correlations, which can be extended to areas such as air quality prediction and crowd flow monitoring. Second, the adaptive parameter learning module provides a new idea to solve the problem of node heterogeneity in graph data, which has inspirational value for scenarios such as social network analysis. Third, the stability of the model in long-term prediction indicates its potential for practical deployment, which can provide more reliable decision support for urban traffic management. Compared with the literature [37,38], the DGCRAN model has a wider applicability in terms of the dynamic graph generation mechanism, and is able to automatically adapt to the spatial and temporal variations in different traffic scenarios. However, the task-driven graph learning framework and real-time interactive modeling approach proposed in these studies provide important insights for future research, especially in multimodal data fusion and lightweight design.
It is worth noting that the current work still suffers from two limitations: on the one hand, the model’s adaptability to contingencies has not been specifically tested, which is crucial in practical applications. On the other hand, the sensitivity issue of the node-embedding dimension suggests the need to develop more efficient parameter compression techniques.
Analyzing from the perspective of future research, the following directions can be explored in depth: (1) Developing multimodal dynamic graph architectures that incorporate external factors (e.g., weather, events) to enhance the scenario adaptability of the model. (2) Investigating a lightweight version to reduce the computational cost to make it suitable for edge device deployments. (3) Incorporating causal inference techniques to enhance the interpretability of the model, which is crucial for traffic management decisions. In addition, the dynamic graph convolution paradigm proposed in this paper provides a new experimental vehicle for the theoretical study of spatio-temporal graph neural networks, especially in the fusion mechanism between dynamic graph representation learning and traditional temporal modeling, which is worthy of deeper exploration. The development of these directions will further promote the transformation of traffic prediction from laboratory research to practical applications in smart cities.
The DGCRAN model performs excellently in traffic flow prediction experiments, and its innovative architecture enables it to effectively capture spatio-temporal dependencies, solve the problem of heterogeneous traffic patterns, and outperforms the benchmark model in predictions at different time steps. This not only provides support for intelligent transportation systems, but also promotes research in the field of traffic prediction. Based on this, it is recommended to pilot the application in practical traffic management and expand the research with other techniques. However, the model suffers from untested adaptation to unexpected events and a sensitive node-embedding dimension. In the future, the performance should be evaluated by simulating unexpected events, and the model should be improved both in terms of optimizing the structure and adopting compression algorithms in order to enhance the model’s practicality.

6. Conclusions

The DGCRAN model proposed in this paper uses a novel combination of dynamic graph convolution and GRU to construct a dynamic graph convolution recurrent network. It breaks through the limitation of traditional GCN relying on predefined static graphs through end-to-end generated dynamic neighbor matrix, and is able to capture the real-time changing spatio-temporal correlations in the traffic network. Second, Adaptive Graph Convolutional Network (AGCN) achieves the modeling of personalized node features through node embedding technique, which solves the problem of heterogeneous traffic patterns that are difficult to be handled by traditional methods. Finally, the synergy of the dual modules enables the model to capture global spatio-temporal dynamics as well as focus on local feature differences.
Through various experiments on the PEMS03, PEMS04, and PEMS08 datasets, the traffic prediction ability of the DGCRAN model was demonstrated to be superior to existing methods. In future work, the DGCRAN model can be combined with other deep learning methods to better learn the spatio-temporal features hidden in the traffic data for more accurate predictions.

Author Contributions

Conceptualization, G.Y. and W.L.; Methodology, G.Y. and W.L.; Software, G.Y.; Validation, G.Y., Z.X. and X.Z.; Formal analysis, G.Y., Z.X. and X.M.; Resources, Z.X.; Data curation, G.Y.; Writing—original draft, G.Y.; Writing—review and editing, W.L. and G.Y.; Visualization, Z.X.; Supervision, Z.X. and X.M.; Project administration, W.L.; Funding acquisition, W.L. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Natural Science Foundation of China (62066038, 61962001), Scientific research project of the Key Laboratory of Monitoring, Early Warning and Risk Management of Agricultural Meteorological Disasters with Specialties in Dry Areas of China Meteorological Administration (CAMF-202403), the Ningxia Higher Education Scientific Research Project (NYG2024086), Natural Science Foundation of Ningxia (2021AAC03215) and Graduate Student Innovation Program of North Minzu University (YCX24362).

Data Availability Statement

No new data were created or analyzed in this study. Data sharing is not applicable to this article.

Acknowledgments

We sincerely thank all the creators and funding programs that have been involved in the writing of this paper, as well as the School of Computer Science and Engineering at Northern Nationalities University for the support of the experimental facilities.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Structural sequence prediction.
Figure 1. Structural sequence prediction.
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Figure 2. DGCRAN model structure diagram.
Figure 2. DGCRAN model structure diagram.
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Figure 3. DGCRN structure model diagram.
Figure 3. DGCRN structure model diagram.
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Figure 4. Prediction errors of PEMS04 and PEMS08 at different horizons: (a) a comparison of the performance of the correlation model in different layers of the dataset PEMS04; (b) a performance comparison of the correlation model for different layers on the dataset PEMS08.
Figure 4. Prediction errors of PEMS04 and PEMS08 at different horizons: (a) a comparison of the performance of the correlation model in different layers of the dataset PEMS04; (b) a performance comparison of the correlation model for different layers on the dataset PEMS08.
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Figure 5. Impact of embedding dimensions.
Figure 5. Impact of embedding dimensions.
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Table 1. The statistics of the dataset.
Table 1. The statistics of the dataset.
DatasetsNodesTime StepsRateTime RangeType
PEMS033585 min26,2081 September 2018~30 November 2018Volume
PEMS043075 min16,9921 January 2018~28 February 2018Volume
PEMS081705 min17,8561 July 2016~31 August 2016Volume
Table 2. A performance comparison of DGCRAN and the benchmark model on three datasets.
Table 2. A performance comparison of DGCRAN and the benchmark model on three datasets.
MoldPEMS03PEMS04PEMS08
MAERMSEMAPE/%MAERMSEMAPE/%MAERMSEMAPE/%
HA31.5852.3933.7838.0359.2427.8834.8659.2427.88
VAR23.65 38.2624.5124.54 38.6117.2419.19 29.81 13.10
DSANet 21.29 34.55 23.2122.79 35.77 16.0317.14 26.96 11.32
DCRNN 17.99 30.31 18.3421.22 33.44 14.1716.82 26.36 10.92
ASTGCN 17.34 29.56 17.2122.92 35.22 16.5618.25 28.06 11.64
LSGCN 17.94 29.85 16.9821.53 33.86 13.1817.73 26.76 11.20
STSGCN 17.48 29.21 16.7821.19 33.65 13.9017.13 26.80 10.96
STFGNN 16.77 28.34 16.3020.48 32.51 16.7716.94 26.25 10.60
STGODE 16.50 27.84 16.6920.84 32.82 13.7716.81 25.97 10.62
Z-GCNETs 16.64 28.15 16.3919.50 31.61 12.7815.76 25.11 10.01
AGCRN 15.98 28.25 15.2319.83 32.26 12.9715.95 25.22 10.09
STG-NCDE 15.57 27.09 15.0619.21 31.09 12.7615.45 24.81 9.92
DSTAGNN 15.57 27.21 14.68 19.30 31.46 12.7015.67 24.77 9.94
DDGCRN 14.63 25.07 14.22 18.45 30.51 12.1914.40 23.75 9.40
PDG2Seq 14.62 25.47 14.88 18.24 30.0812.09 13.60 23.37 8.99
DGCRAN (Ours)14.6124.8914.0618.1230.0211.9313.5323.238.86
Table 3. Ablation experiments of PeMS04 and PeMS08.
Table 3. Ablation experiments of PeMS04 and PeMS08.
ModulePEMS04PEMS08
MAERMSEMAPE/%MAERMSEMAPE/%
GCGRU24.53 36.97 16.6722.08 29.67 13.71
DGCRN19.82 32.23 12.9715.9525.22 10.09
w/o adaptive19.4531.9512.7515.0424.529.96
DGCRAN18.1230.0211.9313.5323.228.86
Table 4. Calculation cost of PEMS04 dataset.
Table 4. Calculation cost of PEMS04 dataset.
ModuleParametersTraining Time (Epoch/s)RMSE
DCRNN149,05736.3933.44
STGCN211,59616.3633.65
ASTGCN450,03149.4735.22
AGCRN748,81035.3632.26
DGCRAN (dim = 6)126,84925.8630.29
DGCRAN (dim = 12)410,68142.1330.02
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Li, W.; Yang, G.; Xiong, Z.; Zhu, X.; Ma, X. A Traffic Flow Prediction Model Based on Dynamic Graph Convolution and Adaptive Spatial Feature Extraction. Symmetry 2025, 17, 1007. https://doi.org/10.3390/sym17071007

AMA Style

Li W, Yang G, Xiong Z, Zhu X, Ma X. A Traffic Flow Prediction Model Based on Dynamic Graph Convolution and Adaptive Spatial Feature Extraction. Symmetry. 2025; 17(7):1007. https://doi.org/10.3390/sym17071007

Chicago/Turabian Style

Li, Weijun, Guoliang Yang, Zhangyou Xiong, Xiaojuan Zhu, and Xinyu Ma. 2025. "A Traffic Flow Prediction Model Based on Dynamic Graph Convolution and Adaptive Spatial Feature Extraction" Symmetry 17, no. 7: 1007. https://doi.org/10.3390/sym17071007

APA Style

Li, W., Yang, G., Xiong, Z., Zhu, X., & Ma, X. (2025). A Traffic Flow Prediction Model Based on Dynamic Graph Convolution and Adaptive Spatial Feature Extraction. Symmetry, 17(7), 1007. https://doi.org/10.3390/sym17071007

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