LSTM (Long Short Term Memory) and GNN (Global Navigation Network) fused air-railway combined transportation network passenger flow prediction method

Abstract

The invention provides an air-railway combined transportation network passenger flow prediction method fusing LSTM and GNN. The method comprises the steps that firstly, a graph model of a user travel scheme interaction data set is established through a user portrait data set and a travel scheme record data set; then constructing a weight matrix as the input of the traffic prediction model; and predicting the future traffic of the air-railway combined transportation travel scheme by adopting a traffic prediction model based on a long-short-term memory network and a graph neural network. According to the method, the long-term dependency relationship in the time sequence data is captured by using the LSTM, and the graph structure between the travel schemes is constructed in combination with the GNN to process the spatial relationship data, so that the complex characteristics of the traffic change of the travel schemes can be captured more comprehensively. Simulation results show that the proposed method is superior to a single LSTM, GNN or SFM or other benchmark methods in indexes such as MSE, MAE, RMSE and MAPE.

Description

Technical Field

[0001] The present invention is an application technology of computer technology in transportation network, specifically a method for predicting passenger flow in air-rail transport network by integrating LSTM and GNN. Background Art

[0002] As a core component of the urban transportation system, the operational efficiency and service quality of the air-rail transport network system have a direct impact on passengers' travel choices and satisfaction. However, due to the complex time dependence and spatial correlation within the system, and the fact that passenger flow is profoundly affected by seasonal activities, holiday effects, and even emergencies, accurately predicting passenger flow has become an extremely challenging task [1]. The nodes of the air-rail transport network system not only cover geographical spatial locations, but also involve the connection and conversion between different transportation modes, which makes the system present an intricate network structure [2]. The complexity of this network structure requires the prediction model to have a deep understanding of the intrinsic connection between time dynamics and spatial structure in order to provide more accurate and reliable passenger flow predictions.

[0003] In a complex decision-making environment, accurately predicting passenger flow changes is of great significance for optimizing resource allocation, improving service quality, and reducing passenger waiting time. Traditional prediction methods mostly rely on linear models, which are often insufficient when dealing with complex spatiotemporal dependencies. With the rapid development of deep learning and neural networks, researchers have new tools to deal with such complex dependencies. However, traditional prediction methods, such as autoregressive models[3] and seasonal decomposition models[4], show obvious limitations when dealing with complex air-rail transport systems. These methods are difficult to effectively capture the inherent nonlinear characteristics and long-term time series dependencies in passenger flow data, and ignore the spatial relationship between nodes within the system, which restricts the accuracy and generalization ability of the prediction results. This limitation is particularly prominent when dealing with passenger flow fluctuations caused by holidays and special events.

[0004] Although GNN and LSTM have shown excellent performance in their respective fields, they have limitations in processing such data with complex graph structures and time series [5][6]. GNN usually uses a message passing mechanism to update the representation of nodes, but there is a certain distance limit when transmitting information, that is, it can only be directly transmitted to adjacent nodes. This limitation may cause the model to perform poorly when processing node data with long-distance dependencies or data with complex spatial structures but lacking clear graph structures. LSTM may have difficulties in modeling long-term dependencies when processing long sequence data. Although LSTM has designed a gating mechanism to solve the problem of gradient vanishing or gradient exploding, there may still be information loss or memory overflow in long sequences, affecting the accuracy of the model. This limits their application in passenger flow prediction of air-rail intermodal networks. In addition, these highly complex models are often regarded as "black boxes" and their decision-making process lacks transparency, which to some extent restricts their practical application. Summary of the invention

[0005] As people's requirements for travel efficiency and comfort are increasing, air-rail transport, as an efficient, fast and environmentally friendly mode of transportation, has attracted widespread attention due to its unique advantages. However, air-rail transport still faces challenges in accurately predicting the future traffic demand of itinerary plans. To this end, the present invention proposes a traffic prediction method based on long short-term memory network (LSTM) and graph neural network (GNN) - LSTM-GNN hybrid model to solve this problem.

[0006] This method uses LSTM to capture long-term dependencies in time series data, and combines GNN to construct a graph structure between itinerary plans to process spatial relationship data, which can more comprehensively capture the complex characteristics of itinerary plan traffic changes.

[0007] Simulation results show that the proposed method is superior to benchmark methods such as single LSTM, GNN or SFM in terms of MSE, MAE, RMSE and MAPE. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 A graphical model to represent user-trip plans;

[0009] Figure 2 Represents the importance ranking of features in the dataset;

[0010] Figure 3 Represents the LSTM-GNN model architecture;

[0011] Figure 4It shows the comparison of evaluation indicators of four models: LSTM-GNN, GNN, LSTM and SFM;

[0012] Figure 5 Comparison of training loss values ​​of four models: LSTM-GNN, GNN, LSTM, and SFM;

[0013] Figure 6 Comparison of test loss values ​​of four models: LSTM-GNN, GNN, LSTM, and SFM;

[0014] Figure 7(a) to Figure 7(d) They respectively represent the prediction results of the hybrid model LSTM-GNN, the single graph neural network model GNN, the single long short-term memory network model LSTM, and the static feature model SFM. DETAILED DESCRIPTION

[0015] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0016] 1. Overview

[0017] In view of the problems in the prior art, the present invention proposes a hybrid model combining LSTM and GNN, namely LSTM-GNN, to predict the passenger flow of air-rail transport (trip plan). The LSTM-GNN model can effectively capture long-term time series dependencies and predict future passenger flow trends through the LSTM component; while the GNN component uses its advantage in processing graph structure data to analyze the complex relationships between nodes in the air-rail transport network.

[0018] This method not only makes up for the shortcomings of traditional models in temporal and spatial analysis, but also overcomes the limitations faced when using GNN or LSTM alone. It aims to simultaneously capture the temporal dependence and spatial structural characteristics of passenger flow changes in the air-rail intermodal network system.

[0019] The main contributions of the present invention include:

[0020] (1) By integrating LSTM and GNN, an innovative LSTM-GNN hybrid model is proposed for traffic flow prediction of air-rail intermodal itinerary schemes. This effectively combines the advantages of both (LSTM and GNN) in time series and graph structure data analysis to provide a new solution for passenger flow prediction of complex air-rail intermodal itinerary schemes.

[0021] (2) The LSTM-GNN model is trained using a dataset that integrates user profiles and air-rail intermodal itinerary data. The dataset is converted into a weight matrix through data preprocessing to further improve the robustness and prediction accuracy of the model.

[0022] (3) Introducing regularization techniques such as Batch Normalization[7] and model structure adjustment methods for hyperparameter optimization. These methods help reduce the model’s reliance on a single data feature and promote faster model convergence, thereby further improving the model’s accuracy and generalization ability.

[0023] 2. Related Work in the Prior Art

[0024] In recent years, domestic and foreign scholars have conducted extensive and in-depth research in the fields of network node feature analysis, traffic flow prediction, and recommendation algorithms. In terms of data prediction, some innovative methods based on hybrid models such as LSTM and GNN have been proposed, providing new solutions and technical means to solve the shortcomings of traditional models in processing complex network data, improving prediction accuracy, and realizing personalized recommendations. Reference [8] proposed a method based on LSTM to build a model for predicting the market value of the stock market. The prediction accuracy of the model was evaluated by machine learning algorithms, and the prediction model was improved. Reference [9] proposed a demand prediction method based on a multi-layer LSTM network. Through the grid search method, the best combination of LSTM hyperparameters in a given time series is automatically selected to construct the optimal prediction model. This method can capture nonlinear patterns in time series data and fully consider the inherent characteristics of non-stationary time series data, thereby improving the accuracy and reliability of prediction.

[0025] When processing complex networks, the GNN algorithm can accurately capture the dependencies and behavior patterns between different nodes, demonstrating its powerful processing capabilities. The GPT-GNN hybrid model proposed in the literature

[10] uses generative pre-training to initialize the GNN and introduces a self-supervised attribution graph generation task, enabling the GNN to more comprehensively capture the structure and semantic properties of the graph, providing a new perspective for the processing and analysis of graph data.

[0026] Unlike traditional data prediction tasks, air-rail intermodal trip data involves different individuals, including users, airplanes, and trains. These individuals also contain different types of data structures. It is difficult for a single network model to take into account the different characteristics of the data when processing such complex data structures. Hybrid models can better process such data by relying on the respective advantages of different components. Reference

[11] combines GNN and LSTM to propose a graph long short-term memory (GLSTM) model. This model constructs an unweighted directed graph of the road network and trains it based on the encoder-decoder architecture and message passing mechanism of GNN to effectively capture the spatial and temporal dependencies in the traffic network and improve the accuracy of prediction. Reference

[12] further models the spatial dependency of traffic as a diffusion process on a directed graph and proposes a diffusion convolutional recurrent neural network (DCRNN). This network can simultaneously capture the spatial and temporal dependencies between time series, providing a powerful tool for traffic flow prediction and analysis. The LSTM-GNN hybrid model proposed in reference

[13] connects similar patients and uses diagnosis as relationship information. It combines LSTM and GNN to extract time features and patient neighborhood information respectively, effectively predicts the patient's prognosis, and provides important reference for medical decision-making. Reference

[14] proposed a hybrid model method combining GCN and LSTM, which is specifically used for sentiment classification of comments published in different fields. The CNN model is used for deep learning to automatically extract social big data features; LSTM is used to capture the long-term relationship between words in a sentence. In the field of traffic flow prediction, reference

[15] models the traffic network as a graph and proposes a new deep learning framework - Traffic Graph Convolutional Long Short-Term Memory Neural Network (TGC-LSTM). This framework learns the interaction between roads in the traffic network and predicts the traffic conditions of the entire network, and defines the flow graph convolution based on the physical network topology, thereby improving the framework's ability to predict the flow of specific road sections.

[0027] 3. Data Preprocessing

[0028] 3.1 Graph Model Construction

[0029] In the preparation work for building the graph input for LSTM-GNN model training, the user portrait dataset and the user's itinerary plan historical purchase behavior dataset are involved. Information is extracted and integrated from these two datasets to build a static data containing binary features of user portraits and a time series that can reflect the long and short-term memory between nodes in the graph model.

[0030] The user portrait dataset contains basic information about users, including age, gender, occupation, historical purchase records, and social network information. Features are extracted from this dataset to measure their position and influence in the social network and evaluate the importance of features to ensure that the subsequent LSTM-GNN model does not rely too much on a single feature.

[0031] The itinerary record dataset provides detailed information about the itinerary, including the stops involved in the itinerary, the time spent, the monetary cost, and the itinerary ID. From this dataset, not only the specific information of each itinerary is extracted, but also which itineraries share the same stops. This is used to comprehensively consider the static characteristics of the itinerary itself and the impact of the time series on the prediction results in the entire LSTM-GNN model training.

[0032] By fusing the features extracted from the two datasets, a user itinerary interaction dataset is constructed. In this process, the user ID is used as the connection key to fuse the user's personal characteristics and itinerary selection behavior characteristics. This makes each user's behavior no longer an isolated record, but a complete portrait combined with their personal characteristics and social relationships. Such fusion not only increases the data dimension, but also provides a theoretical basis for understanding how users choose corresponding itineraries based on their own characteristics. In the user itinerary interaction dataset, each row represents a unique instance of user purchase behavior. Figure 1 The graphical model of the user-trip plan is used as the graph data input of the LSTM-GNN model in the present invention.

[0033] After integrating the features of the dataset, we build a dataset graph model. We divide the node types and edge attributes according to the characteristics of the heterogeneous network and analyze and design the overall architecture of the network model. The main steps are summarized as follows.

[0034] (1) Define nodes: In the upper layer of heterogeneous networks, each user is defined as a node. The lower layer consists of nodes composed of detailed information of itinerary plans, and each node represents a itinerary plan.

[0035] (2) Edge construction: The edges between the upper-level nodes represent the social relationships and similar purchasing behaviors between users. The edges between the lower-level nodes represent the shared station information between itineraries. The edges between the two layers are determined by the user's purchasing behavior and time point for the itinerary.

[0036] (3) Integrate features: For each node, integrate relevant features from the dataset, including the user’s social network characteristics, the cost and time of the travel plan, etc.

[0037] (4) Model construction: Using the defined nodes and edges, GNN is used to capture the complex relationships between nodes, and LSTM is used to process time series data.

[0038] 3.2 Weight Matrix Construction

[0039] In order to ensure the consistency and completeness of the fused dataset, data cleaning and feature extraction steps are also required to construct a weight matrix that can be used as input for the LSTM-GNN model.

[0040] In the data cleaning stage, outlier detection and missing value processing algorithms are used to ensure the quality of the data set. This section uses the IQR (interquartile range) method, an outlier detection technique based on statistical methods, to identify and remove points that do not conform to the normal distribution of the data set. For missing values, interpolation methods and / or prediction methods based on neural network models are used to fill them according to the characteristics of the data to maintain data integrity.

[0041] In the feature extraction phase, by analyzing the correlation between user behavior and itinerary information, multi-dimensional feature engineering techniques

[16] (such as one-hot encoding, normalization, and PCA (principal component analysis) methods, etc.) are used to extract the features that have the greatest impact on the prediction model. In this example, the features of the data set are ranked by importance based on the random forest model, and the average contribution of each feature to reducing impurity in the decision tree node splitting is calculated. The feature importance ranking in the data set is as follows: Figure 2 shown.

[0042] The adjacency matrix is ​​established through the above data preprocessing and feature extraction methods. The social relationships between users and the choice of itinerary options are converted into a graph structure, and the weight of the edge in the graph structure reflects the strength of the connection between users. This conversion process uses the basic graph construction method and introduces the technology of social network analysis (including community detection and network centrality analysis) to further explore the potential connection between node features, and converts the processed fusion data set into a weight matrix as the final input of the LSTM-GNN model to ensure that it is suitable for advanced model training. This process is divided into the following key steps:

[0043] (1) Feature normalization: All numerical features are processed using the Z-score normalization method to eliminate the impact of dimension and accelerate the convergence of the model. For categorical features, one-hot encoding is used to convert them into numerical data for easy model processing.

[0044] (2) Time series processing: For time series data, a sliding window mechanism is used to construct learning samples, which is particularly critical for capturing the dynamic changes of time series. Through this method, the model can learn the time dependency from the past to the future.

[0045] (3) Graph data preprocessing: When processing graph data, an adjacency matrix is ​​used to represent the graph structure, where the nodes of the graph represent users and itinerary plans, and the edges represent interactions between users or sharing of itinerary plans. Graph embedding technology is used to convert graph data into a vector form that is easy for machine learning models to process.

[0046] (4) Dataset division: The dataset is divided into training set, validation set and test set according to the structure of 70%, 15%, and 15% to support model training, parameter adjustment and performance evaluation. Stratified sampling is used to ensure that the proportion of each category of data in each dataset is consistent to avoid training bias.

[0047] 4. LSTM-GNN model construction

[0048] After constructing the graph model as input data, the itinerary prediction problem is abstracted into a node prediction task. The main variables and symbol definitions used to quantify the feature relationship between nodes in this process are shown in Table 1.

[0049] Table 1 Main variables and symbol definitions

[0050]

[0051] 4.1 Model design

[0052] This section uses the LSTM-GNN hybrid model to analyze the node prediction task. The model construction process is as follows Figure 3 shown.

[0053] In the graph structure constructed by the weight matrix, each node i has a time series and static features (Including other variables of static features, such as age, etc.). The weight matrix with static features and temporal attribute features is passed as input to the LSTM-GNN model for end-to-end training. The LSTM-GNN produces three types of embeddings: LSTM, GNN, and static embeddings, which are connected and passed to the fully connected layer to obtain the prediction of each node.

[0054] exist Figure 3 In the model architecture, a similarity score is first assigned between user nodes, and the user static features are converted into the user's multi-hot vector to obtain the feature matrix D∈R N×m, where m is the number of static features, N is the number of users, and the similarity score M between nodes i and j is i,j Defined as

[0055]

[0056] d μ is the occurrence of the binary static feature μ, a and c are adjustable constants. In the “shared feature” part of formula (4-1), It means that it is more important for two users to share a rare static feature than a common static feature. The "all features" part indicates the total number of penalized features to prevent some user nodes from becoming highly connected "hubs" in the network graph, which leads to incorrect matching with other non-shared features. This section examines the dynamic changes of M under the k-nearest neighbor (k-NN) scheme to establish k edges for each node, where parameters a, c, and k are used as hyperparameters. In the final model, c = 0.001, a = 5, and k = 3.

[0057] In the LSTM-GNN hybrid model, the LSTM network uses its powerful time series data processing capabilities to capture the dynamic characteristics of the flow changes in the itinerary plan. Through its unique gating mechanism, it can effectively solve the long-term dependency problem, which is particularly critical when predicting the passenger flow of future itineraries

[17] . i,t First, it passes through a bidirectional LSTM, which outputs a hidden state vector sequence h in both the forward and reverse directions. i,(T) The vectors corresponding to the last time step are concatenated to produce h i,T , which is a time embedding for each node. In the gating mechanism of the LSTM component, the forget gate is responsible for deciding which information should be forgotten or retained from the cell state. It operates on the hidden state of the previous time step and the current input, and outputs a value between 0 and 1, where 0 means complete forgetfulness and 1 means complete retention. This mechanism helps the network remember important information while ignoring irrelevant information. The forget gate formula is expressed as

[0058] f t =σ(W f ·[h t-1 ,x i,t ]+b f ) (4-2)

[0059] In formula (4-2), f t represents the output of the forget gate, σ is the sigmoid function, W f is the weight matrix of the forget gate, h t-1 is the hidden state of the previous time step, x i,tis the input of the current time step, b f is the bias term of the forget gate.

[0060] The input gate determines the new information added to the cell state. It consists of an "input gate layer" and a "candidate value layer". The input gate layer determines which information will be retained, while the candidate value layer generates a candidate value vector by processing the current input and the previous hidden state. The vector contains new information that may be added to the cell state. The result of the input gate is x t =σ(W i ·[h t-1 ,x i,t ]+b x ) (4-3)

[0061]

[0062] The input gate determines what new information is added to the cell state. is a candidate value for new information, generated by the tanh activation function.

[0063] The cell state is the core storage unit of LSTM. It updates the current cell state by linearly combining the cell state and candidate value at the previous moment, combined with the information of the forget gate and input gate. This mechanism enables LSTM to maintain memory of long-term information when processing sequence data. The cell state is updated to

[0064]

[0065] Unit Status C t is the state of the previous unit C t-1 After forgetting part of the state through the forget gate, add the current candidate unit state The information obtained by input gate control.

[0066] The output gate determines the amount of information from the cell state. It determines which information will be used as the output h of the current LSTM cell based on the filtered cell state. i,t , which in turn affects the subsequent units and the final network output. The output gate formula is expressed as

[0067] o t =σ(W o ·[h t-1 ,x i,t ]+b o ) (4-6)

[0068] h i,t =o t *tanh(C t )(4-7)o t is the activation value of the output gate.

[0069] In these formulas, W and b represent the weight matrix and bias term, and * represents element-by-element multiplication. The sigmoid function is used to compress the input to between 0 and 1, helping the model determine the amount of information to be transmitted. The tanh function compresses the input to between -1 and 1, helping to adjust the strength of the information flow so that the network can process signals of different strengths.

[0070] After the LSTM component processes the time series in the graph input data center, the GNN component follows to process the complex interactions between users. GNN can use the information of nodes (users) and edges (interactions between users or shared relationships of itinerary plans) in the graph structure to learn a high-dimensional representation of each node through a neighbor aggregation mechanism. This representation not only captures the characteristics of individual users, but also integrates the structural information in the user's social network to provide rich contextual information for model prediction. The GNN component propagates the time embedding of each node within its neighborhood. Specifically, this is done by embedding the time embedding h of each node i,T This is achieved by locally smoothing the feature vectors of its neighboring nodes, that is, h i,T Re-weight the feature vectors in its local neighborhood to generate a new node representation h i,N This step is part of the core workflow of the GNN module, which allows the model to capture and fuse complex interactions between nodes through a graph structure. At the same time, the present invention passes the static input x through a fully connected layer i,S , calculate h i,S , and then concatenate the previously learned representations together so that

[0071] h i =(h i,T ||h i,N ||h i,S ) (4-8)

[0072] Finally, h i Pass through a fully connected layer to get the prediction

[0073] In the parameter transfer process of the entire architecture described above, LSTM-GNN is trained in an end-to-end and scalable manner. By adopting the neighborhood sampling method proposed by Shi X et al.

[18] , small batch training of LSTM is achieved. That is, at each iteration, a set of fixed-size sets is uniformly sampled in the graph input. This fixes the computational and time costs after iterations and makes LSTM-GNN scalable to the entire user-trip heterogeneous graph (i.e., the graph model).

[0074] During training, only nodes and their neighborhoods in the training set are sampled. During testing, neighbors are sampled from the entire dataset, but only the performance of the test nodes is evaluated. The introduction of the GNN component leads to a decrease in the performance of the LSTM component, so in order to promote the learning efficiency of the two components, the loss function is defined as

[0075] L=L LSTM-GNN +αL LSTM (4-9)

[0076] Among them, L LSTM-GNN is the full model prediction The loss, L LSTM is composed of LSTM components (By making h T The loss of prediction is calculated by passing through different fully connected layers), and α is a hyperparameter.

[0077] 4.2 Fitting Process

[0078] When developing and deploying LSTM-GNN models, it is important to ensure that the model performs well on hidden data while also considering the model's generalization ability. This section uses some strategies to optimize model performance in response to the problems of overfitting and underfitting

[19] . Overfitting and underfitting describe situations where the model overfits to the training data and underfits to the training data, respectively, both of which impair the model's performance on new data. In order to balance the performance of the model on the training set and the test set, this section uses the following methods:

[0079] Data enhancement: In order to increase the complexity of model training, the study implemented time offset, scaling, and adding random noise to the time series data to increase the model's ability to recognize different time patterns. By randomly deleting or adding edges to simulate different network connection scenarios, the model's adaptability to changes in graph structure is improved.

[0080] Early stopping: During model training, the performance of the model is monitored on an independent validation set. Once the performance of the model on the validation set begins to decline (i.e., signs of overfitting appear), training is stopped. This strategy effectively avoids overfitting of the model to the training data.

[0081] Cross-validation: K-fold cross-validation is used to ensure that the model has good generalization ability. By dividing the dataset into K subsets and taking turns to use one of the subsets as the validation set and the other datasets as the training set, the performance of the model can be evaluated from multiple aspects, thus avoiding overfitting and underfitting.

[0082] 4.3 Regularization and Model Structure Adjustment

[0083] In order to further improve the generalization ability of the model, regularization techniques and model structure adjustment methods are used in the process of model training to improve the generalization of the model and reduce the risk of overfitting during training. This section adopts some regularization techniques

[20] and model structure adjustment measures

[21] .

[0084] (1) Regularization technique:

[0085] L1 / L2 regularization: By adding the L1 or L2 norm of the weight as a regularization term in the loss function, the size of the model weight is limited to prevent the model weight from being too large and causing overfitting.

[0086] Dropout: During the training process, a certain proportion of neurons are randomly discarded, forcing the model to learn the characteristics of the data through the remaining neurons, reducing the model's dependence on a single data feature and increasing the model's generalization ability.

[0087] Batch Normalization: By standardizing each small batch of data, the covariate shift between input layers is reduced, which helps the model converge faster and also has a certain regularization effect.

[0088] (2) Model structure adjustment method:

[0089] Model simplification: For overly complex model structures, simplify the model by reducing the number of layers or parameters to avoid overfitting. At the same time, this also makes the model easier to train and debug.

[0090] Hyperparameter optimization: By systematically exploring the hyperparameter space (such as learning rate, number of hidden layer units, etc.), using methods such as grid search and Bayesian optimization to find the optimal model configuration, ensuring that the model can achieve the best performance on different datasets.

[0091] Introduction of attention mechanism: The introduction of attention mechanism in GNN components enables the model to automatically learn the importance priority of nodes and edges in the graph according to the requirements of the task, improve the prediction accuracy of the model, and increase the interpretability of the model.

[0092] Through the implementation of these strategies, not only can the performance of the LSTM-GNN model in air-rail intermodal schedule flow prediction be significantly improved, but it can also ensure that the model has good generalization ability and stability, laying the foundation for the subsequent application and research of the model.

[0093] 4.4 Model Tuning

[0094] Table 2 LSTM-GNN model hyperparameter settings

[0095]

[0096] Table 2 shows the hyperparameter definition and setting details of the LSTM-GNN model. Before training the LSTM-GNN hybrid model, hyperparameter search techniques (grid search and random search) are used to systematically explore and evaluate the performance of the model under different hyperparameter combinations to find the optimal model configuration. Cross-validation techniques are also introduced to evaluate the robustness of the model on different data subsets, which helps to more accurately estimate the generalization ability of the model during the research process. In addition, considering the complexity and time cost of model training, this section also uses the Bayesian optimization method to search the hyperparameter space. This method is based on the principle of Bayesian reasoning and can find parameter combinations close to the optimal solution in a smaller number of iterations.

[0097] During model training, gradient clipping is used to prevent gradient explosion

[22] , and the Adam optimizer (Adaptive Moment Estimation) is used to adjust the learning rate

[23] to ensure the stability and efficiency of the model during training.

[0098] 5. Simulation Experiment

[0099] 5.1 Selection of evaluation indicators

[0100] In order to comprehensively evaluate the prediction performance of the LSTM-GNN model and analyze the differences between this model and other comparison models, this section uses the following evaluation indicators:

[0101] Mean Squared Error (MSE): It calculates the average of the squares of the difference between the predicted value and the true value, and is a common indicator for evaluating the prediction accuracy of the model. The smaller the value of MSE, the higher the prediction accuracy of the model.

[0102] Mean Absolute Error (MAE): This metric measures the average level of the absolute value of the difference between the predicted value and the actual value. Compared with MSE, MAE is less sensitive to outliers and can provide an intuitive understanding of the size of the prediction error.

[0103] Root Mean Squared Error (RMSE): It is the square root of MSE and is also used to measure the difference between the predicted value and the actual value. Since RMSE brings the error measure to the scale of the original data, it is particularly suitable for comparing and evaluating the prediction performance of different models or experiments.

[0104] Mean Absolute Percentage Error (MAPE): MAPE measures the average level of the percentage difference between the predicted value and the actual value. MAPE is a commonly used evaluation metric, especially for scenarios where you need to understand the percentage of the predicted error relative to the actual value.

[0105] These indicators were selected based on their wide application in statistics and machine learning, and can provide a comprehensive and objective evaluation of model performance. Through the comprehensive analysis of these indicators, we can deeply understand the performance of the model in the task of air-rail intermodal schedule flow prediction in the performance comparison stage, and optimize the model structure and parameter settings accordingly to improve the prediction accuracy.

[0106] 5.2 Performance Comparison Analysis

[0107] In this study, the traffic of the air-rail intermodal itinerary scheme is predicted by combining a hybrid model of LSTM and GNN. The experimental results show that the model exhibits significant prediction ability in prediction tasks of different time steps. Through a comprehensive analysis of evaluation indicators such as mean square error (MSE), mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE), this study obtained more accurate and reliable performance evaluation results. In subsequent research work, based on the current research results, the optimization potential of the model will be further explored, including adjusting the structure and parameters of the model and adopting more complex data preprocessing techniques to improve the accuracy of prediction.

[0108] In addition, this study also compares the performance of the LSTM-GNN hybrid model with traditional time series prediction models and other graph neural network models, aiming to evaluate the competitiveness and application value of the LSTM-GNN model in the field of air-rail intermodal schedule flow prediction from a broader perspective. This comparative analysis is based on the same data set to ensure the fairness and consistency of the evaluation results. The following are four different models used in the comparative analysis:

[0109] (1) LSTM-GNN hybrid model: The full structure of the LSTM-GNN model is used for prediction as a performance baseline.

[0110] (2) Single graph neural network model: Remove the LSTM component in the hybrid model and rely only on the GNN component to process graph structure data for prediction.

[0111] (3) Single long short-term memory network model: Remove the GNN component in the model and only use the LSTM component to process time series data for prediction.

[0112] (4) Static feature model: Instead of using time series or graph structure data, a static feature model (SFM) is used to make predictions based on static features (such as user profile data and basic itinerary information).

[0113] Table 3 Comparison of model performance indicators

[0114]

[0115] In this research phase, the performance of four models - LSTM-GNN hybrid model, single graph neural network model, single long short-term memory network model and static feature model - in processing time series and graph data was examined in detail. As shown in Table 3, the final results were obtained by comparing the performance of multiple evaluation criteria including mean square error (MSE), mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE). It is revealed that the LSTM-GNN hybrid model significantly outperforms other models due to its unique ability to integrate the dynamic characteristics of time series data and the structural properties of graph data. And the model's outstanding ability to capture long-term dependencies and spatial relationships between data is difficult to match by other models.

[0116] like Figure 4 As shown in the figure, the LSTM-GNN model performs best in all the performance indicators examined, with MSE, MAE, RMSE and MAPE values ​​of 0.014, 0.073, 0.118 and 0.044 respectively. These results highlight the high accuracy and reliability of the strategy combining LSTM and GNN in predicting the flow of air-rail intermodal itinerary plans. Compared with the application of GNN or LSTM alone, the LSTM-GNN model can more effectively integrate the dynamic characteristics of time series data and the complex spatial dependencies in flow data to achieve more accurate predictions.

[0117] The performance of the single GNN model is second only to LSTM-GNN in various performance indicators, with MSE, MAE, RMSE and MAPE of 0.026, 0.086, 0.162 and 0.057 respectively. This reflects that GNN has certain advantages in capturing spatial relationships, but its ability to process dynamic time series data is not as good as that of the LSTM-GNN model.

[0118] The performance of the LSTM model alone is slightly lower than that of the GNN model, and is also inferior to the performance of LSTM-GNN in terms of numerical value. Its MSE, MAE, RMSE, and MAPE are 0.029, 0.090, 0.171, and 0.065, respectively. This shows that although LSTM is effective in processing time series data, it lacks full utilization of the spatial dependencies between itinerary plans, which limits its prediction performance.

[0119] The SFM model performed the weakest in the comparison, with MSE, MAE, RMSE, and MAPE of 0.106, 0.192, 0.325, and 0.124, respectively. This result further verifies the superiority of the LSTM-GNN model over the traditional simple model in complex prediction tasks.

[0120] like Figure 5 and Figure 6 As shown in the figure, by comparing the change curves of the training loss value and the test loss value during the training process, the training and testing processes of the four models, LSTM-GNN, single GNN, single LSTM, and SFM, in the itinerary flow prediction task are deeply analyzed, especially the differences in their training efficiency, convergence speed, and convergence performance.

[0121] The LSTM-GNN model combines LSTM and GNN, and is specifically designed to solve complex prediction tasks that include both time series dependencies and spatial dependencies. During the training process, the LSTM-GNN model showed a faster convergence speed and lower final loss value, which fully proves that the model can quickly capture complex patterns in the data and effectively reduce prediction errors. The reason why LSTM-GNN shows such excellent performance is that it can capture both temporal dynamics and spatial structure at the same time, which is crucial for solving problems such as itinerary flow prediction.

[0122] The GNN model focuses on capturing the spatial dependencies of data and intuitively displays the relationships between entities through graph structures. Figure 5 As shown in the figure, although the convergence speed of the single GNN model is slightly slower than that of the LSTM-GNN hybrid model in experimental verification, it still shows a robust learning ability. This is mainly because the single GNN model effectively processes spatial structure information, but it does not directly integrate time series analysis technology, so it is slightly insufficient in capturing the dynamic change characteristics in time series data.

[0123] On the other hand, as an advanced time series analysis tool, the core advantage of the LSTM model lies in its ability to remember long-term dependent information. Through the analysis of the training process, it can be found that although a single LSTM model can effectively learn and remember the dynamic changes in the time series, its ability to handle spatial relationships is weak. Since the spatial dependency relationship between nodes is not directly modeled, it is inferior to the LSTM-GNN model in terms of convergence speed and final prediction performance.

[0124] These observations emphasize that when faced with complex forecasting tasks that have both time series characteristics and spatial dependencies, a single network model tool or component is not sufficient to meet the needs of practical applications. A hybrid model that can comprehensively handle temporal dynamics and spatial structures is particularly important.

[0125] As a relatively simple sequence prediction method, the SFM model performed the worst among the four models in this experiment. This is mainly because SFM lacks the comprehensive ability to handle complex spatial dependencies and temporal dynamics. During the training and testing process, the loss of the SFM model decreased significantly slower than that of other models, which directly reflects its limitations in dealing with this prediction task.

[0126] In contrast, the LSTM-GNN hybrid model exhibits excellent performance in both the training and testing phases. Its ability to converge quickly and its high stability after multiple iterations highlight the model's adaptability and robustness to different feature data distributions. Compared with the LSTM-GNN model, although the single LSTM model and GNN model can also achieve a certain stability, they are inferior to the LSTM-GNN model in terms of convergence speed and final performance. Throughout the training process, the SFM model exhibited relatively low stability, which further highlights the difficulties and limitations of simple models when faced with complex prediction tasks. This phenomenon emphasizes that when designing a prediction model, it is necessary to fully consider the model's ability to handle complex data characteristics. In particular, when the prediction task involves complex time series and spatial dependencies, it becomes particularly important to select or develop advanced models that can fully consider these factors.

[0127] 5.3 Prediction effect analysis

[0128] After completing the training of the four models, a specific travel plan is selected and the prediction time step is set to 40 days. This section evaluates the prediction performance of these models based on actual traffic data, directly observing and evaluating the effectiveness of each model in predicting future travel traffic, especially when dealing with complex data containing time series and spatial dependencies. In order to compare and analyze more intuitively, this section combines the prediction results of each model with the actual traffic data, and then draws the prediction results of the four models. In this way, the differences in the prediction capabilities of each model can be clearly demonstrated, especially their performance in capturing and understanding the temporal dynamics and spatial structure in the travel plan.

[0129] like Figure 7(a) to Figure 7(d)As shown in the figure, the LSTM-GNN model shows significant advantages in the forecast result graph analysis. Compared with the other three models, the LSTM-GNN model has a strong ability to learn complex patterns in data and capture dynamic changes in the flow of itinerary plans. At the same time, the LSTM-GNN model can accurately predict the flow changes of itinerary plans in the next 40 days, and the prediction curve is highly consistent with the actual flow data, reflecting its high accuracy. This accuracy is attributed to the structural design of the LSTM-GNN model, which combines the time series analysis capabilities of LSTM with the spatial relationship modeling capabilities of GNN. This combination enables the model to not only understand the continuity and pattern changes in time, but also capture the complex spatial connections between itineraries, thereby providing more accurate flow forecasts.

[0130] Although GNN and LSTM models also show predictive capabilities in some aspects, they are still inferior to LSTM-GNN models in terms of accuracy and generalization. Although the GNN model can better understand spatial relationships, it lacks in-depth analysis of time series dynamics. On the contrary, LSTM can effectively capture dynamic features in time series, but lacks the ability to handle spatial dependencies. As a simpler sequence prediction tool, the SFM model has the weakest performance in this prediction task, which further highlights the superiority of the LSTM-GNN model.

[0131] 6 Conclusion

[0132] After deeply analyzing the performance of the LSTM-GNN model in traffic forecasting for air-rail intermodal itinerary solutions, this section focuses on the model's advantages, key factors for performance improvement, and practical application value revealed through case studies. The following are the key factors for model performance improvement:

[0133] Deep optimization of data preprocessing: This paper uses data cleaning technology, including outlier detection based on machine learning and intelligent missing value filling strategy, to significantly improve data quality. In addition, through feature selection and transformation technology, the features that contribute most to prediction are accurately identified, effectively reducing the complexity of the model and the risk of overfitting.

[0134] Fusion processing of time series and graph data: The core advantage of the LSTM-GNN model is that it can simultaneously handle time series data and graph structure data, deeply capturing the dynamic evolution of the air-rail transport network system and the intricate interactions between users. This multi-dimensional data fusion provides the model with richer contextual information, thereby improving the accuracy of the model's predictions.

[0135] Innovation and optimization of model structure: By adjusting the LSTM components and GNN components, this paper designs a model that can more effectively capture time dependencies and network structure characteristics. In particular, in the design of the GNN layer, by introducing the self-attention mechanism, the model can adaptively focus on important nodes and edges, further improving the prediction performance.

[0136] Through in-depth analysis and case studies of the LSTM-GNN model, this paper not only verifies the excellent performance of the model in air-rail intermodal schedule flow forecasting, but also demonstrates its great potential in practical applications. The successful application of the model further proves the advanced nature of the fusion processing of time series and graph data, and shows the broad application prospects in the field of complex system prediction.

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Claims

1. A passenger flow prediction method for air-rail transport network integrating LSTM and GNN, which uses a passenger flow prediction model to take user profiles and air-rail transport itinerary data as input to predict the passenger flow of the air-rail transport network; its characteristics are The steps include: 1) data preprocessing; 2) using the LSTM-GNN model as a passenger flow prediction model to predict the data obtained in step 1); The step 1) comprises: 1.1) Constructing a graph model for the user-trip plan dataset First, collect data: the collected data sets include user portrait data sets and itinerary plan record data sets; The user portrait dataset includes age, gender, occupation, the user's travel plan purchase history and the user's social network information; The trip plan record dataset includes the stops involved in the trip, the time consumed, the monetary cost, and the trip ID; Then, we build a user itinerary interaction dataset: We extract features from the user portrait dataset and the itinerary plan record dataset, use the user as the connection key, and fuse the user's personal features and itinerary selection behavior features to obtain the user itinerary interaction dataset. Finally, a graph model of the user trip interaction dataset is established. The structure of the graph model consists of two layers, the upper and lower layers, and the definitions include: Define nodes: Each node in the upper layer represents a user; each node in the lower layer represents a travel plan; Constructing edges: The edges between nodes in the upper layer represent the social relationships and similar purchasing behaviors between users; the edges between nodes in the lower layer represent the shared station information between itineraries; the edges between nodes in the upper and lower layers are determined by the purchasing behavior and time points of users for itineraries; Integrate features: For each node, integrate relevant features from the dataset, including the user's social network characteristics, the cost and time of the travel plan; 1.2) Construct the weight matrix as the input of the LSTM-GNN model; First, data cleaning is performed using outlier detection and missing value processing algorithms; Then, by analyzing the correlation between user behavior and itinerary information, feature engineering technology is used to extract the most influential features for the passenger flow prediction model; then the features of the data set are ranked in importance; Finally, an adjacency matrix is ​​established to transform the social relationships between users and the relationship between the choices of itinerary plans into a graph structure. The weights of the edges in the graph structure reflect the strength of the connection between users. The weight matrix serves as the final input of the LSTM-GNN model. In step 2), after constructing the graph model as input data, the itinerary prediction problem is abstracted into a node prediction task; the LSTM-GNN hybrid model is used to parse the node prediction task: In the graph structure constructed by the weight matrix, each node i has a time series x i,T and the static feature x i,S ; The weight matrix with static features and temporal attribute features is passed as input to the LSTM-GNN model; The LSTM-GNN model produces three types of embeddings: LSTM, GNN, and static embeddings, which are concatenated and passed to the fully connected layer to obtain the prediction of each node; In the LSTM-GNN model, a similarity score is first assigned between user nodes, and the user static features are converted into the user's multi-hot vector to obtain the feature matrix D∈R N×m , where m is the number of static features, N is the number of users, and the similarity score M between nodes i and j is i,j Defined as d μ is the occurrence of the binary static characteristic μ, a and c are adjustable constants, D i,μ , D j,μ The feature matrices representing the static features of nodes i and j respectively; In the "shared features" part of formula (1), It means that it is more important for two users to share a rare static feature than a common static feature. The "all features" part indicates the total number of penalized features. At the same time, the k-nearest neighbor (k-NN) method is used to test the dynamic changes of the similarity score to establish k edges for each node, where parameters a, c, and k are used as hyperparameters. In the LSTM-GNN model, LSTM captures the dynamic characteristics of the flow changes in the itinerary plan; the time series x i,t First, it passes through a bidirectional LSTM, which outputs a hidden state vector sequence h in both the forward and reverse directions. i,(T) ; The vectors corresponding to the last time step are concatenated to produce h i,T , which is a temporal embedding for each node; In the gating mechanism of LSTM: The forget gate is responsible for deciding which information should be forgotten or retained from the cell state. The forget gate operates on the hidden state of the previous time step and the current input, and outputs a value between 0 and 1, where 0 means complete forgetfulness and 1 means complete retention. The formula of the forget gate is expressed as f t =σ(W f ·[h t-1 ,x i,t ]+b f ) (2) In formula (2), f t represents the output of the forget gate, σ is the sigmoid function, W f is the weight matrix of the forget gate, h t-1 is the hidden state of the previous time step, x i,t is the input of the current time step, b f is the bias term of the forget gate; The input gate determines the new information added to the cell state. The input gate includes an input gate layer and a candidate value layer. The input gate layer determines which information will be retained. The candidate value layer generates a candidate value vector by processing the current input and the previous hidden state. The vector contains the new information that may be added to the cell state. The result of the input gate is x t =σ(W i ·[h t-1 ,x i,t ]+b x ) (3) The input gate determines what new information is added to the cell state. is the candidate value of the new information, generated by the tanh activation function; W i represents the weight matrix of the input gate, b x represents the bias term of the input gate, W C represents the learnable weight, b C represents the learnable bias, x t Represents the input gate activation value at the current moment; The cell state is the core storage unit of LSTM. It updates the current cell state by linearly combining the cell state and candidate value at the previous moment, combined with the information of the forget gate and input gate; the cell state is updated to Unit Status C t is the state of the previous unit C t-1 After forgetting a part through the forget gate, add the current candidate unit state The information obtained through the input gate control; The output gate determines the amount of information in the cell state. Based on the filtered cell state, the output gate determines which information will be used as the output h of the current LSTM. i,t , which in turn affects the subsequent units and the final network output; the output gate formula is expressed as the t =σ(W o ·[h t-1 ,x i,t ]+b o ) (6) h i,t =o t *tanh(C t ) (7) o t is the activation value of the output gate, W o represents the weight matrix of the output gate, b o Represents the bias term of the output gate; In formulas (2) to (7), W and b represent the weight matrix and bias term, and * represents element-by-element multiplication. The sigmoid function is used to compress the input to between 0 and 1, helping LSTM to determine the amount of information to be transmitted. The tanh function compresses the input to between -1 and 1, helping LSTM to adjust the strength of the information flow. After LSTM processes the time series of the input data center, GNN processes the interaction relationship between users; GNN uses the node and edge information in the graph structure to learn the high-dimensional representation of each node through the neighbor aggregation mechanism; the GNN component propagates the time embedding of each node in its neighborhood; specifically, by embedding the time of each node h i,T This is achieved by locally smoothing the feature vectors of its neighboring nodes, that is, h i,T Re-weight the feature vectors in its local neighborhood to generate a new node representation h i,N ; At the same time, pass the static input x through a fully connected layer i,S , calculate h i,S , and then concatenate the previously learned representations together so that h i =(h i,T ||h i,N ||h i,S ) (8) Finally, h i Pass a fully connected layer to obtain the full model prediction for node i In the parameter transfer process of the entire LSTM-GNN model architecture, LSTM-GNN is trained in an end-to-end and scalable manner. By adopting the neighborhood sampling method, small batch training of LSTM is achieved, that is, a set of fixed-size samples is uniformly sampled in the graph input at each iteration; During training, only nodes in the training set and their neighborhoods are sampled; During testing, neighbors are sampled from the entire dataset, but only the performance of the test node is evaluated; The loss function is defined as L=L LSTM-GNN +αL LSTM (9) Among them, L LSTM-GNN is the full model prediction The loss, L LSTM is composed of LSTM components The loss of the prediction made, α is a hyperparameter.

2. The method for predicting passenger flow in air-rail transport network by integrating LSTM and GNN according to claim 1 is characterized in that In step 1.2), During the data cleaning phase, the interquartile range (IQR) method, an outlier detection technique based on statistical methods, is used to identify and remove points that do not conform to the normal distribution of the data set; for missing values, interpolation methods and / or prediction methods based on neural network models are used to fill them according to the characteristics of the data; In the feature extraction phase, by analyzing the correlation between user behavior and itinerary information, the most influential features for the prediction model are extracted using One-Hot Encoding, Normalization, and Principal Component Analysis (PCA) methods; the Random Forest model is used to rank the importance of the features of the data set; In the process of converting the social relationships between users and the relationship between the choice of itinerary plans into a graph structure, the basic graph construction method is adopted, and community detection and network centrality analysis are introduced to further explore the potential connections between node features, and the processed fusion data set is converted into a weight matrix as the final input of the LSTM-GNN model.

3. The air-rail transport network passenger flow prediction method integrating LSTM and GNN according to claim 1 is characterized by: Step 1.2) includes: 1.2.1) Feature normalization: Use the Z-score normalization method to process all numerical features; use the one-hot encoding method to convert categorical features into numerical data; 1.2.2) Time series processing: For time series data, a sliding window mechanism is used to construct learning samples so that the prediction model can learn the time dependency from the past to the future; 1.2.3) Graph data preprocessing: When processing graph data, an adjacency matrix is ​​used to represent the graph structure, where the nodes of the graph represent users and itinerary plans, and the edges represent the interactions between users or the sharing of itinerary plans. Graph embedding technology is used to convert graph data into vector form. 1.2.4) Dataset division: The dataset is divided into training set, validation set and test set, which are used for training, parameter adjustment and performance evaluation of the prediction model respectively. The stratified sampling method is used to make the proportion of each category of data in each dataset consistent.

4. The air-rail transport network passenger flow prediction method integrating LSTM and GNN according to claim 1 is characterized in that LSTM -During the training process of the GNN model, balance the performance of the model on the training set and the test set to solve the problem of overfitting and underfitting. The methods include: Data enhancement: We implemented time shift, scaling, and random noise addition on the time series data, and simulated different network connection scenarios by randomly deleting or adding edges, thereby improving the model's adaptability to changes in graph structure. Early stopping: During model training, monitor the performance of the model on an independent validation set. Once the performance of the model on the validation set begins to decline, indicating signs of overfitting, stop training immediately. Cross-validation: K-fold cross-validation is used to ensure that the model has good generalization ability. That is, by dividing the dataset into K subsets and using one of the subsets as the validation set and the other datasets as the training set in turn, the performance of the model is evaluated from multiple aspects to avoid overfitting and underfitting.

5. The method for predicting passenger flow in air-rail transport network by integrating LSTM and GNN according to claim 1 is characterized in that During the model training process, regularization technology and model structure adjustment methods are used to improve the generalization of the model, including: Regularization Techniques: L1 / L2 regularization: By adding the L1 or L2 norm of the weight as a regularization term in the loss function, the size of the model weight is limited; Dropout: During the training process, some neurons are randomly discarded, forcing the model to learn the characteristics of the data through the remaining neurons; Batch Normalization: By normalizing each mini-batch of data, the covariate shift between input layers is reduced; Model structure adjustment method: Model simplification: For overly complex model structures, simplify the model by reducing the number of layers or parameters; Hyperparameter optimization: By exploring the hyperparameter space including learning rate and number of hidden layer units, we use grid search and Bayesian optimization to find the optimal model configuration, ensuring that the model can achieve the best performance on different data sets; Introduction of attention mechanism: The attention mechanism is introduced in the GNN component, so that the model can automatically learn the importance priority of nodes and edges in the graph according to the requirements of the task.

6. The method for predicting passenger flow in air-rail transport network by integrating LSTM and GNN according to claim 1 is characterized by: The tuning method of the LSTM-GNN model is: Before model training: A hyperparameter search method is used to explore and evaluate the performance of the LSTM-GNN model under different hyperparameter combinations, and then find the optimal model configuration; Cross-validation techniques were used to evaluate the robustness of the model on different data subsets; Use Bayesian optimization to search the hyperparameter space and reduce the number of iterations required to find a parameter combination close to the optimal solution. During model training: Use gradient clipping to prevent gradient explosion problem; use Adam optimizer to adjust learning rate.

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