A method for modeling multi-element collaborative change based on geospatially and temporally weighted vector autoregression

Abstract

The application is suitable for the technical field of geographic element data analysis, and provides a kind of geographic space-time weighted vector autoregressive multi-element collaborative change modeling method, comprising: constructing GTWR-VAR model, combining the multivariate feedback mechanism of vector autoregression with the locality of geographic space-time weighted regression, for quantifying the space-time heterogeneity of mutual influence between geographic elements, then introducing the Bayesian optimization mechanism, to verify the minimum mean square error minimization as the goal, adaptively determine the optimal lag order, spatial bandwidth and time bandwidth, finally using Monte Carlo block replacement test, under the premise of preserving the inherent time autocorrelation of data, evaluate and eliminate the insignificant items in local coefficient, ensure the statistical validity of the result. The application discloses the continuous change rule of influence mechanism between geographic elements in time and space, and provides more accurate and reliable basis for fine management, prediction and regional response research under climate change.

Description

Technical Field

[0001] This application belongs to the field of geographic element data analysis technology, and in particular relates to a multi-element collaborative change modeling method of geographic spatiotemporal weighted vector autoregression. Background Technology

[0002] Multiple geographical elements, such as soil moisture, actual evapotranspiration, and precipitation, exhibit complex dynamic synergistic relationships, mutually constraining and feedback each other to form a highly coupled system. For example, precipitation is the primary input to soil moisture, which in turn determines the intensity of actual evapotranspiration by controlling water availability. Simultaneously, actual evapotranspiration, by influencing latent heat and sensible heat fluxes, in turn affects atmospheric and precipitation processes, forming a complex dynamic synergistic relationship. This relationship is key to driving regional hydrological, climatic, and ecological processes. However, due to the complexity of the geographical environment and the nonlinearity of climate, these interaction mechanisms often exhibit significant spatiotemporal heterogeneity and dynamic feedback effects at different geographical locations and time scales.

[0003] Traditional global statistical models struggle to capture the complex spatiotemporal heterogeneity and dynamic feedback effects of relationships between geographic elements, and in practical applications, they face the problem of hyperparameter selection relying on experience. Summary of the Invention

[0004] This application provides a multi-factor collaborative change modeling method based on geographic spatiotemporal weighted vector autoregression. This method can solve the problem that traditional global statistical models are unable to capture the complex spatiotemporal heterogeneity and dynamic feedback effects of relationships between geographic elements, and face the problem of hyperparameter selection relying on experience in practical applications.

[0005] In a first aspect, embodiments of this application provide a multi-factor collaborative change modeling method using geographic spatiotemporal weighted vector autoregression (GTWR), comprising: S1, acquiring spatiotemporal sequence data of multi-source geographic elements, wherein the spatiotemporal sequence data includes at least two dependent variables with mutual feedback mechanisms and at least two covariates at the current time; after processing the spatiotemporal sequence data according to a preset processing method, constructing an independent variable matrix X and a dependent variable matrix Y; S2, training a preset GTWR-VAR model based on the independent variable matrix X and the dependent variable matrix Y, using a Bayesian optimization method, with the goal of minimizing the prediction error on the validation set, adaptively determining the optimal hyperparameter combination of the preset GTWR-VAR model, wherein the optimal hyperparameter combination includes lag order, spatial bandwidth, and temporal bandwidth; S3, running the preset GTWR-VAR model on a fully valid dataset based on the optimal hyperparameter combination, and for each spatiotemporal observation point, constructing a least squares model using composite Gaussian kernel weights, and solving the least squares model to obtain the local regression coefficient matrix for each spatiotemporal observation point. S4. Perform a Monte Carlo test on the local regression coefficient matrix for each spatiotemporal observation point to obtain the corresponding P-value. Empty the local regression coefficient matrix for those P-values ​​greater than or equal to the preset significance level to obtain the significance coefficient matrix. .

[0006] In one possible implementation of the first aspect, step S1 above involves acquiring spatiotemporal series data of multi-source geographic elements. The spatiotemporal series data includes at least two dependent variables with a mutual feedback mechanism and at least two covariates at the current time. After processing the spatiotemporal series data according to a preset processing method, an independent variable matrix X and a dependent variable matrix Y are constructed. Specifically, this includes:

[0007] S101. Loading and cropping: Acquire spatiotemporal sequence data of multi-source geographic elements and uniformly crop all spatiotemporal sequence data according to the spatial extent of the study area.

[0008] S102. Standardization: Perform standardization on all variables, including the dependent variable and covariates, with a mean of 0 and a standard deviation of 1.

[0009] S103. Deseasonalization: For each variable after standardization, subtract the climatological mean spatial field of its corresponding month to eliminate fixed seasonal periodic signals.

[0010] S104. Construct the basic independent variable matrix: Based on the lag order to be optimized, construct the basic independent variable matrix x, which contains the lag term of the dependent variable and the linear term of the covariate at the current time.

[0011] S105. Feature Enhancement: In the basic independent variable matrix x, nonlinear terms and interaction terms based on domain knowledge are introduced to enhance the model's ability to capture complex coupling relationships.

[0012] S106. Feature selection: When the number of enhanced independent variables exceeds the preset maximum number of features, a comprehensive scoring mechanism based on spatiotemporal variance and domain knowledge priority is adopted to select the preset number of features and generate an independent variable matrix X.

[0013] S107. Construct the dependent variable matrix: Construct the dependent variable matrix Y from at least two dependent variables that have a mutual feedback mechanism at the current moment.

[0014] Optionally, in another possible implementation of the first aspect, step S2 above, training the preset GTWR-VAR model based on the independent variable matrix X and the dependent variable matrix Y, and using a Bayesian optimization method to adaptively determine the optimal hyperparameter combination of the preset GTWR-VAR model with the goal of minimizing the prediction error on the validation set, specifically includes:

[0015] S201. Effective Data Slicing and Time Series Partitioning: Starting from the initial time point corresponding to the lag order, the independent variable matrix X and the dependent variable matrix Y are sliced ​​along the time axis into effective data blocks; the effective data blocks are divided into training set and validation set according to time order.

[0016] S202. Define the hyperparameter search space: Define the hyperparameter search space for Bayesian optimization. The hyperparameters include the candidate set of lag order, the continuous range of spatial bandwidth, and the continuous range of temporal bandwidth.

[0017] S203. Define the objective function: Define a fitness function that minimizes the prediction error on the validation set as the objective function; the calculation steps of the objective function include: running the preset GTWR-VAR model on the training set to obtain the coefficient matrix of the model at the last time step on the training set; using the coefficient matrix and the independent variable matrix of the validation set to calculate the predicted value of the dependent variable on the validation set; calculating the mean square error between the predicted value and the true value of the dependent variable on the validation set as the fitness value of the hyperparameter combination;

[0018] S204. Iterative optimization: Using a Gaussian process as a surrogate model, multiple hyperparameter combinations are selected iteratively based on the acquisition function for evaluation, and the surrogate model is updated until the preset number of iterations or convergence conditions are reached.

[0019] S205. Output optimal parameters: From all evaluated hyperparameter combinations, select the hyperparameter combination that minimizes the objective function value and determine it as the optimal hyperparameter combination. The optimal hyperparameter combination includes the optimal lag order, the optimal spatial bandwidth, and the optimal temporal bandwidth.

[0020] Optionally, in another possible implementation of the first aspect, step S3 above involves running a pre-defined GTWR-VAR model on the fully valid dataset based on the optimal hyperparameter combination, and constructing a least squares model for each spatiotemporal observation point using composite Gaussian kernel weights, and solving the least squares model to obtain the local regression coefficient matrix for each spatiotemporal observation point. Specifically, it includes:

[0021] S301. Construct the composite Gaussian kernel spatiotemporal weight matrix: For each spatiotemporal observation point i, perform the following operations: Calculate the spatial distance between this point and all other points in the fully valid dataset. and time distance Using the optimal spatial bandwidth and optimal temporal bandwidth, the spatial weight components and temporal weight components are calculated using the Gaussian kernel function, respectively. Multiplying the spatial weight components by the temporal weight components yields the composite Gaussian kernel spatiotemporal weight matrix W for the spatiotemporal observation point i. i ;

[0022] S302. Construct the design matrix with an intercept term: Add an intercept term to the independent variable matrix X for subsequent weighted least squares solution;

[0023] S303. Perform local weighted least squares calculation: For each spatiotemporal observation point i, use the spatiotemporal weight matrix W corresponding to S301. i The local regression coefficient vector at this point is solved using the following weighted least squares formula:

[0024]

[0025] in, This is a vector of local regression coefficients. Let X be the transpose of the independent variable matrix X;

[0026] S304, Integrated Local Coefficient Matrix: The local regression coefficient vector obtained by solving for all spatiotemporal observation points i The results are integrated to form a local regression coefficient matrix containing the coefficients of all points in the entire spatiotemporal domain. .

[0027] Optionally, in another possible implementation of the first aspect, step S4 above involves performing a Monte Carlo test on the local regression coefficient matrix for each spatiotemporal observation point to obtain the corresponding P-value, and then emptying the local regression coefficient matrix whose P-value is greater than or equal to a preset significance level to obtain the significance coefficient matrix. Specifically, it includes:

[0028] S401. Set the number of simulations and significance level: Set the number of Monte Carlo simulations to N, and set the preset significance level to α;

[0029] S402. Constructing the Null Hypothesis Dataset by Performing Block Permutations: Perform N simulations. In the k-th simulation, perform the following operations for each explanatory variable in the independent variable matrix X: Define each spatial grid point as an independent statistical block. Within each statistical block, independently and randomly shuffle the time series observations of that explanatory variable. After performing the above operations on all explanatory variables, a randomized explanatory variable matrix satisfying the null hypothesis is generated. Where k = 1, 2, ..., N;

[0030] S403. Calculate the set of random coefficients: Calculate the N randomized explanatory variable matrices generated in step S402. Using the same optimal hyperparameter combination as in step S3, run the preset GTWR-VAR model to obtain N corresponding stochastic local regression coefficient matrices. ;

[0031] S404. Calculate the P-value matrix: For the local regression coefficient matrix For the coefficients at each spatiotemporal point in the N simulations, perform the following operations: Statistically... The absolute value of the corresponding random coefficient Greater than the absolute value of the coefficient The number of times; divide this number by the number of simulations N, and calculate the P value of the local coefficient;

[0032] S405. Selecting Significance Coefficients and Generating the Final Result: Compare the P-values ​​obtained in step S404 with the significance level α. Set the local regression coefficients with P-values ​​greater than or equal to α to empty, and retain the significant coefficients with P-values ​​less than α, forming the final significance coefficient matrix. .

[0033] Beneficial Effects: This application provides a multi-factor collaborative change modeling method using geographic spatiotemporal weighted vector autoregression (GTWR). First, spatiotemporal sequence data of multi-source geographic elements are acquired. After processing the spatiotemporal sequence data according to a preset processing method, independent variable matrices X and dependent variable matrices Y are constructed. Then, a preset GTWR-VAR model is trained based on the independent variable matrix X and dependent variable matrix Y. A Bayesian optimization method is used, with the goal of minimizing the prediction error on the validation set, to adaptively determine the optimal hyperparameter combination of the preset GTWR-VAR model. Next, based on the optimal hyperparameter combination, the preset GTWR-VAR model is run on the full effective dataset. For each spatiotemporal observation point, a least squares model is constructed using composite Gaussian kernel weights. Solving the least squares model yields the local regression coefficient matrix for each spatiotemporal observation point. Finally, a Monte Carlo test was performed on the local regression coefficient matrix for each spatiotemporal observation point to obtain the corresponding P-value. Local regression coefficient matrices with P-values ​​greater than or equal to the preset significance level were then empty to obtain the significance coefficient matrix. This application reveals the continuous temporal and spatial variation patterns of the influence mechanisms among geographical elements, deepens the understanding of processes such as the regional water cycle, and provides more accurate and reliable scientific support for refined management, forecasting, and regional response research under climate change. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1This is a flowchart illustrating a multi-factor collaborative change modeling method based on geographic spatiotemporal weighted vector autoregression provided in an embodiment of this application;

[0036] Figure 2 This is a flowchart illustrating a multi-factor collaborative change modeling method based on geographic spatiotemporal weighted vector autoregression, provided in another embodiment of this application. Detailed Implementation

[0037] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0038] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0039] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0040] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0041] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0042] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0043] The following is a detailed description of a multi-factor collaborative change modeling method based on geographic spatiotemporal weighted vector autoregression provided in this application, with reference to the accompanying drawings.

[0044] Figure 1 The illustration shows a flowchart of a multi-factor collaborative change modeling method based on geographic spatiotemporal weighted vector autoregression provided in an embodiment of this application.

[0045] like Figure 1 As shown, this geographic spatiotemporal weighted vector autoregressive multi-factor collaborative change modeling method includes:

[0046] S1. Obtain spatiotemporal series data of multi-source geographic elements. The spatiotemporal series data includes at least two dependent variables with mutual feedback mechanisms and at least two covariates at the current time. After processing the spatiotemporal series data according to the preset processing method, construct the independent variable matrix X and the dependent variable matrix Y.

[0047] Furthermore, in this embodiment of the application, step S1 includes:

[0048] S101. Loading and cropping: Acquire spatiotemporal sequence data of multi-source geographic elements and uniformly crop all spatiotemporal sequence data according to the spatial extent of the study area.

[0049] S102. Standardization: Perform standardization on all variables, including the dependent variable and covariates, with a mean of 0 and a standard deviation of 1.

[0050] S103. Deseasonalization: For each variable after standardization, subtract the climatological mean spatial field of its corresponding month to eliminate fixed seasonal periodic signals.

[0051] S104. Construct the basic independent variable matrix: Based on the lag order to be optimized, construct the basic independent variable matrix x, which contains the lag term of the dependent variable and the linear term of the covariate at the current time.

[0052] S105. Feature Enhancement: In the basic independent variable matrix x, nonlinear terms and interaction terms based on domain knowledge are introduced to enhance the model's ability to capture complex coupling relationships.

[0053] S106. Feature selection: When the number of enhanced independent variables exceeds the preset maximum number of features, a comprehensive scoring mechanism based on spatiotemporal variance and domain knowledge priority is adopted to select the preset number of features and generate an independent variable matrix X.

[0054] S107. Construct the dependent variable matrix: Construct the dependent variable matrix Y from at least two dependent variables that have a mutual feedback mechanism at the current moment.

[0055] S2. The preset GTWR-VAR model is trained based on the independent variable matrix X and the dependent variable matrix Y. The Bayesian optimization method is used to adaptively determine the optimal hyperparameter combination of the preset GTWR-VAR model with the goal of minimizing the prediction error of the validation set. The optimal hyperparameter combination includes lag order, spatial bandwidth and temporal bandwidth.

[0056] Furthermore, in this embodiment of the application, step S2 includes:

[0057] S201. Effective Data Slicing and Time Series Partitioning: Starting from the initial time point corresponding to the lag order, the independent variable matrix X and the dependent variable matrix Y are sliced ​​along the time axis into effective data blocks; the effective data blocks are divided into training set and validation set according to time order.

[0058] S202. Define the hyperparameter search space: Define the hyperparameter search space for Bayesian optimization. The hyperparameters include the candidate set of lag order, the continuous range of spatial bandwidth, and the continuous range of temporal bandwidth.

[0059] S203. Define the objective function: Define a fitness function that minimizes the prediction error on the validation set as the objective function; the calculation steps of the objective function include: running the preset GTWR-VAR model on the training set to obtain the coefficient matrix of the model at the last time step on the training set; using the coefficient matrix and the independent variable matrix of the validation set to calculate the predicted value of the dependent variable on the validation set; calculating the mean square error between the predicted value and the true value of the dependent variable on the validation set as the fitness value of the hyperparameter combination;

[0060] S204. Iterative optimization: Using a Gaussian process as a surrogate model, multiple hyperparameter combinations are selected iteratively based on the acquisition function for evaluation, and the surrogate model is updated until the preset number of iterations or convergence conditions are reached.

[0061] S205. Output optimal parameters: From all evaluated hyperparameter combinations, select the hyperparameter combination that minimizes the objective function value and determine it as the optimal hyperparameter combination. The optimal hyperparameter combination includes the optimal lag order, the optimal spatial bandwidth, and the optimal temporal bandwidth.

[0062] S3. Based on the optimal hyperparameter combination, run the preset GTWR-VAR model on the full effective dataset, and for each spatiotemporal observation point, construct the least squares model through composite Gaussian kernel weights, and solve the least squares model to obtain the local regression coefficient matrix of each spatiotemporal observation point.

[0063] Furthermore, in this embodiment of the application, step S3 includes:

[0064] S301. Construct the composite Gaussian kernel spatiotemporal weight matrix: For each spatiotemporal observation point i, perform the following operations: Calculate the spatial distance between this point and all other points in the fully valid dataset. and time distance Using the optimal spatial bandwidth and optimal temporal bandwidth, the spatial weight components and temporal weight components are calculated using the Gaussian kernel function, respectively. Multiplying the spatial weight components by the temporal weight components yields the composite Gaussian kernel spatiotemporal weight matrix W for the spatiotemporal observation point i. i ;

[0065] S302. Construct the design matrix with an intercept term: Add an intercept term to the independent variable matrix X for subsequent weighted least squares solution;

[0066] S303. Perform local weighted least squares calculation: For each spatiotemporal observation point i, use the spatiotemporal weight matrix W corresponding to S301. i The local regression coefficient vector at this point is solved using the following weighted least squares formula:

[0067]

[0068] in, This is a vector of local regression coefficients. Let X be the transpose of the independent variable matrix X;

[0069] S304, Integrated Local Coefficient Matrix: The local regression coefficient vector obtained by solving for all spatiotemporal observation points i The results are integrated to form a local regression coefficient matrix containing the coefficients of all points in the entire spatiotemporal domain. .

[0070] S4. Perform a Monte Carlo test on the local regression coefficient matrix for each spatiotemporal observation point to obtain the corresponding P-value. Set the local regression coefficient matrix with a P-value greater than or equal to the preset significance level to empty to obtain the significance coefficient matrix.

[0071] Furthermore, in this embodiment of the application, step S4 includes:

[0072] S401. Set the number of simulations and significance level: Set the number of Monte Carlo simulations to N, and set the preset significance level to α;

[0073] S402. Constructing the Null Hypothesis Dataset by Performing Block Permutations: Perform N simulations. In the k-th simulation, perform the following operations for each explanatory variable in the independent variable matrix X: Define each spatial grid point as an independent statistical block. Within each statistical block, independently and randomly shuffle the time series observations of that explanatory variable. After performing the above operations on all explanatory variables, a randomized explanatory variable matrix satisfying the null hypothesis is generated. Where k = 1, 2, ..., N;

[0074] S403. Calculate the set of random coefficients: Calculate the N randomized explanatory variable matrices generated in step S402. Using the same optimal hyperparameter combination as in step S3, run the preset GTWR-VAR model to obtain N corresponding stochastic local regression coefficient matrices. ;

[0075] S404. Calculate the P-value matrix: For the local regression coefficient matrix For the coefficients at each spatiotemporal point in the N simulations, perform the following operations: Statistically... The absolute value of the corresponding random coefficient Greater than the absolute value of the coefficient The number of times; divide this number by the number of simulations N, and calculate the P value of the local coefficient;

[0076] S405. Selecting Significance Coefficients and Generating the Final Result: Compare the P-values ​​obtained in step S404 with the significance level α. Set the local regression coefficients with P-values ​​greater than or equal to α to empty, and retain the significant coefficients with P-values ​​less than α, forming the final significance coefficient matrix. .

[0077] The specific process of the multi-factor collaborative change modeling method based on geospatial-temporal weighted vector autoregression provided in this application is as follows: Figure 2 As shown.

[0078] This application provides a multi-factor collaborative change modeling method using geographic spatiotemporal weighted vector autoregression (GTWR). First, spatiotemporal sequence data of multi-source geographic elements are acquired. After processing the spatiotemporal sequence data according to a preset processing method, independent variable matrices X and dependent variable matrices Y are constructed. Then, a preset GTWR-VAR model is trained based on the independent variable matrix X and dependent variable matrix Y. A Bayesian optimization method is used to adaptively determine the optimal hyperparameter combination of the preset GTWR-VAR model, aiming to minimize the prediction error on the validation set. Next, based on the optimal hyperparameter combination, the preset GTWR-VAR model is run on the full valid dataset. For each spatiotemporal observation point, a least squares model is constructed using composite Gaussian kernel weights. The local regression coefficient matrix for each spatiotemporal observation point is obtained by solving the least squares model. Finally, a Monte Carlo test was performed on the local regression coefficient matrix for each spatiotemporal observation point to obtain the corresponding P-value. Local regression coefficient matrices with P-values ​​greater than or equal to the preset significance level were then empty to obtain the significance coefficient matrix. This application reveals the continuous temporal and spatial variation patterns of the influence mechanisms among geographical elements, deepens the understanding of processes such as the regional water cycle, and provides more accurate and reliable scientific support for refined management, forecasting, and regional response research under climate change.

[0079] The following specific embodiment illustrates the solution of this application.

[0080] The available data include ERA5-Land soil moisture data (depths of 0-7, 7-28, and 28-100 cm), actual evapotranspiration data from GLEAM, shortwave radiation data from ERA5, and precipitation data from MSWEP. The time range for this example is monthly data from 1982 to 1986, and the spatial range is a certain western province.

[0081] Step 1: Load soil moisture, actual evapotranspiration, and shortwave radiation data for the western province, and trim according to the province's boundaries. Perform linear weighting on multi-layered soil moisture (weights of 0.07, 0.21, and 0.72) to synthesize soil moisture data for a 1m soil column. Standardize all variables to a mean of 0 and a standard deviation of 1. Deseasonalize the standardized variables by subtracting the average spatial field of the corresponding month to separate seasonal cyclic signals, ensuring that subsequent model analysis focuses on spatiotemporal anomalies. Construct lag terms and build the basic independent variable matrix based on the determined lag order. This includes the lag term of the dependent variable ( , ), and the linear terms of the covariates precipitation (PRE) and surface shortwave radiation (SSRD) at the current time. Based on this, construct nonlinear features Used to capture soil saturation effect, interaction term This is used to capture the hydrothermal synergistic confinement effect of evapotranspiration (E) processes; As a trans-runoff regulation term, it is used to quantify the impact of soil moisture saturation on the conversion of current precipitation into stock. This is used to demonstrate the combined coupling effect of water and heat supply at the same lag time.

[0082] Step 2: Hybrid Model Structure and Bayesian Optimization. The independent and dependent variable matrices are sliced, and the sliced ​​dataset is strictly divided into a training set (80%) and a validation set (20%) according to time order. The model combines the multivariate feedback mechanism of Vector Autoregression (VAR) with the locality of Geospatial-Geoweighted Regression (GTWR) to calculate local regression coefficients. The hyperparameter search space and lag order are defined. Spatial bandwidth Time bandwidth Then, run the GTWR-VAR model on the training set and extract the coefficient matrix corresponding to the last time step from the coefficients obtained from the training set. . use Independent variables of the validation set Predict the dependent variable of the validation set ,calculate The weighted mean square error between the true value and the actual value ( ), as the objective function By using a Gaussian process proxy model and acquisition function, an iterative search is performed to minimize... Optimal combination of hyperparameters , To be the optimal lag order, For optimal spatial bandwidth This represents the optimal time bandwidth.

[0083] Step 3: Spatiotemporal weight construction: For each spatiotemporal observation point i, a Gaussian kernel function is used to construct the spatial weight W. S and time weight W T The spatial bandwidth and temporal bandwidth adopt the optimal parameter combination determined in step 2 above. The optimal spatial bandwidth and optimal temporal bandwidth are determined by W. S and W T Multiply to construct the composite Gaussian kernel spatiotemporal weight matrix W i Using optimal parameters In the fully valid dataset , The GTWR-VAR model is then run, and the final local regression coefficient matrix is ​​obtained at each spatiotemporal point. .

[0084] Step 4, Monte Carlo Significance Test and Result Screening: To assess the statistical significance of all local regression coefficients, 100 Monte Carlo simulations are performed. In each simulation, the statistical significance of the coefficients is evaluated. All independent variables in the model undergo spatial location block permutation, which independently and randomly shuffles the time series of the feature at each spatial grid point, thereby constructing a matrix of 100 randomized explanatory variables that satisfy the null hypothesis. (Where k = 1, 2, ..., 100). The calculation of the random coefficient set involves N randomized matrices. The optimal parameters determined in step 3 Next, the GTWR-VAR model was run, and N random coefficient matrices were obtained. (where k=1,2,…,N) forms a coefficient set, and calculations are performed based on the original... The obtained actual coefficient matrix Calculate the P-value of the local coefficient. The P-value is defined as the frequency at which the absolute value of the random coefficient is greater than or equal to the absolute value of the actual coefficient. Based on the preset significance level of 0.05, local regression coefficients with P values ​​greater than or equal to this significance level are set to null.

[0085] Step 5, Result Output and Storage, aims to standardize and save the rigorously tested and screened model results for easy subsequent analysis and application. NetCDF file format is output for each significance coefficient matrix after significance testing in step S4. It is then converted into a NetCDF (Network Common Data Form) file format with three dimensions: time, latitude, and longitude, for output.

[0086] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0087] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A multi-factor collaborative change modeling method based on geographic spatiotemporal weighted vector autoregression, characterized in that, Includes the following steps: S1. Obtain spatiotemporal sequence data of multi-source geographic elements. The spatiotemporal sequence data includes at least two dependent variables with mutual feedback mechanisms and at least two covariates at the current time. After processing the spatiotemporal sequence data according to a preset processing method, construct the independent variable matrix X and the dependent variable matrix Y. S2. The preset GTWR-VAR model is trained based on the independent variable matrix X and the dependent variable matrix Y. The Bayesian optimization method is used to adaptively determine the optimal hyperparameter combination of the preset GTWR-VAR model with the goal of minimizing the prediction error of the validation set. The optimal hyperparameter combination includes lag order, spatial bandwidth and temporal bandwidth. S3. Based on the optimal hyperparameter combination, run the preset GTWR-VAR model on the full valid dataset, and for each spatiotemporal observation point, construct a least squares model using composite Gaussian kernel weights, and solve the least squares model to obtain the local regression coefficient matrix for each spatiotemporal observation point. ; S4. Perform a Monte Carlo test on the local regression coefficient matrix for each spatiotemporal observation point to obtain the corresponding P-value. Empty the local regression coefficient matrix for those P-values ​​greater than or equal to the preset significance level to obtain the significance coefficient matrix. ; Step S2, training the preset GTWR-VAR model based on the independent variable matrix X and the dependent variable matrix Y, and using a Bayesian optimization method to adaptively determine the optimal hyperparameter combination of the preset GTWR-VAR model with the goal of minimizing the prediction error on the validation set, specifically includes: S201. Effective data slicing and time series partitioning: The independent variable matrix X and the dependent variable matrix Y are sliced ​​along the time axis from the starting time point corresponding to the lag order to form effective data blocks; the effective data blocks are divided into training set and validation set according to time order. S202. Define the hyperparameter search space: Define the hyperparameter search space for Bayesian optimization, wherein the hyperparameters include a candidate set of lag orders, a continuous range of values ​​for spatial bandwidth, and a continuous range of values ​​for temporal bandwidth. S203. Define the objective function: Define a fitness function that minimizes the prediction error of the validation set as the objective function; the calculation steps of the objective function include: running a preset GTWR-VAR model on the training set to obtain the coefficient matrix of the model at the last time step of the training set; using the coefficient matrix and the independent variable matrix of the validation set to calculate the predicted value of the dependent variable of the validation set; calculating the mean square error between the predicted value and the true value of the dependent variable of the validation set as the fitness value of the hyperparameter combination; S204. Iterative optimization: Using a Gaussian process as a surrogate model, multiple hyperparameter combinations are selected iteratively based on the acquisition function for evaluation, and the surrogate model is updated until the preset number of iterations or convergence conditions are reached. S205. Output optimal parameters: From all evaluated hyperparameter combinations, select the hyperparameter combination that minimizes the objective function value and determine it as the optimal hyperparameter combination. The optimal hyperparameter combination includes the optimal lag order, the optimal spatial bandwidth, and the optimal temporal bandwidth. In step S3, based on the optimal hyperparameter combination, the preset GTWR-VAR model is run on the full effective dataset. For each spatiotemporal observation point, a least squares model is constructed using composite Gaussian kernel weights, and the local regression coefficient matrix for each spatiotemporal observation point is obtained by solving the least squares model. Specifically, it includes: S301. Construct the composite Gaussian kernel spatiotemporal weight matrix: For each spatiotemporal observation point i, perform the following operations: Calculate the spatial distance between this point and all other points in the fully valid dataset. and time distance Using the optimal spatial bandwidth and optimal temporal bandwidth, the spatial weight components and temporal weight components are calculated using a Gaussian kernel function, respectively. The spatial weight components are multiplied by the temporal weight components to obtain the composite Gaussian kernel spatiotemporal weight matrix W for the spatiotemporal observation point i. i ; S302. Construct a design matrix with an intercept term: Add an intercept term to the independent variable matrix X for subsequent weighted least squares solution; S303. Perform local weighted least squares calculation: For each spatiotemporal observation point i, use the spatiotemporal weight matrix W corresponding to S301. i The local regression coefficient vector at this point is solved using the following weighted least squares formula: ； in, This is a vector of local regression coefficients. Let X be the transpose of the independent variable matrix X; S304, Integrated Local Coefficient Matrix: The local regression coefficient vector obtained by solving for all spatiotemporal observation points i The results are integrated to form a local regression coefficient matrix containing the coefficients of all points in the entire spatiotemporal domain. .

2. The method according to claim 1, characterized in that, Step S1 involves acquiring spatiotemporal series data of multi-source geographic elements. This spatiotemporal series data includes at least two dependent variables with a mutual feedback mechanism and at least two covariates for the current time. After processing the spatiotemporal series data according to a preset processing method, an independent variable matrix X and a dependent variable matrix Y are constructed. Specifically, this includes: S101. Loading and cropping: Acquire spatiotemporal sequence data of multi-source geographic elements and uniformly crop all spatiotemporal sequence data according to the spatial extent of the study area. S102. Standardization: Perform standardization on all variables, including the dependent variable and covariates, with a mean of 0 and a standard deviation of 1. S103. Deseasonalization: For each variable after standardization, subtract the climatological mean spatial field of its corresponding month to eliminate fixed seasonal periodic signals. S104. Construct the basic independent variable matrix: Based on the lag order to be optimized, construct the basic independent variable matrix x, where x contains the lag term of the dependent variable and the linear term of the covariate at the current time. S105. Feature Enhancement: In the basic independent variable matrix x, nonlinear terms and interaction terms based on domain knowledge are introduced to enhance the model's ability to capture complex coupling relationships. S106. Feature selection: When the number of enhanced independent variables exceeds the preset maximum number of features, a comprehensive scoring mechanism based on spatiotemporal variance and domain knowledge priority is adopted to select a preset number of features and generate the independent variable matrix X. S107. Construct the dependent variable matrix: Construct the dependent variable matrix Y from at least two dependent variables that have a mutual feedback mechanism at the current moment.

3. The method according to claim 2, characterized in that, In step S4, a Monte Carlo test is performed on the local regression coefficient matrix for each spatiotemporal observation point to obtain the corresponding P-value. Local regression coefficient matrices with P-values ​​greater than or equal to a preset significance level are then empty to obtain the significance coefficient matrix. Specifically, it includes: S401. Set the number of simulations and significance level: Set the number of Monte Carlo simulations to N, and set the preset significance level to α; S402. Constructing the Null Hypothesis Dataset by Performing Block Permutation: Perform N simulations. In the k-th simulation, perform the following operations for each explanatory variable in the independent variable matrix X: Define each spatial grid point as an independent statistical block; within each statistical block, independently and randomly shuffle the time-series observations of that explanatory variable; after performing the above operations on all explanatory variables, generate a randomized explanatory variable matrix that satisfies the null hypothesis. Where k = 1, 2, ..., N; S403. Calculate the set of random coefficients: Calculate the N randomized explanatory variable matrices generated in step S402. Using the same optimal hyperparameter combination as in step S3, the preset GTWR-VAR model is run to obtain N corresponding stochastic local regression coefficient matrices. ; S404. Calculate the P-value matrix: For the local regression coefficient matrix... For the coefficients at each spatiotemporal point in the N simulations, perform the following operations: Statistically... The absolute value of the corresponding random coefficient Greater than the absolute value of the coefficient The number of times; divide this number by the number of simulations N, and calculate the P value of the local coefficient; S405. Filtering Significance Coefficients and Generating the Final Result: Compare the P-values ​​obtained in step S404 with the significance level α. Set the local regression coefficients with P-values ​​greater than or equal to α to empty, and retain the significant coefficients with P-values ​​less than α, forming the final significance coefficient matrix. .

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