Traffic flow prediction method based on adaptive decomposition and attention mechanism

The traffic flow prediction method based on adaptive decomposition and attention mechanism solves the problem that existing methods fail to effectively handle different mode characteristics and time lag effects, and achieves higher accuracy and robustness in traffic flow prediction.

CN121884590APending Publication Date: 2026-04-17CHONGQING UNIV OF POSTS & TELECOMM
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
CHONGQING UNIV OF POSTS & TELECOMM
Filing Date
2026-01-16
Publication Date
2026-04-17

AI Technical Summary

Technical Problem

Existing traffic flow prediction methods fail to effectively separate and process the characteristics of different modes, and fail to fully capture the time lag effect of traffic flow, making it difficult to improve prediction accuracy.

Method used

An adaptive decomposition module is used to decompose the time series of traffic flow into intrinsic and diffuse terms. Spatiotemporal information is introduced through a data embedding layer. Combined with an adaptive fusion module and an attention mechanism, the dynamic information in the road network space and the node’s own attributes are processed respectively. Temporal convolution and trend category learning modules are designed to capture temporal and spatial dependencies.

Benefits of technology

It improves the accuracy and robustness of traffic flow forecasting, reduces noise interference, and can more accurately capture the dynamic changes and delays in traffic flow.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention proposes a traffic flow prediction method based on adaptive decomposition and an attention mechanism, and the method comprises the steps: decoupling historical traffic data into an inherent term and a diffusion term through an adaptive decomposition module, and introducing time embedded information to enhance the expression capability of time sequence features. For an inherent item, a time convolution module, a time attention module and a trend category learning module are adopted to emphatically extract trend information of a node; for diffusion terms, spatial dependencies and delayed transfer effects in the road network are captured using temporal convolution and a multi-time slice spatial attention gating module. And finally, integrating the processed two outputs through an adaptive fusion module, and carrying out model training in combination with a weighted loss function (including prediction loss, reconstruction loss, smooth loss and sparse loss), thereby remarkably improving prediction accuracy and robustness. The method can improve the prediction precision while effectively processing the spatio-temporal information, and is suitable for flow prediction in a complex traffic scene.
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Description

Technical Field

[0001] This invention belongs to the field of traffic flow prediction, specifically relating to a traffic flow prediction method based on adaptive decomposition and attention mechanism. Background Technology

[0002] With the acceleration of urbanization, urban transportation systems are facing increasingly severe congestion problems, leading to reduced traffic efficiency, increased air pollution, and a rise in traffic accidents. To address these challenges, intelligent transportation systems are being applied more and more widely, with traffic flow prediction being one of the core technologies. This technology helps traffic management departments intervene in advance to optimize traffic flow distribution and control. However, traffic flow prediction is extremely challenging due to the complex spatiotemporal dependencies, nonlinearity, and dynamic nature of traffic data.

[0003] Traditional traffic flow prediction methods, such as statistical time series analysis or regression analysis, are effective for simple or linear data, but their predictive power is insufficient when faced with complex, nonlinear traffic data. Deep learning techniques have been applied to traffic flow prediction. Convolutional neural networks (CNNs) can capture spatial features of urban traffic networks by transforming traffic data into a gridded image format, but they are weak at capturing global spatiotemporal relationships. Recurrent neural networks (RNNs) and their variants can capture the temporal dependencies of traffic flow data, but they face challenges in learning long-term dependencies. These models still have limitations when predicting complex traffic flow data.

[0004] Existing graph convolutional network-based methods, such as spatiotemporal graph convolutional networks, can make predictions by combining the topology and spatiotemporal dependencies of traffic networks. However, these methods usually rely on fixed graph structures and are difficult to adapt to traffic flow prediction when the graph structure is missing.

[0005] Furthermore, existing traffic flow prediction methods often fail to adequately consider the diversity and complexity of traffic flow data. Traffic data not only exhibits significant spatiotemporal dependencies but also contains change patterns triggered by a variety of different causes. The causes influencing a node's pattern are typically categorized into incidental events and long-term trends. Most existing methods fail to effectively separate and process the characteristics of these different patterns, resulting in difficulty in improving prediction accuracy. Secondly, traffic data exhibits delayed transitivity, meaning that traffic conditions in some areas will affect other areas after a certain period. However, many models based on spatiotemporal neural networks or graph convolutional networks fail to fully capture this delayed transitivity, considering only synchronous spatiotemporal relationships and ignoring time lag effects.

[0006] In practical applications, traffic flow forecasting faces challenges such as missing data, outlier handling, and real-time requirements. These issues have prompted researchers to continuously explore more advanced modeling methods to improve the accuracy and robustness of traffic flow forecasting. Summary of the Invention

[0007] The purpose of this invention is to address the problems in existing traffic flow prediction methods that fail to effectively separate and process the characteristics of different modes and fail to fully capture the time lag effect of traffic flow, and to provide a traffic flow prediction method based on adaptive decomposition and attention mechanism.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] S1. Collect historical traffic data over a period of time using traffic sensors within the area to obtain the raw input data for the model.

[0010] S2. The time series information is decomposed into intrinsic and diffuse terms using an adaptive decomposition module, and spatiotemporal information is introduced into the two terms obtained by the decomposition through a data embedding layer; then the intrinsic and diffuse terms are merged through an adaptive fusion module to obtain the reconstructed sequence.

[0011] S3. Construct an intrinsic item processing branch and input the intrinsic items into the processing branch, focusing on capturing traffic patterns determined by the node's own attributes.

[0012] S4. Construct a diffusion term processing branch and input the diffusion term into this processing branch, focusing on capturing dynamic information propagating in the road network space during traffic.

[0013] S5. Adaptively fuse the obtained intrinsic and diffusion terms to obtain the final result. Calculate the weighted loss of each part of the model and train the model.

[0014] Specifically, step S2 includes:

[0015] The adaptive decomposition module of this invention decouples traffic flow time series data, decomposing the complex time series into intrinsic terms and diffusion terms.

[0016] S2.1 Decompose different sequence patterns using one-dimensional convolution;

[0017] Adaptive decomposition uses one-dimensional convolution to adaptively extract intrinsic and diffuse terms. Taking the intrinsic term as an example, for a single node's time series, the input is represented as... , No. Each convolutional kernel is represented as For the first Each convolutional kernel at time position Output:

[0018]

[0019] in It is the convolution stride. It's convolutional padding. For the first Bias terms for each convolution kernel.

[0020] The total output of multiple time slices after convolution is:

[0021]

[0022] Finally, the sequence of intrinsic terms obtained by decomposing a single node is:

[0023]

[0024] in , It is a weight matrix. , This is the bias term. The decomposition sequence of the diffusion term is similar.

[0025] S2.2 Spatiotemporal characteristics of embedded nodes;

[0026] To better incorporate spatiotemporal information into the model and thus improve the accuracy and robustness of traffic flow prediction, the model uses a data embedding layer to embed the time information of the prediction moment (the day of the week and the specific time of day) and node features. This embedding is based on... This is represented by the terms, which are then concatenated with the two terms obtained from the decomposition to obtain the final intrinsic and diffusion terms:

[0027]

[0028]

[0029] Subsequently, to improve the robustness of the fusion module, we used adaptive fusion to reconstruct the original input. This process is crucial for data... and By applying an attention mechanism, an adaptive preliminary fusion result is first obtained, and then combined with... The results are added together and then passed through a fully connected layer to obtain the final fused result:

[0030]

[0031] in, These are learnable parameters. It will be used to calculate the reconstruction loss.

[0032] Further, step S3 includes:

[0033] S3.1 Initially extracts temporal information through temporal convolution;

[0034] Because the data being processed is time-series information, which inherently possesses temporal characteristics—meaning that information at any given moment should not contain information from future times—temporal convolution processes the data by stacking multiple convolutional layers with dilated causal convolutions. In this convolutional structure, the output at each time step depends only on past inputs and does not introduce information from future moments, ensuring that causality is preserved. For the... Layer convolution, dilation rate The convolution formula is as follows:

[0035]

[0036] in It is the kernel size. It is a time step. It is the first Layer convolution kernel in the th The weight matrix of each offset, As a bias term, causality is determined by... ensure.

[0037] S3.2 Time Attention Module Extracts Time Information:

[0038] For the input of this module , will the The time slice of each sensor is represented as .

[0039] To effectively model the relationships between time slices within a node, this method applies a self-attention mechanism in the time dimension. Specifically, the self-attention mechanism is first used to calculate the... The temporal dependencies between all time slices in each sensor are then modeled using attention weights to aggregate information from different time slices, thus establishing long-term temporal dependencies among all time slices. Finally, the temporal attention module's relationship with the first sensor is obtained. The output of each sensor :

[0040]

[0041] in, These are learnable parameters.

[0042] The S3.3 Trend Category Learning Module integrates trend category information;

[0043] To better extract the inherent trend information of nodes in the intrinsic components, this invention designs a trend category learning module. This module adaptively learns the trend features of each node, effectively capturing the trend change patterns of different nodes.

[0044] For input Obtain category attention score

[0045]

[0046] in, , These are learnable parameters. It represents the number of trend categories.

[0047] Using attention weights We perform a weighted summation of the categorical data to obtain an output that incorporates categorical information. :

[0048]

[0049] in, These are learnable parameters, This is the final output of step S3.

[0050] Furthermore, step S4 includes:

[0051] S4.1 Initially extracts temporal information through temporal convolution;

[0052] The operations involved here are the same as in step S3.1, except for the input.

[0053] The S4.2 multi-time-slice spatial attention gating module extracts spatial information;

[0054] For the input of this module To incorporate graph structure information, the first part of the Laplacian characteristic matrix of the graph is taken. From the feature vectors, we obtain the graph embedding representation. Combine it with the original input:

[0055]

[0056] in, These are learnable parameters.

[0057] The data after incorporating graph structure information The data from all sensors during the time slice are represented as follows: .

[0058] Given data Applying a self-attention mechanism in the spatial dimension, the first step is to compute the time slice... The model identifies the dependencies between all sensors and captures their spatial correlations through a self-attention mechanism. Then, the average first-pass time is introduced as a mask matrix for the attention score, thereby incorporating road network information into the model.

[0059] Let the state be to state The average transit time is Its recursive definition is:

[0060]

[0061] For each target node The average first-pass time from this node to all other nodes can be calculated using the following formula:

[0062]

[0063] in It is the state transition probability matrix. After calculating the average first-pass time to other nodes for each node, the mask matrix is ​​obtained. The final attention score between nodes is:

[0064]

[0065] Next, the spatial dependencies between these sensors are aggregated to capture their mutual influence. Finally, the spatial attention module obtains information about... Output of sensor internal relationship under time slice :

[0066]

[0067] in, These are learnable parameters.

[0068] Then we will enter The first time step was copied to obtain Then remove the input. The last time slice was obtained Finally in front The time-slice delay input can be obtained by concatenating the two parts.

[0069] Will The key and value matrices, which serve as the attention mechanism, are used to obtain the time slices in the same way. Lower sensor and time slice Spatial dependency of sensors in

[0070] Then and The gating weights are obtained by splicing and passing through a fully connected layer. And separate the weights to obtain and Finally, perform a weighted summation:

[0071]

[0072] by This is the final output of step S4.

[0073] Furthermore, step S5 includes:

[0074] The main purpose of this step is to process the results obtained in step S3. The result obtained in step S4 Perform adaptive fusion and calculate various types of losses.

[0075] For data and Following the adaptive fusion method in step S2, the final prediction result is obtained by fusion. The loss during model training includes... , , , Four items. Among them By calculating the predicted value Compared with the true value The mean absolute error is obtained; By calculating the reconstructed value With the original input The mean absolute error is obtained. For the intrinsic terms obtained after adaptive decomposition The first-order difference is used to constrain its smoothness, and its calculation formula is as follows:

[0076]

[0077] For the diffusion term obtained after adaptive decomposition The sparsity loss is used to constrain its sparsity, and its calculation formula is as follows:

[0078]

[0079] The final loss for model optimization is:

[0080]

[0081] The beneficial effects of this invention are as follows:

[0082] 1) By performing pattern separation on traffic flow sequences and processing intrinsic and diffuse information separately, the dynamic changes in traffic flow can be captured more accurately, noise interference can be reduced, and the accuracy of prediction can be improved.

[0083] 2) A specific category module was designed to process data of different categories or patterns in traffic flow. This module enables the model to adaptively learn for different categories of traffic characteristics.

[0084] 3) A multi-time-slice module was designed to process event information, capturing the time lag effect of traffic data through a delayed delivery mechanism. Graph information was also introduced into the attention mechanism through graph encoding and average first-pass time. Attached Figure Description

[0085] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0086] Figure 2 This is a schematic diagram of the model framework of the present invention. Detailed Implementation

[0087] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0088] Define historical traffic data and traffic flow prediction:

[0089] Definition 1: Historical traffic data. For a given... ,in It represents a time slice. The first in the time road network Traffic flow values ​​recorded by individual sensors. Furthermore, time slices can be... The historical traffic flow values ​​recorded by all sensors on the time-road network are represented as follows: ,in Indicates the number of sensors.

[0090] Definition 2: Traffic Flow Prediction. Given all sensor data in historical data... Historical traffic data recorded in each time slice Traffic flow prediction tasks use functions pass Predicting all sensors in the future Traffic data at a time slice It corresponds to the real future. Real traffic data at a specific time frame The process of traffic flow prediction can be represented as:

[0091]

[0092] This invention proposes a traffic flow prediction method based on adaptive decomposition and attention mechanism. The main process of the method is as follows: Figure 1 As shown, the specific implementation process is as follows:

[0093] S1. Collect historical traffic data over a period of time using traffic sensors within the area to obtain the raw input data for the model.

[0094] S2. The time series information is decomposed into intrinsic and diffuse terms using an adaptive decomposition module, and spatiotemporal information is introduced into the two terms obtained by the decomposition through a data embedding layer; then the intrinsic and diffuse terms are merged through an adaptive fusion module to obtain the reconstructed sequence.

[0095] S3. Construct an intrinsic item processing branch and input the intrinsic items into the processing branch, focusing on capturing traffic patterns determined by the node's own attributes.

[0096] S4. Construct a diffusion term processing branch and input the diffusion term into this processing branch, focusing on capturing dynamic information propagating in the road network space during traffic.

[0097] S5. Adaptively fuse the obtained intrinsic and diffusion terms to obtain the final result. Calculate the weighted loss of each part of the model and train the model.

[0098] Specifically, step S2 includes:

[0099] The adaptive decomposition module of this invention decouples traffic flow time series data, decomposing the complex time series into intrinsic terms and diffusion terms.

[0100] S2.1 Decompose different sequence patterns using one-dimensional convolution;

[0101] Adaptive decomposition uses one-dimensional convolution to adaptively extract intrinsic and diffuse terms. Taking the intrinsic term as an example, for a single node's time series, the input is represented as... , No. Each convolutional kernel is represented as For the first Each convolutional kernel at time position Output:

[0102]

[0103] in It is the convolution stride. It's convolutional padding. For the first Bias terms for each convolution kernel.

[0104] The total output of multiple time slices after convolution is:

[0105]

[0106] Finally, the sequence of intrinsic terms obtained by decomposing a single node is:

[0107]

[0108] in , It is a weight matrix. , This is the bias term. The decomposition sequence of the diffusion term is similar.

[0109] S2.2 Spatiotemporal characteristics of embedded nodes;

[0110] To better incorporate spatiotemporal information into the model and thus improve the accuracy and robustness of traffic flow prediction, the model uses a data embedding layer to embed the time information of the prediction moment (the day of the week and the specific time of day) and node features. This embedding is based on... This is represented by the terms, which are then concatenated with the two terms obtained from the decomposition to obtain the final intrinsic and diffusion terms:

[0111]

[0112]

[0113] Subsequently, to improve the robustness of the fusion module, we used adaptive fusion to reconstruct the original input. This process is crucial for data... and By applying an attention mechanism, an adaptive preliminary fusion result is first obtained, and then combined with... The results are added together and then passed through a fully connected layer to obtain the final fused result:

[0114]

[0115] in, These are learnable parameters. It will be used to calculate the reconstruction loss.

[0116] Further, step S3 includes:

[0117] S3.1 Initially extracts temporal information through temporal convolution;

[0118] Because the data being processed is time-series information, which inherently possesses temporal characteristics—meaning that information at any given moment should not contain information from future times—temporal convolution processes the data by stacking multiple convolutional layers with dilated causal convolutions. In this convolutional structure, the output at each time step depends only on past inputs and does not introduce information from future moments, ensuring that causality is preserved. For the... Layer convolution, dilation rate The convolution formula is as follows:

[0119]

[0120] in It is the kernel size. It is a time step. It is the first Layer convolution kernel in the th The weight matrix of each offset, As a bias term, causality is determined by... ensure.

[0121] S3.2 Time Attention Module Extracts Time Information:

[0122] For the input of this module , will the The time slice of each sensor is represented as .

[0123] To effectively model the relationships between time slices within a node, this method applies a self-attention mechanism in the time dimension. Specifically, the self-attention mechanism is first used to calculate the... The temporal dependencies between all time slices in each sensor are then modeled using attention weights to aggregate information from different time slices, thus establishing long-term temporal dependencies among all time slices. Finally, the temporal attention module's relationship with the first sensor is obtained. The output of each sensor :

[0124]

[0125] in, These are learnable parameters.

[0126] The S3.3 Trend Category Learning Module integrates trend category information;

[0127] To better extract the inherent trend information of nodes in the intrinsic components, this invention designs a trend category learning module. This module adaptively learns the trend features of each node, effectively capturing the trend change patterns of different nodes.

[0128] For input Obtain category attention score

[0129]

[0130] in, , These are learnable parameters. It represents the number of trend categories.

[0131] Using attention weights We perform a weighted summation of the categorical data to obtain an output that incorporates categorical information. :

[0132]

[0133] in, These are learnable parameters, This is the final output of step S3.

[0134] Furthermore, step S4 includes:

[0135] S4.1 Initially extracts temporal information through temporal convolution;

[0136] The operations involved here are the same as in step S3.1, except for the input.

[0137] The S4.2 multi-time-slice spatial attention gating module extracts spatial information;

[0138] For the input of this module To incorporate graph structure information, the first part of the Laplacian characteristic matrix of the graph is taken. From the feature vectors, we obtain the graph embedding representation. Combine it with the original input:

[0139]

[0140] in, These are learnable parameters.

[0141] The data after incorporating graph structure information The data from all sensors during the time slice are represented as follows: .

[0142] Given data Applying a self-attention mechanism in the spatial dimension, the first step is to compute the time slice... The model identifies the dependencies between all sensors and captures their spatial correlations through a self-attention mechanism. Then, the average first-pass time is introduced as a mask matrix for the attention score, thereby incorporating road network information into the model.

[0143] Let the state be to state The average transit time is Its recursive definition is:

[0144]

[0145] For each target node The average first-pass time from this node to all other nodes can be calculated using the following formula:

[0146]

[0147] in It is the state transition probability matrix. After calculating the average first-pass time to other nodes for each node, the mask matrix is ​​obtained. The final attention score between nodes is:

[0148]

[0149] Next, the spatial dependencies between these sensors are aggregated to capture their mutual influence. Finally, the spatial attention module obtains information about... Output of sensor internal relationship under time slice :

[0150]

[0151] in, These are learnable parameters.

[0152] Then we will enter The first time step was copied to obtain Then remove the input. The last time slice was obtained Finally in front The time-slice delay input can be obtained by concatenating the two parts.

[0153] Will The key and value matrices, which serve as the attention mechanism, are used to obtain the time slices in the same way. Lower sensor and time slice Spatial dependency of sensors in

[0154] Then and The gating weights are obtained by splicing and passing through a fully connected layer. And separate the weights to obtain and Finally, perform a weighted summation:

[0155]

[0156] by This is the final output of step S4.

[0157] Furthermore, step S5 includes:

[0158] The main purpose of this step is to process the results obtained in step S3. The result obtained in step S4 Perform adaptive fusion and calculate various types of losses.

[0159] For data and Following the adaptive fusion method in step S2, the final prediction result is obtained by fusion. The loss during model training includes... , , , Four items. Among them By calculating the predicted value Compared with the true value The mean absolute error is obtained; By calculating the reconstructed value With the original input The mean absolute error is obtained. For the intrinsic terms obtained after adaptive decomposition The first-order difference is used to constrain its smoothness, and its calculation formula is as follows:

[0160]

[0161] For the diffusion term obtained after adaptive decomposition The sparsity loss is used to constrain its sparsity, and its calculation formula is as follows:

[0162]

[0163] The final loss for model optimization is:

[0164]

[0165] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A traffic flow prediction method based on adaptive decomposition and attention mechanism, characterized in that, Includes the following steps: S1. Collect historical traffic data over a period of time using traffic sensors within the area to obtain the raw input data for the model; S2. Use the adaptive decomposition module to decompose the time series information into intrinsic terms and diffusion terms, and introduce spatiotemporal information into the two terms obtained by the decomposition through the data embedding layer; then use the adaptive fusion module to merge the intrinsic terms and diffusion terms to obtain the reconstructed sequence; S3. Construct an intrinsic term processing branch and input the intrinsic terms into the processing branch, focusing on capturing the traffic patterns determined by the node's own attributes; S4. Construct a diffusion term processing branch and input the diffusion term into this processing branch to focus on capturing dynamic information propagating in the road network space during traffic. S5. Adaptively fuse the obtained intrinsic and diffusion terms to obtain the final result; calculate the weighted loss of each part of the model and train the model.

2. The traffic flow prediction method based on adaptive decomposition and attention mechanism according to claim 1, characterized in that, Step S2 includes: S2.

1. Adaptive decomposition: Two independent adaptive decomposition modules are used to extract features from the original sequence. Each module performs one-dimensional convolution and fully connected transformation operations in sequence to decouple the intrinsic term and the diffusion term. S2.

2. Spatiotemporal Information Embedding: Through the data embedding layer, the temporal information and node features of the prediction time are embedded and represented, and then concatenated with the intrinsic and diffusion terms obtained from the decomposition. S2.

3. Sequence Reconstruction: Through the adaptive fusion module, the attention mechanism is applied to initially fuse the spliced ​​intrinsic terms and diffusion terms, and the fusion result is added to the intrinsic terms and then adjusted through a fully connected layer to obtain the reconstructed sequence.

3. The traffic flow prediction method based on adaptive decomposition and attention mechanism according to claim 1, characterized in that, Step S3 includes: S3.

1. Temporal Convolution: The temporal information of the intrinsic terms is initially extracted through a temporal convolution module containing multiple layers of dilated causal convolution to ensure the causality of information processing; S3.

2. Temporal Attention: Using the temporal attention module, a self-attention mechanism is applied in the time dimension to model the long-term dependencies between time slices; S3.

3. Trend Category Learning: Through the trend category learning module, trend category information is integrated to generate a category attention score, and the trend categories are weighted and summed using this score to output an inherent term that integrates category information.

4. The traffic flow prediction method based on adaptive decomposition and attention mechanism according to claim 1, characterized in that, Step S4 includes: S4.

1. Temporal Convolution: Temporal information of the diffusion term is initially extracted through a temporal convolution module containing multiple dilated causal convolutions to ensure the causality of information processing; S4.

2. Spatial Attention and Delay Propagation: Spatial information is extracted through a multi-time-slice spatial attention gating module, specifically: a) Introducing graph embedding representation to combine graph structure information; b) Applying a self-attention mechanism in the spatial dimension and introducing a mask matrix based on the average first-pass time to capture the spatial dependencies between sensors; c) Calculating the spatial dependencies between the current time slice and the previous time slice sensors through a delay propagation mechanism; d) Fusing the current spatial information and delayed spatial information through a gating mechanism to obtain the final output of the diffusion term.

5. The traffic flow prediction method based on adaptive decomposition and attention mechanism according to claim 1, characterized in that, The weighted loss in step S5 includes: a) prediction loss: calculating the mean absolute error between the final prediction result and the true value; b) reconstruction loss: calculating the mean absolute error between the reconstructed sequence and the original input data; c) smoothing loss: applying first-order difference constraints to the intrinsic terms to promote their smoothness; d) sparsity loss: applying sparsity constraints to the diffusion terms to promote their sparsity; the total loss of the model is the weighted sum of the above losses.