A traffic flow interpolation and prediction method based on double-map adversarial generation and diffusion convolution cycle

Abstract

The application discloses a traffic flow interpolation and prediction method based on a double-graph adversarial generation and diffusion convolution cycle, comprising the following steps: S1, abstracting a traffic network into a space-time dynamic graph, and introducing a mask matrix to represent missing positions; S2, constructing a physical adjacency graph and a traffic correlation graph; S3, respectively extracting features of the physical adjacency graph and the traffic correlation graph and splicing them; S4, introducing a compression excitation attention mechanism; S5, adopting a generative adversarial network paradigm composed of a generator and a discriminator, and realizing high-fidelity missing data interpolation through adversarial training; S6, adopting an encoder-decoder architecture, encoding complete generated data into a context vector containing global space-time information; based on the context vector, a prediction sequence of a future time step is gradually generated in a self-recurrent manner; S7, extending a standard graph convolution to a bidirectional diffusion process, and constructing a support matrix of forward and reverse information flow; S8, constructing a diffusion convolution cycle unit; and S9, designing a composite loss function.

Description

Technical Field

[0001] This application relates to the fields of intelligent transportation and artificial intelligence technology, specifically to a traffic flow interpolation and prediction method based on bi-graph adversarial generation and diffusing convolutional loop. Background Technology

[0002] Traffic flow prediction, by estimating short-term traffic conditions, can effectively assist traffic management departments in proactively intervening in road networks, thereby enabling more rational signal timing, traffic guidance, trip scheduling, and congestion mitigation. Traditional traffic flow prediction methods are mostly based on historical statistical patterns, classical time series analysis, or shallow machine learning models, which are insufficient to fully characterize the prevalent nonlinear characteristics, spatiotemporal correlations, and propagation of traffic systems. Their prediction accuracy falls short of the application requirements of today's complex traffic environments. With the development of deep learning, graph neural networks, and sequence modeling techniques, graph-based spatiotemporal traffic flow prediction methods have gradually become mainstream. Related research shows that traffic flow exhibits regional coupling in space and trend and periodic characteristics in time. Deep learning-based spatiotemporal models can more effectively uncover these potential relationships, achieving higher-precision traffic prediction. However, most existing methods are based on the ideal assumption of complete and available data, which is difficult to guarantee in reality. In actual traffic monitoring systems, data gaps are common and exhibit complex and diverse characteristics. Furthermore, many methods rely solely on physical topology or historical time series, failing to fully utilize the multidimensional correlation information in the traffic network and neglecting the consistency of statistical distribution under data sparsity conditions. Therefore, in scenarios where traffic monitoring data has completely missing nodes, how to construct a traffic data interpolation and prediction model that is robust, interpretable, and highly accurate has become a key scientific problem that urgently needs to be solved in the fields of traffic information engineering and intelligent transportation systems. Therefore, further research is needed. Summary of the Invention

[0003] The purpose of this application is to provide a traffic flow interpolation and prediction method based on dual-graph adversarial generation and diffusing convolutional loop, and the specific technical solution is as follows:

[0004] A traffic flow interpolation and prediction method based on dual-graph adversarial generation and diffusing convolutional recurrent methods includes: S1, for traffic network scenarios with completely missing nodes, the traffic network is abstracted into a spatiotemporal dynamic graph, and the sensor node set is divided into an observed node set and an unobserved node set, introducing a mask matrix to represent the missing locations; S2, a physical adjacency graph is constructed based on the actual geographical location and connection relationships of the sensor nodes, and a traffic correlation graph is constructed through the functional similarity between sensor nodes; S3, a layer-by-layer neighborhood feature aggregation method is used to process the physical adjacency graph and the traffic correlation graph in S2, respectively. Spatial features are extracted, and the extracted physical adjacency graph features and traffic correlation graph features are concatenated to obtain a dual-graph feature tensor. S4 introduces a compression-excitation attention mechanism to adaptively calibrate the dual-graph feature tensor, enhancing the weights of key feature channels through compression, excitation, and recalibration. S5 uses the dual-graph feature extraction network from S3 and the compression-excitation attention mechanism from S4 as the core, with a cascaded multilayer perceptron as the head to construct a generator. This generator maps the observed data from S1 to complete generated data, and an independent discriminator network calculates the confidence level of the complete generated data. A generative adversarial network paradigm consisting of a generator and a discriminator is adopted to achieve high-fidelity imputation of missing data through adversarial training. In step S6, an encoder-decoder architecture is used. The encoder's stacked diffusing convolutional layers encode the complete generated data from step S5 into a context vector containing global spatiotemporal information. Based on this context vector, the decoder's stacked diffusing convolutional layers progressively generate prediction sequences for future time steps in an autoregressive manner. In step S7, the diffusing convolutional layers in the encoder-decoder architecture of step S6 generalize standard graph convolution to a bidirectional diffusing process, constructing support matrices for both forward and reverse information flows. The diffusion approximation of the graph signal is calculated using the Chebyshev polynomial recursive formula to capture the multi-hop spatial propagation effect of traffic flow in the road network; S8, a diffusion convolution recurrent unit is constructed, integrating the diffusion convolution operation in S7 into the gated recurrent unit, replacing the linear transformation in the traditional gated recurrent unit, and realizing spatiotemporal dynamic joint modeling; S9, a composite loss function including interpolation reconstruction loss, prediction loss and generative adversarial loss is designed, and a unified optimization objective is formed by weighted summation, realizing end-to-end collaborative training between the interpolation stage and the prediction stage, avoiding error accumulation and amplification in the two-stage method.

[0005] S1 includes:

[0006] S1.1. The traffic network is abstracted into a spatiotemporal dynamic graph to describe the attribute characteristics and topological relationships of sensor nodes in the network, expressed as:

[0007] ,

[0008] The set of attribute features of all sensor nodes within a historical time window is expressed as:

[0009] ,

[0010] in, This represents the total number of sensor nodes in the road network. For a single sensor node, the feature dimension at each time step.

[0011] The spatial adjacency matrix between sensor nodes, used to encode the topology of the road network, is expressed as:

[0012] ,

[0013] Among them, if sensor node With sensor nodes If they are physically connected or have a significant relationship, then ,otherwise .

[0014] S1.2, Set up sensor nodes Divided into observation node set With unobserved node set ,satisfy and Observe node attributes and missing node attributes satisfy and The true and complete feature dataset is represented as .

[0015] S1.3, Introduction Define a mask matrix to extract the observable portion of the real data; its mathematical definition is:

[0016] ,

[0017] Wherein, the mask matrix satisfies .

[0018] When constructing the physical adjacency graph and traffic correlation graph in S2, the following are included:

[0019] S2.1 Based on the Euclidean distance between sensor nodes, a Gaussian kernel function is used to convert the distance into similarity weights. Set threshold By filtering strongly correlated connections and forming a weighted adjacency matrix, a physical adjacency graph can be constructed. , expressed as:

[0020] ,

[0021] Among them, nodes and nodes Weighted values ​​between Expressed as:

[0022] ,

[0023] in, For nodes and nodes The distance between them Let the standard deviation of the distances between all nodes be denoted as . This represents the natural exponential function.

[0024] S2.2 Based on historical traffic flow data, functional similarity between nodes is mined using a data-driven approach to construct a traffic correlation graph. Specifically, it includes:

[0025] S2.21 Select traffic flow data from a sufficiently long historical time window. ( (where the number of time steps is 1), calculate the Pearson correlation coefficient between any two historical sequences to form the original correlation matrix. , expressed as:

[0026] .

[0027] S2.22, Based on the original correlation matrix in S2.21 All negative correlation coefficients are truncated to zero to obtain the non-negative correlation matrix. .

[0028] S2.23, Based on the nonnegative correlation matrix in S2.22 Calculate the number of strongly correlated neighbors for each sensor node. , expressed as:

[0029] ,

[0030] in, This is the scaling factor.

[0031] S2.24, based on the number of strongly correlated neighbors in S2.23 For each sensor node Non-negative correlation value Sort in descending order and select the top... The most relevant nodes form a neighbor set. To construct a traffic correlation map , expressed as:

[0032] ,

[0033] in, This is used to ensure that the individual information of each sensor node is preserved during the aggregation process.

[0034] When obtaining the bi-graph feature tensor in S3, the following are included:

[0035] S3.1 In GraphSAGE, mean pooling is used to process the physical adjacency graph. The features of neighboring nodes are aggregated.

[0036] S3.2. Combine the neighborhood representation obtained in S3.1 with the node's own features.

[0037] S3.3. The concatenated vector from S3.2 is activated using ReLU to obtain the physical adjacency graph features. , expressed as:

[0038] ,

[0039] in, Represents the physical adjacency graph. Layer input feature matrix, and The trainable weight matrices correspond to the features of the node itself and the features of its neighborhood, respectively. Indicates feature splicing, This represents the activation function F.relu. This indicates the output physical adjacency graph feature matrix.

[0040] S3.4 In GraphSAGE, mean pooling is used to process the traffic correlation graph. The features of neighboring nodes are aggregated.

[0041] S3.5. Combine the neighborhood representation obtained in S3.4 with the node's own features.

[0042] S3.6. Apply ReLU activation to the concatenated vector from S3.5 to obtain the traffic correlation map features. , expressed as:

[0043] ,

[0044] in, The traffic correlation diagram shows the first... Layer input feature matrix, and The trainable weight matrices correspond to the features of the node itself and the features of its neighborhood, respectively. Indicates feature splicing, This represents the activation function F.relu. This indicates the output physical adjacency graph feature matrix.

[0045] S3.7. The physical adjacency graph features extracted from the two stacked GraphSAGE layers S3.1-S3.3 and S3.4-S3.6 respectively. Feature analysis with traffic correlation maps The features are then concatenated to obtain the bi-image feature tensor. , expressed as:

[0046] .

[0047] When introducing the compressed incentive attention mechanism in S4, it includes:

[0048] S4.1, Based on the bi-graph feature tensor obtained in S3.7 Global average pooling aggregates the global spatial information of each feature channel across all nodes, compressing the two-dimensional feature map of each channel into a scalar channel descriptor. For the first feature channel in a batch... The first sample Each channel has a descriptor calculated as follows:

[0049] ,

[0050] This involves generating the compressed descriptor vector. This captures the global response distribution for each channel.

[0051] S4.2, Building upon S4.1, we model channel dependencies. Using a bottleneck structure containing two fully connected layers, we learn the non-linear dependencies between channels and generate the weights for each channel. The calculation process is as follows:

[0052] ,

[0053] ,

[0054] in, This represents the Sigmoid function. The channel attention weights obtained through learning, For the reduction rate, and These are the transposes of the corresponding weight matrices. , This is a bias term.

[0055] S4.3, Based on S4.2, feature recalibration is performed, applying the learned channel attention weights. Channel-level multiplication is applied to the original input features. This achieves recalibration of the feature channels, expressed as:

[0056] ,

[0057] Among them, the calibrated features With input Dimensions are consistent.

[0058] When performing missing data imputation in S5, the following are included:

[0059] S5.1 uses the dual-graph feature extraction network in S3 and the compressed excitation attention mechanism in S4 as the core, and a cascaded multilayer perceptron as the head generator, inputting the historical traffic sequence of the observed nodes in S1. The output is the interpolated node features. Its forward propagation process is formally represented as:

[0060] ,

[0061] in, , , and All are learnable parameters. The Sigmoid function ensures that the interpolated output value is normalized to the (0, 1) interval, consistent with the actual data range.

[0062] S5.2 The discriminator is an independent MLP network that receives real and complete data. Data synthesized with generator As input, the output scalar value represents the confidence level that the sample is real data.

[0063] S5.3. The loss function of Wasserstein GAN is designed to ensure complete data generation. The statistical distribution approximates the true complete data. Statistical distribution, discriminator loss generator loss They are respectively:

[0064] ,

[0065] ,

[0066] in, This represents the output of the discriminator. and Representing real and complete data respectively Distributed and complete generated data distributed.

[0067] When making predictions for future time steps in S6, the following are included:

[0068] S6.1, Based on the complete generated data obtained in S5 ( ),Will Encoded as a context vector containing global spatiotemporal information The encoding process is formally represented as

[0069] ,

[0070] Wherein, the encoder at each time step and each layer Update its hidden state The state update depends on the hidden state of the previous time step, the current input, and the road network topology. , The multi-hop spatial information is represented as:

[0071] ,

[0072] Among them, when hour, Context vector Take the hidden state of the last layer at the final time step.

[0073] S6.2, from the context vector in S6.1 Initialization, i.e. Generate future prediction sequences using an autoregressive approach , expressed as:

[0074] ,

[0075] The training phase employs a teacher-mandated strategy, based on probability. Using the actual value from the previous time step as input, with probability The model uses its previous prediction to balance training stability and exposure bias; the inference phase relies entirely on its own historical predictions for iteration, and its state update is represented as:

[0076] ,

[0077] In this process, the output layer of the decoder maps the hidden state of the top layer at each time step to the final predicted value. .

[0078] In S7, spatial diffusion modeling of diffusion convolutional layers includes:

[0079] S7.1, Order This is the original adjacency matrix. Given the inverse of its degree matrix, the random walk transition matrix is ​​defined as:

[0080] ,

[0081] Among them, from node Transfer to node in one step The probability is expressed as ,from Construct two-direction normalized adjacency matrices and These are used to model the forward and reverse information flows, respectively, and are represented as:

[0082] ,

[0083] in, and The degree matrices are respectively and .

[0084] S7.2, Adjacency matrix normalized in two directions based on S7.1 and Diffusion convolution is performed The bidirectional diffusion of the order is approximated by calculating the diffusion of the graph signal using the Chebyshev polynomial recursive formula, capturing multi-hop dependencies. The recursive formula is as follows:

[0085] ,

[0086] ,

[0087] ,

[0088] in, Pick or , The input feature matrix of the diffusing convolutional layer (in the encoder) In the decoder ).

[0089] S7.3, from two directions, all orders (total) The diffusion characteristics of the group were spliced ​​together to obtain the aggregated representation. Finally, it is mapped to the DiffConv output space through a trainable linear transformation, as follows:

[0090] ,

[0091] in, and These are trainable parameters.

[0092] When constructing a diffusing convolutional recurrent unit in S8, at each time step The diffusing convolution recurrent unit receives the current input. Compared to the previous hidden state and with diffusion matrix , Together as unit inputs, specifically including:

[0093] S8.1. Concatenate the current input with the previous hidden state, as follows:

[0094] .

[0095] S8.2 Calculate the forget gates contained in the diffusing convolution loop units respectively. Update door and candidate gate Three gated structures, all linear transformations are performed by spread convolution operations. The substitution, specifically calculated as follows:

[0096] S8.21, Forgotten Gate The calculation, learning, determines which historical information should be discarded; its expression is:

[0097] .

[0098] S8.22, Update Gate The calculation determines the magnitude by which the hidden state should be updated, and its expression is:

[0099] .

[0100] S8.23, Candidate Gate After partially resetting historical information, the candidate hidden state is calculated based on the current input. First, the reset input is calculated, and its expression is:

[0101] ,

[0102] .

[0103] S8.24 Hidden state update: Combine the update gate, previous hidden states, and candidate gates to calculate the hidden state at the current time step. , expressed as:

[0104] ,

[0105] in, and These are the gating activation function and the candidate hidden state activation function, respectively.

[0106] In S9, the composite loss function is derived from the interpolation reconstruction loss. Predicting losses and generating adversarial loss ( , Composed of, wherein:

[0107] S9.1, Interpolation Reconstruction Loss Completed data used to measure the generator output With complete historical data The difference between them is calculated using the mean squared error and expressed as:

[0108] .

[0109] S9.2, Predicting Losses Used to measure the output of the prediction module With real future traffic data The difference between them is calculated using the mean squared error and expressed as:

[0110] .

[0111] S9.3, Generative adversarial loss includes discriminator loss. generator loss The expression, as shown in S5.3, is used to force the interpolated data to follow the overall statistical distribution of the actual traffic flow.

[0112] S9.4 The overall loss function is formed by the weighted sum of the four losses in S9.1-S9.3, and its expression is:

[0113] ,

[0114] in, , , and Hyperparameters used to balance the importance of various tasks.

[0115] S9.5, train and minimize end-to-end This enables deep collaboration between the interpolation module and the prediction module.

[0116] The beneficial effects of this application lie in the construction of a high-fidelity data interpolation module based on a dual-graph structure and adversarial training: Addressing the limitations of a single graph structure in capturing spatial dependencies, the module constructs a physical adjacency graph and a traffic pattern correlation graph in parallel, comprehensively aggregating node information from both geographical connectivity and functional similarity dimensions. Key features are extracted and fused through a dual-graph sampling aggregation network and an SE channel attention mechanism, and adversarial training using a generative adversarial network ensures that the generated interpolated data is not only numerically accurate but also statistically approximates real traffic flow. A robust spatiotemporal prediction module based on a diffusing convolutional recurrent neural network is designed: This module takes the interpolated complete historical data as input and employs an encoder-decoder architecture. Its core unit, the diffusing convolutional gated recurrent unit, can simultaneously model the dynamic evolution of traffic flow over time and the spatial diffusion (propagation) effect on the road network topology, thereby achieving a deep characterization of complex spatiotemporal dependencies. Comprehensive and rigorous experimental verification and analysis were conducted: Experimental scenarios with various missing rates (10%-70%) and prediction step lengths (5-60 minutes) were set up on two publicly available real-world traffic datasets, PeMS04 and PeMS08, and compared with representative baseline models such as KNN, GRU, BRITS, and MoGERNN. Experimental results show that: in data imputation, DGAN-DCRNN achieves the best performance under all settings, especially with a significant advantage at high missing rates, verifying the effectiveness of its adversarial generative imputation mechanism; in traffic prediction, the model exhibits the highest accuracy and strongest robustness in both short-term and long-term predictions, with its prediction error showing the most gradual increase with missing rate and prediction step length; in terms of efficiency and interpretability, the model achieves significant performance improvements within acceptable inference latency, and ablation experiments and visualization examples further confirm the necessity and practical effectiveness of each core component. Attached Figure Description

[0117] Figure 1 This is a schematic diagram of the model structure of this application;

[0118] Figure 2 A schematic diagram of the prediction model process under missing node information;

[0119] Figure 3 A comparative analysis chart of the performance and efficiency of different models;

[0120] Figure 4 A comparison chart showing the evolution of model performance under different prediction step sizes;

[0121] Figure 5 A visualization of the inference and prediction performance for typical missing nodes; Detailed Implementation

[0122] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to specific embodiments and accompanying drawings. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of this application. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concepts of this application.

[0123] like Figure 1 As shown, a traffic flow interpolation and prediction method based on dual-graph adversarial generation and diffusing convolutional recurrence includes:

[0124] S1. For traffic network scenarios with completely missing nodes, the traffic network is abstracted as a spatiotemporal dynamic graph. The sensor node set is divided into an observed node set and an unobserved node set, and a mask matrix is ​​introduced to represent the missing locations. Specifically, this includes:

[0125] S1.1. The traffic network is abstracted into a spatiotemporal dynamic graph to describe the attribute characteristics and topological relationships of sensor nodes in the network, expressed as:

[0126] ,

[0127] The set of attribute features of all sensor nodes within a historical time window is expressed as:

[0128] ,

[0129] in, This represents the total number of sensor nodes in the road network. For a single sensor node, the feature dimension at each time step.

[0130] The spatial adjacency matrix between sensor nodes, used to encode the topology of the road network, is expressed as:

[0131] ,

[0132] Among them, if sensor node With sensor nodes If they are physically connected or have a significant relationship, then ,otherwise .

[0133] S1.2, Set up sensor nodes Divided into observation node set With unobserved node set ,satisfy and Observe node attributes and missing node attributes satisfy and The true and complete feature dataset is represented as .

[0134] S1.3, Introduction Define a mask matrix to extract the observable portion of the real data; its mathematical definition is:

[0135] ,

[0136] Wherein, the mask matrix satisfies .

[0137] S2. Construct a physical adjacency graph based on the actual geographical locations and connectivity relationships of the sensor nodes, and construct a traffic correlation graph based on the functional similarity between sensor nodes. Specifically, constructing the physical adjacency graph and the traffic correlation graph includes:

[0138] S2.1 Based on the Euclidean distance between sensor nodes, a Gaussian kernel function is used to convert the distance into similarity weights. Set threshold By filtering strongly correlated connections and forming a weighted adjacency matrix, a physical adjacency graph can be constructed. , expressed as:

[0139] ,

[0140] Among them, nodes and nodes Weighted values ​​between Expressed as:

[0141] ,

[0142] in, For nodes and nodes The distance between them Let the standard deviation of the distances between all nodes be denoted as . This represents the natural exponential function.

[0143] S2.2 Based on historical traffic flow data, functional similarity between nodes is mined using a data-driven approach to construct a traffic correlation graph. Specifically, it includes:

[0144] S2.21 Select traffic flow data from a sufficiently long historical time window. ( (where the number of time steps is 1), calculate the Pearson correlation coefficient between any two historical sequences to form the original correlation matrix. , expressed as:

[0145] .

[0146] S2.22, Based on the original correlation matrix in S2.21 All negative correlation coefficients are truncated to zero to obtain the non-negative correlation matrix. .

[0147] S2.23, Based on the nonnegative correlation matrix in S2.22 Calculate the number of strongly correlated neighbors for each sensor node. , expressed as:

[0148] ,

[0149] in, This is the scaling factor.

[0150] S2.24, based on the number of strongly correlated neighbors in S2.23 For each sensor node Non-negative correlation value Sort in descending order and select the top... The most relevant nodes form a neighbor set. To construct a traffic correlation map , expressed as:

[0151] ,

[0152] in, This is used to ensure that the individual information of each sensor node is preserved during the aggregation process.

[0153] S3. A hierarchical spatial feature extraction method is used to extract the physical adjacency graph and the traffic correlation graph in S2, respectively. The extracted physical adjacency graph features and traffic correlation graph features are then concatenated to obtain a bi-graph feature tensor. Specifically, obtaining the bi-graph feature tensor includes:

[0154] S3.1 In GraphSAGE, mean pooling is used to process the physical adjacency graph. The features of neighboring nodes are aggregated.

[0155] S3.2. Combine the neighborhood representation obtained in S3.1 with the node's own features.

[0156] S3.3. The concatenated vector from S3.2 is activated using ReLU to obtain the physical adjacency graph features. , expressed as:

[0157] ,

[0158] in, Represents the physical adjacency graph. Layer input feature matrix, and The trainable weight matrices correspond to the features of the node itself and the features of its neighborhood, respectively. Indicates feature splicing, This represents the activation function F.relu. This indicates the output physical adjacency graph feature matrix.

[0159] S3.4 In GraphSAGE, mean pooling is used to process the traffic correlation graph. The features of neighboring nodes are aggregated.

[0160] S3.5. Combine the neighborhood representation obtained in S3.4 with the node's own features.

[0161] S3.6. Apply ReLU activation to the concatenated vector from S3.5 to obtain the traffic correlation map features. , expressed as:

[0162] ,

[0163] in, The traffic correlation diagram shows the first... Layer input feature matrix, and The trainable weight matrices correspond to the features of the node itself and the features of its neighborhood, respectively. Indicates feature splicing, This represents the activation function F.relu. This indicates the output physical adjacency graph feature matrix.

[0164] S3.7. The physical adjacency graph features extracted from the two stacked GraphSAGE layers S3.1-S3.3 and S3.4-S3.6 respectively. Feature analysis with traffic correlation maps The features are then concatenated to obtain the bi-image feature tensor. , expressed as:

[0165] .

[0166] S4. Introduce a compressed activation attention mechanism to adaptively calibrate the bi-graph feature tensor, enhancing the weights of key feature channels through compression, activation, and recalibration. Specifically, the compressed activation attention mechanism includes:

[0167] S4.1, Based on the bi-graph feature tensor obtained in S3.7 Global average pooling aggregates the global spatial information of each feature channel across all nodes, compressing the two-dimensional feature map of each channel into a scalar channel descriptor. For the first feature channel in a batch... The first sample Each channel has a descriptor calculated as follows:

[0168] ,

[0169] This involves generating the compressed descriptor vector. This captures the global response distribution for each channel.

[0170] S4.2, Building upon S4.1, we model channel dependencies. Using a bottleneck structure containing two fully connected layers, we learn the non-linear dependencies between channels and generate the weights for each channel. The calculation process is as follows:

[0171] ,

[0172] ,

[0173] in, This represents the Sigmoid function. The channel attention weights obtained through learning, For the reduction rate, and These are the transposes of the corresponding weight matrices. , This is a bias term.

[0174] S4.3, Based on S4.2, feature recalibration is performed, applying the learned channel attention weights. Channel-level multiplication is applied to the original input features. This achieves recalibration of the feature channels, expressed as:

[0175] ,

[0176] Among them, the calibrated features With input Dimensions are consistent.

[0177] S5 uses the dual-image feature extraction network from S3 and the compressed excitation attention mechanism from S4 as the core, and a cascaded multilayer perceptron as the head to construct the generator. This generator maps the observed data from S1 to complete generated data. An independent discriminator network is used to calculate the confidence level of the complete generated data. A generative adversarial network paradigm consisting of the generator and discriminator is adopted, and high-fidelity missing data imputation is achieved through adversarial training. Specifically, the missing data imputation process includes:

[0178] S5.1 uses the dual-graph feature extraction network in S3 and the compressed excitation attention mechanism in S4 as the core, and a cascaded multilayer perceptron as the head generator, inputting the historical traffic sequence of the observed nodes in S1. The output is the interpolated node features. Its forward propagation process is formally represented as:

[0179] ,

[0180] in, , , and All are learnable parameters. The Sigmoid function ensures that the interpolated output value is normalized to the (0, 1) interval, consistent with the actual data range.

[0181] S5.2 The discriminator is an independent MLP network that receives real and complete data. Data synthesized with generator As input, the output scalar value represents the confidence level that the sample is real data.

[0182] S5.3. The loss function of Wasserstein GAN is designed to ensure complete data generation. The statistical distribution approximates the true complete data. Statistical distribution, discriminator loss generator loss They are respectively:

[0183] ,

[0184] ,

[0185] in, This represents the output of the discriminator. and Representing real and complete data respectively Distributed and complete generated data distributed.

[0186] S6. An encoder-decoder architecture is adopted. The encoder's stacked diffusing convolutional layers encode the complete data generated in S5 into a context vector containing global spatiotemporal information. Based on this context vector, the decoder's stacked diffusing convolutional layers progressively generate the prediction sequence for future time steps in an autoregressive manner. Specifically, the prediction of future time steps includes:

[0187] S6.1, Based on the complete generated data obtained in S5 ( ),Will Encoded as a context vector containing global spatiotemporal information The encoding process is formally represented as

[0188] ,

[0189] Wherein, the encoder at each time step and each layer Update its hidden state The state update depends on the hidden state of the previous time step, the current input, and the road network topology. , The multi-hop spatial information is represented as:

[0190] ,

[0191] Among them, when hour, Context vector Take the hidden state of the last layer at the final time step.

[0192] S6.2, from the context vector in S6.1 Initialization, i.e. Generate future prediction sequences using an autoregressive approach , expressed as:

[0193] ,

[0194] The training phase employs a teacher-mandated strategy, based on probability. Using the actual value from the previous time step as input, with probability The model uses its previous prediction to balance training stability and exposure bias; the inference phase relies entirely on its own historical predictions for iteration, and its state update is represented as:

[0195] ,

[0196] In this process, the output layer of the decoder maps the hidden state of the top layer at each time step to the final predicted value. .

[0197] The diffuse convolutional layers in the encoder-decoder architecture of S7 and S6 generalize standard graph convolution to a bidirectional diffusion process, constructing support matrices for both forward and reverse information flows. They calculate the diffusion approximation of the graph signal using the Chebyshev polynomial recursive formula, capturing the multi-hop spatial propagation effect of traffic flow in the road network. Specifically, the spatial diffusion modeling of the diffuse convolutional layers includes:

[0198] S7.1, Order This is the original adjacency matrix. Given the inverse of its degree matrix, the random walk transition matrix is ​​defined as:

[0199] ,

[0200] Among them, from node Transfer to node in one step The probability is expressed as ,from Construct two-direction normalized adjacency matrices and These are used to model the forward and reverse information flows, respectively, and are represented as:

[0201] ,

[0202] in, and The degree matrices are respectively and .

[0203] S7.2, Adjacency matrix normalized in two directions based on S7.1 and Diffusion convolution is performed The bidirectional diffusion of the order is approximated by calculating the diffusion of the graph signal using the Chebyshev polynomial recursive formula, capturing multi-hop dependencies. The recursive formula is as follows:

[0204] ,

[0205] ,

[0206] ,

[0207] in, Pick or , The input feature matrix of the diffusing convolutional layer (in the encoder) In the decoder ).

[0208] S7.3, from two directions, all orders (total) The diffusion characteristics of the group were spliced ​​together to obtain the aggregated representation. Finally, it is mapped to the DiffConv output space through a trainable linear transformation, as follows:

[0209] ,

[0210] in, and These are trainable parameters.

[0211] S8. Construct a diffusing convolution recurrent unit, integrating the diffusing convolution operation from S7 into a gated recurrent unit, replacing the linear transformation in the traditional gated recurrent unit, and achieving spatiotemporal dynamic joint modeling. Specifically, when constructing the diffusing convolution recurrent unit, at each time step... The diffusing convolution recurrent unit receives the current input. Compared to the previous hidden state and with diffusion matrix , Together as unit inputs, specifically including:

[0212] S8.1. Concatenate the current input with the previous hidden state, as follows:

[0213] .

[0214] S8.2 Calculate the forget gates contained in the diffusing convolution loop units respectively. Update door and candidate gate Three gated structures, all linear transformations are performed by spread convolution operations. The substitution, specifically calculated as follows:

[0215] S8.21, Forgotten Gate The calculation, learning, determines which historical information should be discarded; its expression is:

[0216] .

[0217] S8.22, Update Gate The calculation determines the magnitude by which the hidden state should be updated, and its expression is:

[0218] .

[0219] S8.23, Candidate Gate After partially resetting historical information, the candidate hidden state is calculated based on the current input. First, the reset input is calculated, and its expression is:

[0220] ,

[0221] .

[0222] S8.24 Hidden state update: Combine the update gate, previous hidden states, and candidate gates to calculate the hidden state at the current time step. , expressed as:

[0223] ,

[0224] in, and These are the gating activation function and the candidate hidden state activation function, respectively.

[0225] S9. Design a composite loss function comprising interpolation / reconstruction loss, prediction loss, and generative adversarial loss. A unified optimization objective is formed through weighted summation, enabling end-to-end collaborative training between the interpolation and prediction stages, thus avoiding error accumulation and amplification in the two-stage method. Specifically, the composite loss function consists of the interpolation / reconstruction loss... Predicting losses and generating adversarial loss ( , Composed of, wherein:

[0226] S9.1, Interpolation Reconstruction Loss Completed data used to measure the generator output With complete historical data The difference between them is calculated using the mean squared error and expressed as:

[0227] .

[0228] S9.2, Predicting Losses Used to measure the output of the prediction module With real future traffic data The difference between them is calculated using the mean squared error and expressed as:

[0229] .

[0230] S9.3, Generative adversarial loss includes discriminator loss. generator loss The expression, as shown in S5.3, is used to force the interpolated data to follow the overall statistical distribution of the actual traffic flow.

[0231] S9.4 The overall loss function is formed by the weighted sum of the four losses in S9.1-S9.3, and its expression is:

[0232] ,

[0233] in, , , and Hyperparameters used to balance the importance of various tasks.

[0234] S9.5, train and minimize end-to-end This enables deep collaboration between the interpolation module and the prediction module.

[0235] To make this application clearer, the meanings of the symbols are explained in Table 1.

[0236] Table 1: Meaning of Symbols

[0237]

[0238] To make this application easier to understand, the following examples illustrate it further.

[0239] To visually illustrate the tasks of completion and prediction, Figure 2 The evolution of the feature map across different stages and the overall modeling pipeline are shown: (a) Complete map: representing the road network under ideal conditions, where all nodes (1-5) have complete observation attributes; (b) Actual map: simulating the actual scenario, where nodes 2 and 3 are in an "unobserved" state, and their attributes are completely missing (represented by question marks), resulting in a break in the road network topology at the feature level; (c) Completion stage: using the completion model, the historical records of unobserved nodes are restored by capturing the spatiotemporal correlation between observed nodes and missing nodes; (d) Prediction stage: based on the completed spatiotemporal map, deeper feature representations are extracted to support subsequent traffic flow evolution prediction.

[0240] Experimental Dataset: To verify the applicability of the proposed model in real traffic environments, this invention uses the publicly released traffic flow dataset from the California Department of Transportation (Caltrans Performance Measurement System, PeMS), including two subsets, PeMS04 and PeMS08. Both datasets consist of raw traffic parameters collected by road sensors at 30-second intervals, which are then aggregated into standardized traffic flow sequences at 5-minute intervals.

[0241] PeMS04: Data collected in the San Francisco Bay Area (January–February 2018) using 3,848 detectors across 29 roads. This paper analyzes data from 307 selected detectors.

[0242] PeMS08: Collected in San Bernardino (July to August 2016), using 1979 detectors on 8 roads. During this period, this paper uses traffic flow data from 170 detectors.

[0243] To simulate a scenario with no observed nodes, the experiment randomly introduced missing nodes in the node dimension (spatial dimension) with missing rates of 10%, 20%, 30%, 50%, and 70%. All data were mapped to the [-1, 1] interval using the min-max normalization method to ensure numerical stability. A sliding window was used to construct input-output pairs, with each sample containing 12 historical time steps (60 minutes) as input to predict traffic flow for the next 3 time steps (15 minutes). Finally, the dataset was divided into a training set (70%) and a test set (30%) in chronological order to evaluate the model's generalization ability.

[0244] Baseline Model Comparison: This study comprehensively evaluates the performance of the DGAN-DCRNN model proposed in this application, which is based on a dual-graph adversarial generation and diffusing convolutional recurrent traffic flow interpolation and prediction method. Four typical interpolation and prediction models were selected as baselines: KNN-linear, a hybrid model combining graph-based K-nearest neighbor interpolation and linear prediction; GRU, a classic recurrent neural network model where the constructed baseline utilizes the hidden states of gated recurrent units to simultaneously handle interpolation and prediction tasks; BRITS, a bidirectional recurrent interpolation network specifically designed for processing time series data with missing values; and MoGERNN, an advanced graph neural network method for predicting unobserved nodes.

[0245] Experimental performance evaluation indicators: In order to quantitatively and objectively evaluate the performance of each model in the interpolation and prediction tasks, this paper uses mean absolute error and root mean square error as the core evaluation indicators.

[0246] Mean Absolute Error (MAE): Calculated as the average of the absolute deviations between predicted (or interpolated) values ​​and true values. MAE assigns equal weight to the errors of all samples, directly reflecting the average deviation of model predictions. It is insensitive to outliers and provides a robust estimate of model accuracy. The expression is:

[0247] .

[0248] Root Mean Square Error (RMSE): RMSE is calculated as the square root of the average of the sum of squared prediction errors. Due to the squaring operation, RMSE amplifies the contribution of larger prediction errors, making it more sensitive to significant outliers in the predictions. This metric measures the fluctuation of predicted values ​​around the true values ​​and is often used to evaluate the overall accuracy and stability of a model. The expression is:

[0249] .

[0250] In the experiment, these two metrics were used to calculate the model's performance in the data imputation task (comparing the imputation results). With real historical data ) and traffic flow prediction task (comparing prediction results) With real future data The performance of the model is evaluated from multiple dimensions.

[0251] Training Strategy: All experiments were conducted on a hardware platform equipped with an NVIDIA RTX 3070 GPU, using the Python 3.9 programming language and the PyTorch 1.12.1 deep learning framework. To ensure fairness in the comparison, all baseline models and DGAN-DCRNN used the Adam optimizer for parameter updates. For the discriminator part of the generative adversarial network in DGAN-DCRNN, the RMSprop optimizer was used, consistent with common practices in WGAN-GP training. The backbone loss function of all models was set to mean squared error, while for DGAN-DCRNN, the total loss was a weighted sum of the imputation loss, prediction loss, and adversarial loss.

[0252] The optimal configuration of the model was determined by searching for key hyperparameters using the particle swarm optimization algorithm. The values ​​of the hyperparameters for the model in this application are detailed in Table 2.

[0253] Table 2: Model Hyperparameter Settings

[0254]

[0255] Experimental Results Analysis: Based on the above dataset and training strategy, this embodiment compares and analyzes the performance in five aspects: interpolation performance, prediction performance, efficiency analysis, multi-step prediction robustness analysis, and ablation experiment, using performance evaluation metrics.

[0256] Imputation performance analysis: As shown in Table 3, on the two real traffic datasets PeMS04 and PeMS08, the DGAN-DCRNN model achieved the best imputation performance in all scenarios with the set missing rate (10%–70%). Its mean absolute error and root mean square error were significantly lower than all the comparison baselines, which fully verified the excellent performance of the present invention in recovering missing spatiotemporal data, and further verified the robustness and generalization ability of DGAN-DCRNN in dealing with missing spatiotemporal data.

[0257] Table 3: Comparison of imputation performance of different models under different missing rates

[0258]

[0259] Predictive Performance Analysis: To evaluate the predictive performance and generalization ability of DGAN-DCRNN, this invention conducted comprehensive comparative experiments on two datasets (PeMS04 and PeMS08) at different missing rates (10% to 70%). The prediction performance results are shown in Table 4. The prediction error of all models increased with the increase of the missing data rate, reflecting the inherent challenge brought by the incompleteness of the input data to the prediction task. However, DGAN-DCRNN achieved the lowest mean absolute error and root mean square error under all missing rate settings on both datasets, demonstrating excellent prediction accuracy and stability.

[0260] Table 4: Comparison of prediction performance of different models under different missing rates

[0261]

[0262] Model efficiency analysis: Under the condition of a 20% missing value in the PEMS08 dataset, a comprehensive efficiency evaluation of DGAN-DCRNN and four baseline models was conducted. The comparison indicators covered prediction and imputation accuracy, model parameter count (model size), and inference latency per forward propagation. The comprehensive analysis results are as follows: Figure 3 As shown, the DGAN-DCRNN model proposed in this invention achieves a better trade-off between accuracy and efficiency. It contains 404.6k parameters and has a single inference latency of 153 milliseconds. This model does not simply pursue the highest accuracy or the lowest latency, but successfully achieves prediction performance that is significantly better than the baseline model under acceptable real-time inference overhead, demonstrating an excellent performance-efficiency ratio.

[0263] Multi-step prediction robustness analysis: To deeply evaluate the model's prediction robustness and generalization ability under different time horizons, this section conducts comparative experiments for different prediction step lengths. The choice of prediction step length directly corresponds to the needs of assessing short-term, medium-term, and long-term traffic conditions in practical applications. Short-term predictions (1-3 steps, 5-15 minutes) serve real-time guidance, while medium- and long-term predictions (6-12 steps, 30-60 minutes) provide a basis for route planning and congestion warning. Therefore, the performance stability of the model under different prediction step lengths is crucial.

[0264] This experiment, based on the PEMS08 dataset, systematically evaluated the performance of all comparative models in predicting the next 1, 3, 6, 9, and 12 time steps (i.e., 5, 15, 30, 45, and 60 minutes) with a node missing rate of 10%. The experiment also recorded the performance of each model on two tasks: upstream data imputation and downstream traffic flow prediction, under the corresponding prediction step size requirements. Detailed results can be found in [link to results]. Figure 4 .right Figure 4 The analysis in (a) shows that DGAN-DCRNN exhibits extremely high stability in the data imputation task; from the perspective of the evolution of prediction performance, as... Figure 4 As shown in (b), the prediction errors of all models show an upward trend with the increase of the prediction step size, revealing the universality of the error accumulation effect in time series forecasting. However, under this common trend, DGAN-DCRNN stands out. Through comprehensive testing at multiple time steps, DGAN-DCRNN not only demonstrates its leading accuracy in short-term prediction tasks, but more importantly, it exhibits excellent stability and an extremely low error growth rate in long-term predictions.

[0265] Ablation experiments: To thoroughly evaluate the contributions of each core component in the DGAN-DCRNN model, this section conducts a comprehensive ablation study on the PeMS08 dataset. Multiple variant models were constructed by systematically removing or replacing key modules of the model, and tested at different missing rates ranging from 10% to 70%. The experimental results are shown in Table 5.

[0266] Table 5: Performance Comparison of Ablation Models on the PEMS08 Dataset

[0267]

[0268] Experiments clearly demonstrate that each core component of DGAN-DCRNN is indispensable. Generative adversarial training is crucial for ensuring the quality of data generation under high missing rates; the channel attention mechanism optimizes the feature fusion process and enhances the model's discriminative ability; and the dual-graph fusion architecture provides the model with a comprehensive and complementary foundation for spatial relationship modeling. The synergistic work of these three components forms a solid foundation for DGAN-DCRNN to maintain high accuracy and strong robustness in complex missing spatiotemporal data prediction tasks.

[0269] To visually demonstrate the reconstruction and inference capabilities of the DGAN-DCRNN model on real spatiotemporal sequences, this invention selected 139 representative missing nodes from the PEMS08 dataset and performed a visualization analysis of their imputation and prediction results under different missing rates (10% to 70%). Specific results are shown below. Figure 5 As shown.

[0270] Regarding interpolation, from Figure 5 The comparison of curves (a) to (i) shows that at low missing rates (10%-30%), the model's imputation curves highly overlap with the actual values, accurately reproducing traffic flow trends and local fluctuations with high reconstruction fidelity; at high missing rates (50%-70%), although the curves are slightly smoother, they can still identify key time patterns such as morning and evening peak hours, and the GAN module can generate results that conform to the true distribution, avoiding numerical distortion; in terms of prediction, Figure 5The prediction curves from (b) to (j) further validate that the model can accurately capture the main traffic flow patterns at various missing rates. The slightly lower peak prediction is a reasonable performance under high uncertainty, confirming the model's rigorous logic and strong robustness. Single-node visualization verifies that the model's imputation module can provide high-quality data support, and the prediction module has an outstanding ability to maintain trends, intuitively demonstrating its practical value in traffic scenarios.

[0271] In summary, this embodiment systematically validates the DGAN-DCRNN framework for traffic flow prediction and missing data reconstruction tasks, addressing the issue of data block missingness caused by sensor failures and communication interruptions in real-world road networks. On one hand, comparative architectural design demonstrates that this framework abandons the traditional two-stage model, employing end-to-end joint learning to achieve collaborative optimization of imputation and prediction, effectively suppressing error propagation. On the other hand, module function verification shows that the dual-graph structure, channel attention, and adversarial generation mechanism can accurately capture spatiotemporal dependencies, ensuring that the imputed data closely matches real traffic flow in both value and distribution. Simultaneously, prediction performance verification demonstrates that the diffusing convolutional recurrent unit can deeply characterize spatiotemporal dynamics, ensuring robust and reliable prediction results. Furthermore, comparative results on PeMS04 and PeMS08 datasets, with multiple missing rates (10%–70%) and multiple step lengths (5–60 minutes), show that this framework significantly outperforms the baseline model in imputation accuracy and prediction robustness, exhibits gradual error growth, and demonstrates excellent inference efficiency. Ablation and visualization experiments confirm the clear contributions of each component. Experiments have fully demonstrated that DGAN-DCRNN maintains excellent performance in complex scenarios such as high missing values ​​and long time series, and has strong practicality and robustness.

Claims

1. A traffic flow interpolation and prediction method based on bi-graph adversarial generation and diffusing convolutional recurrence, characterized in that, include: S1. For traffic network scenarios with completely missing nodes, the traffic network is abstracted into a spatiotemporal dynamic graph, the sensor node set is divided into an observed node set and an unobserved node set, and a mask matrix is ​​introduced to represent the missing positions. S2. Construct a physical adjacency graph based on the actual geographical location and connection relationship of the sensor nodes, and construct a traffic correlation graph based on the functional similarity between sensor nodes; S3. The hierarchical spatial features of the physical adjacency graph and the traffic correlation graph in S2 are extracted by the layer-by-layer neighborhood feature aggregation method. The extracted physical adjacency graph features and traffic correlation graph features are concatenated to obtain a dual-graph feature tensor. S4. Introduce a compression-excitation attention mechanism to adaptively calibrate the feature tensors of the two graphs, and enhance the weights of key feature channels through compression, excitation and recalibration. S5. Using the dual-image feature extraction network in S3 and the compressed excitation attention mechanism in S4 as the core, and the cascaded multilayer perceptron as the head to build the generator, the observed data in S1 is mapped to complete generated data using the generator. An independent discriminator network is used to calculate the confidence of the complete generated data. A generative adversarial network paradigm composed of the generator and the discriminator is adopted. High-fidelity missing data imputation is achieved through adversarial training. S6. An encoder-decoder architecture is adopted, and the completely generated data in S5 is encoded into a context vector containing global spatiotemporal information through the stacked diffusion convolutional layer of the encoder. Based on context vectors, the predicted sequence for future time steps is gradually generated in an autoregressive manner through stacked diffuse convolutional layers in the decoder. S7. The diffusion convolutional layer of the encoder-decoder architecture in S6 extends the standard graph convolution to a bidirectional diffusion process, constructs the support matrix of the forward and reverse information flows, calculates the diffusion approximation of the graph signal through the Chebyshev polynomial recursive formula, and captures the multi-hop spatial propagation effect of traffic flow in the road network. S8. Construct a diffusing convolution recurrent unit, integrating the diffusing convolution operation in S7 into a gated recurrent unit, replacing the linear transformation in the traditional gated recurrent unit, and realizing spatiotemporal dynamic joint modeling. S9. Design a composite loss function that includes interpolation reconstruction loss, prediction loss and generative adversarial loss. Form a unified optimization objective by weighted summation to achieve end-to-end collaborative training between the interpolation and prediction stages, and avoid error accumulation and amplification in the two-stage method.

2. The traffic flow interpolation and prediction method based on dual-graph adversarial generation and diffusing convolutional loop as described in claim 1, characterized in that, S1 includes: S1.

1. The traffic network is abstracted into a spatiotemporal dynamic graph to describe the attribute characteristics and topological relationships of sensor nodes in the network, expressed as: ， The set of attribute features of all sensor nodes within a historical time window is expressed as: ， in, This represents the total number of sensor nodes in the road network. For a single sensor node, the feature dimension at each time step. The spatial adjacency matrix between sensor nodes, used to encode the topology of the road network, is expressed as: ， Among them, if sensor node With sensor nodes If they are physically connected or have a significant relationship, then ,otherwise ; S1.2, Set up sensor nodes Divided into observation node set With unobserved node set ,satisfy and Observe node attributes and missing node attributes satisfy and The true and complete feature dataset is represented as ; S1.3, Introduction Define a mask matrix to extract the observable portion of the real data; its mathematical definition is: ， Wherein, the mask matrix satisfies .

3. The traffic flow interpolation and prediction method based on dual-graph adversarial generation and diffusing convolutional loop as described in claim 2, characterized in that, The construction of the physical adjacency graph and traffic correlation graph in S2 includes: S2.1 Based on the Euclidean distance between sensor nodes, a Gaussian kernel function is used to convert the distance into similarity weights. Set threshold By filtering strongly correlated connections and forming a weighted adjacency matrix, a physical adjacency graph can be constructed. , expressed as: ， Among them, nodes and nodes Weighted values ​​between Expressed as: ， in, For nodes and nodes The distance between them Let the standard deviation of the distances between all nodes be denoted as . Represents the natural exponential function; S2.2 Based on historical traffic flow data, functional similarity between nodes is mined using a data-driven approach to construct a traffic correlation graph. Specifically, it includes: S2.21 Select traffic flow data from a sufficiently long historical time window. ( (where the number of time steps is 1), calculate the Pearson correlation coefficient between any two historical sequences to form the original correlation matrix. , expressed as: ； S2.22, Based on the original correlation matrix in S2.21 All negative correlation coefficients are truncated to zero to obtain the non-negative correlation matrix. ; S2.23, Based on the non-negative correlation matrix in S2.22 Calculate the number of strongly correlated neighbors for each sensor node. , expressed as: ， in, This is the scaling factor; S2.24, Based on the number of strongly correlated neighbors in S2.23 For each sensor node Non-negative correlation value Sort in descending order and select the top... The most relevant nodes form a neighbor set. To construct a traffic correlation map , expressed as: ， in, This is used to ensure that the individual information of each sensor node is preserved during the aggregation process.

4. The traffic flow interpolation and prediction method based on dual-graph adversarial generation and diffusing convolutional loop as described in claim 3, characterized in that, The process of obtaining the dual-graph feature tensor in S3 includes: S3.1 In GraphSAGE, mean pooling is used to process the physical adjacency graph. Aggregate the features of neighboring nodes in the data; S3.2, Concatenate the neighborhood representation obtained in S3.1 with the features of the node itself; S3.

3. The concatenated vector from S3.2 is activated using ReLU to obtain the physical adjacency graph features. , expressed as: ， in, Represents the physical adjacency graph. Layer input feature matrix, and The trainable weight matrices correspond to the features of the node itself and the features of its neighborhood, respectively. Indicates feature splicing, This represents the activation function F.relu. This indicates the output physical adjacency graph feature matrix; S3.4 In GraphSAGE, mean pooling is used to process the traffic correlation graph. Aggregate the features of neighboring nodes in the data; S3.

5. Concatenate the neighborhood representation obtained in S3.4 with the features of the node itself; S3.

6. The concatenated vector from S3.5 is activated using ReLU to obtain the traffic correlation map features. , expressed as: ， in, The traffic correlation diagram shows the first... Layer input feature matrix, and The trainable weight matrices correspond to the features of the node itself and the features of its neighborhood, respectively. Indicates feature splicing, This represents the activation function F.relu. This indicates the output physical adjacency graph feature matrix; S3.

7. Extract the physical adjacency graph features from the two stacked GraphSAGE layers S3.1-S3.3 and S3.4-S3.6 respectively. Feature analysis with traffic correlation maps The features are then concatenated to obtain the bi-image feature tensor. , expressed as: 。 5. The traffic flow interpolation and prediction method based on dual-graph adversarial generation and diffusing convolutional loop as described in claim 4, characterized in that, When introducing the compressed incentive attention mechanism in S4, it includes: S4.1, Based on the bi-graph feature tensor obtained in S3.7 Global average pooling aggregates the global spatial information of each feature channel across all nodes, compressing the two-dimensional feature map of each channel into a scalar channel descriptor. For the first feature channel in a batch... The first sample Each channel has a descriptor calculated as follows: ， This involves generating the compressed descriptor vector. This captures the global response distribution for each channel; S4.

2. Based on S4.1, model channel dependencies. Through a bottleneck structure containing two fully connected layers, learn the non-linear dependencies between channels and generate the weights for each channel. The calculation process is as follows: ， ， in, This represents the Sigmoid function. The channel attention weights obtained through learning, For the reduction rate, and These are the transposes of the corresponding weight matrices. , For bias terms; S4.

3. Based on S4.2, feature recalibration is performed, and the learned channel attention weights are... Channel-level multiplication is applied to the original input features. This achieves recalibration of the feature channels, expressed as: ， Among them, the calibrated features With input Dimensions are consistent.

6. The traffic flow interpolation and prediction method based on dual-graph adversarial generation and diffusing convolutional recurrence as described in claim 5, characterized in that, The missing data imputation process in S5 includes: S5.1 Using the dual-graph feature extraction network in S3 and the compressed excitation attention mechanism in S4 as the core, and a cascaded multilayer perceptron as the head generator, the historical traffic sequence of the observed nodes in S1 is input. The output is the interpolated node features. Its forward propagation process is formally represented as: ， in, , , and All are learnable parameters. The Sigmoid function ensures that the interpolated output value is normalized to the (0, 1) interval, consistent with the range of the real data. S5.2 The discriminator is an independent MLP network that receives real and complete data. Data synthesized with generator As input, the output scalar value represents the confidence level that the sample is real data; S5.

3. The loss function of Wasserstein GAN is designed to ensure complete data generation. The statistical distribution approximates the true complete data. Statistical distribution, discriminator loss generator loss They are respectively: ， ， in, This represents the output of the discriminator. and Representing real and complete data respectively Distributed and complete generated data distributed.

7. The traffic flow interpolation and prediction method based on dual-graph adversarial generation and diffusing convolutional loop as described in claim 6, characterized in that, The prediction of future time steps in S6 includes: S6.1 Based on the complete generated data obtained in S5 ( ),Will Encoded as a context vector containing global spatiotemporal information The encoding process is formally represented as ， Wherein, the encoder at each time step and each layer Update its hidden state The state update depends on the hidden state of the previous time step, the current input, and the road network topology. , The multi-hop spatial information is represented as: ， Among them, when hour, Context vector Take the hidden state of the last layer at the final time step; S6.2, from the context vector in S6.1 Initialization, i.e. Generate future prediction sequences using an autoregressive approach , expressed as: ， The training phase employs a teacher-mandated strategy, based on probability. Using the actual value from the previous time step as input, with probability The model uses its previous prediction to balance training stability and exposure bias; the inference phase relies entirely on its own historical predictions for iteration, and its state update is represented as: ， In this process, the output layer of the decoder maps the hidden state of the top layer at each time step to the final predicted value. .

8. The traffic flow interpolation and prediction method based on dual-graph adversarial generation and diffusing convolutional recurrence as described in claim 7, characterized in that, The S7 section includes the following when performing spatial diffusion modeling for the diffusion convolutional layer: S7.1, Order This is the original adjacency matrix. Given the inverse of its degree matrix, the random walk transition matrix is ​​defined as: ， Among them, from node Transfer to node in one step The probability is expressed as ,from Construct two-direction normalized adjacency matrices and These are used to model the forward and reverse information flows, respectively, and are represented as: ， in, and The degree matrices are respectively and ; S7.2, Based on the adjacency matrix normalized in the two directions in S7.1 and Diffusion convolution is performed The bidirectional diffusion of the order is approximated by calculating the diffusion of the graph signal using the Chebyshev polynomial recursive formula, capturing multi-hop dependencies. The recursive formula is as follows: ， ， ， in, Pick or , The input feature matrix of the diffusing convolutional layer (in the encoder) In the decoder ); S7.3, from two directions, all orders (total) The diffusion characteristics of the group were spliced ​​together to obtain the aggregated representation. Finally, it is mapped to the DiffConv output space through a trainable linear transformation, as follows: ， in, and These are trainable parameters.

9. The traffic flow interpolation and prediction method based on dual-graph adversarial generation and diffusing convolutional loop as described in claim 8, characterized in that, In S8, when constructing the diffusing convolutional recurrent unit, at each time step... The diffusing convolution recurrent unit receives the current input. Compared to the previous hidden state and with diffusion matrix , Together as unit inputs, specifically including: S8.

1. Concatenate the current input with the previous hidden state, as follows: ； S8.2 Calculate the forget gates contained in the diffusing convolution loop units respectively. Update door and candidate gate Three gated structures, all linear transformations are performed by spread convolution operations. The substitution, specifically calculated as follows: S8.21, Forgotten Gate The calculation, learning, determines which historical information should be discarded; its expression is: ； S8.22, Update Gate The calculation determines the magnitude by which the hidden state should be updated, and its expression is: ； S8.23, Candidate Gate After partially resetting historical information, the candidate hidden state is calculated based on the current input. First, the reset input is calculated, and its expression is: ， ； S8.24 Hidden state update: Combine the update gate, previous hidden states, and candidate gates to calculate the hidden state at the current time step. , expressed as: ， in, and These are the gating activation function and the candidate hidden state activation function, respectively.

10. The traffic flow interpolation and prediction method based on dual-graph adversarial generation and diffusing convolutional loop as described in claim 9, characterized in that, In S9, the composite loss function is composed of interpolation reconstruction loss. Predicting losses and generating adversarial loss ( , Composed of, wherein: S9.1, Interpolation Reconstruction Loss Completed data used to measure the generator output With complete historical data The difference between them is calculated using the mean squared error and expressed as: ； S9.2, Predicting Losses Used to measure the output of the prediction module With real future traffic data The difference between them is calculated using the mean squared error and expressed as: ； S9.3, Generative adversarial loss includes discriminator loss. generator loss The expression, as shown in S5.3, is used to force the interpolated data to follow the overall statistical distribution of the actual traffic flow; S9.4 The overall loss function is constructed by the weighted sum of the four losses described in S9.1-S9.3, and its expression is as follows: ， in, , , and Hyperparameters used to balance the importance of various tasks; S9.5, train and minimize end-to-end This enables deep collaboration between the interpolation module and the prediction module.

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