A physical prior intercity passenger transport demand prediction method and system considering city index similarity

Abstract

The application discloses a kind of considering city index similarity physical prior intercity passenger transport demand prediction method and system, specifically are: intercity passenger transport demand related data are collected, and pretreatment is carried out;Based on city index similarity, consider the influence of adjacent city, correct the quality index of city, finally build the intercity passenger transport demand physical model considering city index similarity;Intercity passenger transport demand physical model is output intercity passenger transport demand prediction result, as physical benchmark prediction item;Based on the deviation between actual intercity passenger transport demand and physical benchmark prediction item result, residual error learning target function is built, residual error correction model based on machine learning model is established, and intercity passenger transport demand residual error correction item is output;Based on city index similarity, dynamically build weight, and the weighted fusion between physical benchmark prediction item and residual error correction item is obtained The final intercity passenger transport demand value.The application has clear structure, can be landed, can be directly realized by programming, and is convenient for engineering application.

Description

Technical Field

[0001] This invention belongs to the field of transportation planning technology, and in particular relates to a physical prior intercity passenger transport demand forecasting method and system that considers the similarity of urban indicators. Background Technology

[0002] Intercity passenger transport demand reflects the spatial distribution patterns of travel between cities and is a core foundation for transportation planning, route optimization, capacity allocation, and policy formulation. Intercity passenger transport demand forecasting mainly falls into two categories: physical mechanism-driven methods and data-driven machine learning methods.

[0003] Physical mechanism-driven methods are based on the macroscopic laws of intercity travel, constructing predictive models based on physical priors such as travel behavior, gravity models, and impedance relationships. These methods have clear physical meaning and strong interpretability, ensuring that the prediction results conform to the basic laws of intercity travel; for example, the larger the city and the closer the distance, the stronger the travel demand. However, traditional physical models have fixed structures, and their parameters are difficult to dynamically adapt to the complex and ever-changing characteristics of urban development and travel. They also struggle to utilize massive amounts of historical passenger flow data to capture nonlinear and dynamically changing travel patterns, resulting in limited prediction accuracy.

[0004] Machine learning models rely on a large amount of historical passenger flow data, city attribute data, and transportation network data for training, and can automatically uncover complex nonlinear relationships in intercity travel, achieving high prediction accuracy. However, purely data-driven models have significant drawbacks: the models only learn features from the data and lack the constraints of the inherent physical laws governing intercity travel, making them prone to predictive results that defy common sense, such as extremely low passenger flow predictions between nearby cities and abnormally low travel demand between large cities; at the same time, the models have weak generalization ability and are prone to inaccurate predictions in data-sparse areas and newly developed urban areas.

[0005] In existing technologies, physical models and machine learning models are typically fused using independent modeling or simple result overlay, failing to achieve deep coupling between prior physical information and the data learning process. Furthermore, most methods only consider basic indicators such as population, GDP, and spatial distance, failing to fully incorporate the spatial correlation effects between neighboring cities and the similarity of multidimensional urban attributes, making it difficult to characterize the impact mechanism of urban agglomeration structure on intercity passenger transport demand. Summary of the Invention

[0006] Purpose of the invention: Based on the spatial distribution prediction process of physical laws, this invention deeply couples physical models with machine learning models, introduces urban indicator similarity features, and proposes a physical prior intercity passenger transport demand prediction method that considers urban indicator similarity. This method is used for spatial distribution prediction of intercity passenger transport demand and solves the problems of insufficient prediction accuracy, lack of physical consistency of results, and poor model generalization ability of existing technologies.

[0007] Technical solution: This invention provides a physical prior intercity passenger transport demand forecasting method that considers the similarity of urban indicators, specifically as follows: Collect data related to intercity passenger transport demand, and perform data cleaning, deduplication, outlier removal, and format standardization. Based on the similarity of city indicators, considering the influence of neighboring cities, the quality indicators of cities are modified, and finally, a physical model of intercity passenger transport demand that takes into account the similarity of city indicators is constructed. Solve for the optimal values ​​of relevant parameters in the physical model of intercity passenger transport demand, and use the intercity passenger transport demand physical model to output the intercity passenger transport demand forecast results as the physical baseline forecast term; Based on the deviation between the actual intercity passenger transport demand and the physical baseline prediction, a residual learning objective function is constructed, a residual correction model based on a machine learning model is established, and the intercity passenger transport demand residual correction term is output. The weights are dynamically constructed based on the similarity of urban indicators, and the weighted fusion between the physical baseline prediction term and the residual correction term is performed to obtain the final intercity passenger transport demand value.

[0008] Furthermore, the relevant data specifically includes intercity passenger transport demand, city size indicators, intercity spatial distance, and city industrial structure, age structure, occupational structure, and land use structure indicators. The city size indicators are the number of permanent residents and GDP; The intercity spatial distance mentioned is the surface spatial distance; The urban industrial structure adopts a structural vector consisting of the proportions of primary, secondary, and tertiary industries. Characterization; The age structure is represented by a vector of the proportion of different age groups in the urban resident population. Characterization; The urban occupational structure adopts a vector of different occupational population proportions. Characterization; The urban land use structure adopts a vector structure of proportions of different types of points of interest. Characterization.

[0009] Furthermore, taking city i as the departure city and city j as the destination city, cosine similarity is used to calculate the city's similarity. Similarity with city j under the k-th indicator ; Taking into account the influence of neighboring cities, the city's quality indicators are adjusted to obtain the revised quality indicators. : ; in, For the city before the revision Quality indicators This is a correction coefficient for the similarity of indicators between neighboring cities. For the city The set of neighboring cities; For the city Comprehensive similarity with city n: ; in, All are weights; Based on the revised quality indicators, a physical model of intercity passenger transport demand is constructed that considers the similarity of city indicators: ; in, This is a demand size correction factor. These are the correction factors for the quality of the departure city and the arrival city, respectively. The similarity correction coefficient between origin and destination cities is the similarity coefficient between city i and city j. This refers to intercity spatial distance.

[0010] Furthermore, the least squares method is used to adjust the demand size factor in the physical model of intercity passenger transport demand that considers the similarity of urban indicators. Correction coefficients for the quality of departure and arrival cities Distance attenuation coefficient Similarity correction coefficient between origin and destination cities City indicator similarity correction coefficient Perform fitting calibration to determine the optimal parameter space.

[0011] Furthermore, construct the feature set. : ; Calculate the actual observed intercity passenger demand With physical baseline predictions residuals between : ; Machine learning is used for residual correction, and the residual correction term is... : ; in, For machine learning models; Set the function to minimize the loss. The machine learning model is trained, and the residual correction term is output from the trained machine learning model: .

[0012] Furthermore, construct the weights between city i and city j. : ; This represents the Sigmoid function. The similarity influence intensity coefficient, The strength coefficient is affected by error. Physical baseline prediction term and residual correction term Perform weighted finite element analysis: .

[0013] Furthermore, by minimizing the following objective function, the parameters are... and Optimization: .

[0014] Furthermore, the goodness-of-fit R-value was used. 2 Pearson correlation coefficient (PCC) and root mean square error (RMSE) were used as evaluation indicators for the prediction results.

[0015] A system for predicting intercity passenger transport demand based on physical priors that consider the similarity of urban indicators includes: The data acquisition and processing module is used to collect data related to intercity passenger transport demand and to clean, deduplicate, remove outliers, and standardize the format of the data. The intercity passenger transport demand physical model construction module is used to modify the quality indicators of cities based on the similarity of city indicators, taking into account the influence of neighboring cities, and finally construct an intercity passenger transport demand physical model that takes into account the similarity of city indicators. The optimization module is used to find the optimal values ​​of relevant parameters in the intercity passenger transport demand physical model, and outputs the intercity passenger transport demand prediction results using the intercity passenger transport demand physical model as the physical baseline prediction term. The prediction result output module is used to construct a residual learning objective function based on the deviation between the actual intercity passenger transport demand and the physical baseline prediction result, establish a residual correction model based on the machine learning model, and output the intercity passenger transport demand residual correction term; based on the similarity of city indicators, weights are dynamically constructed, and the physical baseline prediction term and the residual correction term are weighted and fused to obtain the final intercity passenger transport demand value.

[0016] A computer device includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the processor executes the computer program to implement the steps of a physical prior intercity passenger demand forecasting method considering urban indicator similarity.

[0017] Beneficial effects:

[0018] This invention introduces similarities in urban industrial structure, age structure, occupational structure, and land use structure between originating and destination cities and neighboring cities to construct a physical model of intercity passenger transport demand that considers the similarity of urban indicators. This invention improves prediction accuracy by employing a physical model that considers the similarity of urban indicators, closely aligning with the actual travel patterns of urban agglomerations. Compared to traditional gravity models, it adds two new variables: equivalent quality of neighboring cities and urban similarity, covering two key influencing factors: urban agglomeration linkage and urban attribute matching. It can capture passenger flow differences that traditional models cannot explain, significantly reducing prediction errors, and is particularly suitable for metropolitan areas and contiguous urban agglomerations. This invention deeply couples the physical model with the machine learning model through a residual learning framework and introduces a dynamic weighting mechanism based on urban indicator similarity and prediction error to achieve adaptive fusion prediction of intercity passenger transport demand data. This invention has a clear structure, is practical, and can be directly implemented through programming, facilitating engineering applications. Attached Figure Description

[0019] Figure 1 This is the overall flowchart of the present invention.

[0020] Figure 2 The diagram shows a comparison between actual and predicted intercity passenger transport demand, where (a) is the flow diagram of actual intercity passenger transport demand and (b) is the flow diagram of predicted intercity passenger transport demand. Detailed Implementation

[0021] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0022] like Figure 1 The present invention provides a physical prior intercity passenger transport demand forecasting method considering the similarity of urban indicators, comprising the following steps:

[0023] (1) Collect data related to intercity passenger transport demand. The data specifically includes intercity passenger transport demand, city size indicators, intercity spatial distance, and city industrial structure, age structure, occupational structure, and land use structure indicators. The data is then cleaned, deduplicated, outlier removed, and format standardized.

[0024] The city size indicators specifically refer to the city's permanent resident population and regional GDP, serving as indicators to measure the city's quality and radiating influence.

[0025] The intercity spatial distance uses the surface spatial distance as the spatial distance variable to characterize intercity travel impedance;

[0026] The urban industrial structure is described using a structural vector consisting of the proportions of primary, secondary, and tertiary industries. The following representations are provided: Primary industry ratio: the percentage of the city's primary industry (agriculture, forestry, animal husbandry, and fishery) output value to the city's GDP; Secondary industry ratio: the percentage of the city's secondary industry (industry and construction) total output value to the city's GDP; Tertiary industry ratio: the percentage of the city's tertiary industry's various service industries total output value to the city's GDP; The industrial structure vector I contains three elements, which are the proportions of primary industry, secondary industry, and tertiary industry, respectively, in the form of: (I=[i1,i2,i3]) where: i1 is the primary industry ratio, i2 is the secondary industry ratio, and i3 is the tertiary industry ratio;

[0027] The urban age structure is defined by a vector showing the proportion of different age groups among the city's permanent residents. The characteristics include the proportion of the population aged 0-17, 18-44, 45-59, 60-74, and 75 and above.

[0028] The urban occupational structure adopts a vector of different occupational population proportions. The characteristics include the proportion of leaders of government agencies and public institutions, professional and technical personnel, clerical staff, service industry personnel, agricultural, forestry, animal husbandry and fishery personnel, manufacturing personnel, military personnel and other employees.

[0029] The urban land use structure adopts a vector structure of different types of points of interest. The characteristics include the proportion of points of interest in medical services, science and education services, accommodation services, commercial services, scenic spots and historical sites, and leisure and entertainment services.

[0030] (2) Based on the gravity model, the similarity of indicators of neighboring cities and the similarity of indicators of origin and destination cities are integrated to construct an intercity passenger transport demand physical model that considers the similarity of city indicators.

[0031] The city index similarity is calculated using a joint measurement method combining cosine similarity and normalized difference: for cities With the city In indicator categories The city structure vectors below are respectively and The corresponding city similarity index is defined as:

[0032]

[0033] in , The L2 norm of a vector is used to characterize the magnitude of the urban structure vector. When the city... With the city When the spatial relationship is between origin and destination cities, the similarity characteristics of origin and destination city indicators are obtained; when the city With the city When the spatial relationship is that of adjacent cities, the similarity characteristics of the adjacent city indicators are obtained.

[0034] This embodiment introduces a similarity index to accurately characterize structural travel demand. It can quantify passenger flow fluctuations caused by structural differences in industry, population, and urban functions, and can be used to analyze the driving effect of industrial synergy and urban integration on intercity passenger transport. It can not only complete passenger flow forecasting, but also support the evaluation of integrated urban transportation policies.

[0035] The physical model of intercity passenger transport demand that considers the similarity of urban indicators Defined as:

[0036] ;

[0037] in This is a demand size correction factor. These are the correction factors for the quality of the departure city and the arrival city, respectively. This is the distance attenuation coefficient. This is the similarity correction coefficient for indicators between the origin and destination cities. and The revised urban quality index, which takes into account the impact of neighboring cities, is defined as follows:

[0038] ;

[0039] in, Represents the city Spatial adjacency of cities This is a correction coefficient for the similarity of indicators between neighboring cities.

[0040] The Represents the city With the city The comprehensive similarity features are defined as follows:

[0041] ;

[0042] in, The similarity characteristics of urban industrial structures Urban age structure similarity characteristics Similarity characteristics of urban occupational structure Similarity characteristics of urban land use structure The correction coefficient, and satisfying the constraints. .

[0043] This invention introduces the equivalent city quality after radiation correction from neighboring cities, instead of directly using the original population / GDP indicators (Mi, Mj); and sets independent correction indices for the quality of departure and arrival cities respectively. This distinguishes the differentiated contributions of cities at both ends to passenger flow generation and attraction; a new index-based city indicator similarity adjustment item has been added. The effect of quantifying the similarity of multidimensional urban attributes on intercity passenger transport demand was studied.

[0044] Traditional models only use a city's own population and GDP as quality indicators, ignoring how the spillover of industries and population from neighboring cities within a city cluster alters a city's actual passenger flow radiation capacity. Therefore, this invention introduces... and By weighting the size and connectivity of neighboring cities, an equivalent city quality that reflects the synergistic effect of the city cluster is obtained; then, an independent index is set. This approach adjusts the passenger flow generation capacity of the departure city and the passenger flow attraction capacity of the arrival city respectively, thus solving the problem of indistinguishable weights between the two cities and large fitting deviation in the traditional model.

[0045] Existing models completely ignore the impact of matching degrees of multiple attributes such as urban industrial structure, population age structure, occupational distribution, and urban functional land use on travel: the more similar the indicators of two cities, the higher the matching degree of residents' commuting, business, and leisure travel needs, and the more significantly the passenger flow will increase. Therefore, this embodiment innovatively embeds a city indicator similarity index term:

[0046] .

[0047] This embodiment integrates three layers of factors—embedded city index similarity index, equivalent city quality, and independent correction index—to obtain a complete physical prior model. It retains the interpretable physical basis of the classical gravity model and supplements the two key influencing factors of urban agglomeration radiation and city attribute similarity that are missing in the existing model through two layers of original correction terms.

[0048] This physical model addresses the shortcomings of traditional gravity models that neglect the adjacency radiation effect of urban agglomerations. Existing standard gravity models only use a single indicator of a city's own quality. In urban agglomeration areas, the spillover of population and industry from neighboring cities alters the actual passenger flow radiation capacity of a city, causing predicted values ​​to deviate significantly from actual passenger flow. This application is approved. and Incorporate the influence of neighboring cities to adjust the effective size of the city.

[0049] This physical model addresses the gap in existing models that fail to quantify the impact of multidimensional urban attribute similarity on passenger flow. Existing passenger flow prediction models only use three basic indicators: population, GDP, and distance, completely neglecting the matching degree of urban industries, population structure, and urban functions. In reality, urban attribute similarity is a core driving factor for business commuting and leisure travel, and the absence of this variable will cause a large amount of structural passenger flow bias.

[0050] This physical model addresses the problems of traditional models, such as the lack of distinction between origin and destination city weights and insufficient fitting flexibility. In the classic gravity model, the mass of both origin and destination cities is first-order, which cannot distinguish the differentiated capabilities of urban passenger flow generation and attraction. This application sets up an independent index to independently calibrate the influence weights of the two cities, thereby improving the model's adaptability to differentiated urban samples.

[0051] This physical model overcomes the shortcomings of purely data-driven models, such as the lack of physical constraints and the susceptibility of distorted predictions. As a physical prior benchmark model, this formula can serve as the underlying constraint for correcting machine learning residuals, avoiding extreme predictions that contradict common sense regarding travel patterns in data-sparse small cities and newly built urban areas, while balancing mechanistic interpretability with data fitting ability.

[0052] (3) Determine the optimal parameters of the physical model of intercity passenger demand based on the fitting of intercity passenger demand data, and output the fitting results of intercity passenger demand as the physical benchmark prediction term.

[0053] With the objective of minimizing the sum of squared errors between observed passenger demand and fitted passenger demand globally, the least squares method is used to adjust the demand size correction factor in the physical model of intercity passenger demand that considers the similarity of urban indicators. Correction coefficients for the quality of departure and arrival cities Distance attenuation coefficient Similarity correction coefficient between origin and destination cities City indicator similarity correction coefficient The fitting calibration is performed to determine the optimal parameter space, and then the physical model fitting results of intercity passenger transport demand are output. .

[0054] (4) The fitting results of the physical model of intercity passenger transport demand are used as the physical benchmark prediction term, and a fusion feature set is constructed by combining the city size index, intercity spatial distance and city index similarity characteristics.

[0055] The fusion feature set is defined as follows:

[0056] .

[0057] (5) Based on the deviation between the actual intercity passenger transport demand and the physical baseline prediction, construct the residual learning objective function, establish a residual correction model based on the machine learning model, and output the intercity passenger transport demand residual correction term.

[0058] Based on actual observations of intercity passenger transport demand With physical baseline predictions Construct the residual learning objective function:

[0059] ;

[0060] Construct a residual correction function based on a machine learning model:

[0061] ;

[0062] in, For machine learning models, XGBoost regression models can be used; These are the model parameters.

[0063] By setting the minimum loss function Model training is performed to obtain residual correction terms. :

[0064] ;

[0065] .

[0066] (6) Construct a dynamic fusion weight calculation mechanism between the physical baseline prediction term and the residual correction term to obtain the intercity passenger transport demand prediction results, and evaluate the prediction accuracy of the prediction results.

[0067] The dynamic fusion weight calculation method between the physical baseline prediction term and the residual correction term is as follows:

[0068]

[0069]

[0070] in, This represents the Sigmoid function. The similarity influence intensity coefficient, This is the error influence intensity coefficient. Based on actual observed intercity passenger demand. Based on this, construct the objective function for parameter optimization:

[0071] .

[0072] By minimizing the objective function, the parameters and The model is then optimized and calibrated, and the prediction results after parameter optimization and calibration are output. .

[0073] The prediction accuracy evaluation in this embodiment uses the goodness-of-fit R-squared. 2 The Pearson correlation coefficient (PCC) and root mean square error (RMSE) are used as evaluation indicators, and the calculation formulas for each indicator are as follows:

[0074] ;

[0075] in, To study the total number of cities within a spatial range, Global observation of average intercity passenger transport demand.

[0076] PCC ;

[0077] in, This represents the average value of the global forecast for intercity passenger transport demand.

[0078] ;

[0079] This embodiment takes the Beijing-Tianjin-Hebei urban cluster consisting of Beijing, Tianjin, Cangzhou, Langfang, and Tangshan as the research object, and uses urban attribute data, inter-city spatial distance data, and intercity passenger OD data within the same statistical period for predictive analysis.

[0080] (1) Data acquisition and preprocessing.

[0081] Intercity passenger transport demand data for Beijing, Tianjin, Cangzhou, Langfang, and Tangshan were obtained, as shown in Table 1. Simultaneously, data on city size indicators, intercity spatial distances, and urban industrial structure, age structure, occupational structure, and land use structure indicators for Beijing, Tianjin, Cangzhou, Langfang, and Tangshan were obtained. The acquired data underwent cleaning, deduplication, outlier removal, and format standardization.

[0082] Table 1. Intercity passenger transport demand data for the Beijing-Tianjin-Hebei urban cluster (passenger trips / day)

[0083]

[0084] The urban land use structure adopts a vector structure of proportions of different types of points of interest. The characteristics include the proportion of points of interest in medical services, science and education services, accommodation services, commercial services, scenic spots and historical sites, and leisure and entertainment services;

[0085] Table 2. Research Samples and City Numbers of the Five Cities

[0086]

[0087] Intercity spatial distance, as a spatial distance variable, is used to characterize intercity travel impedance. Table 3 lists the intercity spatial distance matrix between Beijing, Tianjin, Cangzhou, Langfang, and Tangshan, with distances in km.

[0088] Table 3 Spatial distance matrix (km) between cities: Beijing, Tianjin, Cangzhou, Langfang, and Tangshan

[0089]

[0090] (2) Calculation of similarity of city indicators.

[0091] For each city pair, the similarity of city indicators is calculated based on data on industrial structure, age structure, occupational structure, and land use structure.

[0092] (3) Construction of physical model of intercity passenger transport demand considering the similarity of urban indicators.

[0093] (4) Physical model parameter calibration and fusion feature set construction.

[0094] Based on the collected intercity passenger transport OD data, the parameters in the above-mentioned intercity passenger transport demand physical model are calibrated to obtain the physical model fitting results, and these fitting results are used as physical baseline prediction terms.

[0095] After obtaining the physical baseline prediction term, the city size index, intercity spatial distance, corrected city quality, comprehensive similarity features, and various structural similarity features are combined to form a fusion feature set.

[0096] (5) Residual correction model construction: The deviation between the actual observed intercity passenger demand and the physical baseline prediction term is used as the learning target, and the aforementioned fusion feature set is used to train the machine learning residual correction model.

[0097] (6) Dynamic fusion prediction and accuracy evaluation,

[0098] A comparison chart of actual intercity passenger transport demand and projected intercity passenger transport demand can be found here. Figure 2 The prediction process outputs a physical baseline prediction term and a residual correction term, which are then weighted to obtain the predicted intercity passenger transport demand. A comparison between the predicted and actual intercity passenger transport demand shows that the predicted values ​​are all distributed within the range of the actual values, validating the model's high prediction accuracy.

[0099] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the present invention will not describe the various possible combinations separately.

Claims

1. A physical prior intercity passenger transport demand forecasting method considering urban indicator similarity, characterized in that, Specifically: Collect data related to intercity passenger transport demand, and perform data cleaning, deduplication, outlier removal, and format standardization. Based on the similarity of city indicators, considering the influence of neighboring cities, the quality indicators of cities are modified, and finally, a physical model of intercity passenger transport demand that takes into account the similarity of city indicators is constructed. Solve for the optimal values ​​of relevant parameters in the physical model of intercity passenger transport demand, and use the intercity passenger transport demand physical model to output the intercity passenger transport demand forecast results as the physical baseline forecast term; Based on the deviation between the actual intercity passenger transport demand and the physical baseline prediction, a residual learning objective function is constructed, a residual correction model based on a machine learning model is established, and the intercity passenger transport demand residual correction term is output. The weights are dynamically constructed based on the similarity of urban indicators, and the weighted fusion between the physical baseline prediction term and the residual correction term is performed to obtain the final intercity passenger transport demand value.

2. The physical prior intercity passenger transport demand forecasting method considering urban indicator similarity as described in claim 1, characterized in that, The relevant data specifically includes intercity passenger transport demand, city size indicators, intercity spatial distance, and indicators of urban industrial structure, age structure, occupational structure, and land use structure. The city size indicators are the number of permanent residents and GDP; The intercity spatial distance mentioned is the surface spatial distance; The urban industrial structure adopts a structural vector consisting of the proportions of primary, secondary, and tertiary industries. Characterization; The age structure is represented by a vector of the proportion of different age groups in the urban resident population. Characterization; The urban occupational structure adopts a vector of different occupational population proportions. Characterization; The urban land use structure adopts a vector structure of proportions of different types of points of interest. Characterization.

3. The physical prior intercity passenger transport demand forecasting method considering urban indicator similarity according to claim 2, characterized in that, Using city i as the departure city and city j as the destination city, cosine similarity is used to calculate the city's similarity. Similarity with city j under the k-th indicator ; Taking into account the influence of neighboring cities, the city's quality indicators are adjusted to obtain the revised quality indicators. : ； in, For the city before the revision Quality indicators This is a correction coefficient for the similarity of indicators between neighboring cities. For the city The set of neighboring cities; For the city Comprehensive similarity with city n: ； in, All are weights; Based on the revised quality indicators, a physical model of intercity passenger transport demand is constructed that considers the similarity of city indicators: ； in, This is a demand size correction factor. These are the correction factors for the quality of the departure city and the arrival city, respectively. The similarity correction coefficient between origin and destination cities is the similarity coefficient between city i and city j. This refers to intercity spatial distance.

4. The physical prior intercity passenger transport demand forecasting method considering urban indicator similarity according to claim 3, characterized in that, The least squares method is used to adjust the demand size factor in the physical model of intercity passenger transport demand that considers the similarity of city indicators. Correction coefficients for the quality of departure and arrival cities Distance attenuation coefficient Similarity correction coefficient between origin and destination cities City indicator similarity correction coefficient Perform fitting calibration to determine the optimal parameter space.

5. The physical prior intercity passenger transport demand forecasting method considering urban indicator similarity according to claim 4, characterized in that, Constructing feature sets : ； Calculate the actual observed intercity passenger demand With physical baseline predictions residuals between : ； Machine learning is used for residual correction, and the residual correction term is... : ； in, For machine learning models; Set the function to minimize the loss. The machine learning model is trained, and the residual correction term is output from the trained machine learning model: 。 6. The physical prior intercity passenger transport demand forecasting method considering urban indicator similarity according to claim 4, characterized in that, Construct the weights between city i and city j : ； This represents the Sigmoid function. The similarity influence intensity coefficient, The strength coefficient is affected by error; Physical baseline prediction term and residual correction term Perform weighted finite element analysis: 。 7. The physical prior intercity passenger transport demand forecasting method considering urban indicator similarity as described in claim 6, characterized in that, By minimizing the following objective function, the parameters... and Optimization: 。 8. The physical prior intercity passenger transport demand forecasting method considering urban indicator similarity according to claim 1, characterized in that, Using the goodness-of-fit R 2 Pearson correlation coefficient (PCC) and root mean square error (RMSE) were used as evaluation indicators for the prediction results.

9. A system applied to the physical prior intercity passenger transport demand forecasting method considering urban indicator similarity as described in claim 1, characterized in that, include: The data acquisition and processing module is used to collect data related to intercity passenger transport demand and to clean, deduplicate, remove outliers, and standardize the format of the data. The intercity passenger transport demand physical model construction module is used to modify the quality indicators of cities based on the similarity of city indicators, taking into account the influence of neighboring cities, and finally construct an intercity passenger transport demand physical model that takes into account the similarity of city indicators. The optimization module is used to find the optimal values ​​of relevant parameters in the physical model of intercity passenger transport demand, and outputs the intercity passenger transport demand prediction results using the physical model of intercity passenger transport demand as the physical baseline prediction term. The prediction result output module is used to construct a residual learning objective function based on the deviation between the actual intercity passenger transport demand and the physical baseline prediction result, establish a residual correction model based on the machine learning model, and output the intercity passenger transport demand residual correction term; based on the similarity of city indicators, weights are dynamically constructed, and the physical baseline prediction term and the residual correction term are weighted and fused to obtain the final intercity passenger transport demand value.

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of a physical prior intercity passenger demand forecasting method that considers the similarity of urban indicators as described in any one of claims 1 to 8.

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