A hierarchical isometric quadtree and bayesian-based urban expansion early warning method and system

Abstract

The application discloses a kind of based on layered equal-area quadtree and bayesian town expansion early warning method and system, method includes: obtaining multi-source physical space data;Dynamic reconstruction grid is constructed and recursive hierarchical feature tensor is extracted;Calculate the purity index of dominant ground object in each base spherical surface element, when the index is lower than the preset purity threshold, trigger HPQT recursive split instruction;Characteristic tensor and spatial driving factor are input into multi-scale space regression model, and the local curvature iteration along the objective function is obtained using approximate hessian matrix or hessian-vector product, obtain spatial response bandwidth and regression parameter;Regression parameter is input as prior into the bayesian hierarchical model of tree topology, and spatial information is borrowed;Red line breakthrough probability is evaluated using sampling, and early warning instruction is generated to drive terminal screen to render high-risk layer rendering.The application eliminates the error of cross-scale data deformation, significantly improves the computer operation efficiency and system robustness.

Description

Technical Field

[0001] This invention relates to the field of spatial data processing and geographic information system underlying architecture technology, specifically to a town expansion early warning method and system based on hierarchical equal-area quadtree and Bayesian methods. Background Technology

[0002] With the development of smart city infrastructure and Geographic Information System (GIS) technology, the accurate processing and high-level early warning of urban spatial expansion data have become core application scenarios for spatial physical resource computing. Among these, utilizing computer systems to process massive amounts of remote sensing image patches and high-precision population raster data to calculate "urban expansion characteristic indicators" (such as expansion multiples) is fundamental to achieving automated spatial early warning. However, existing computer spatial data processing systems face three significant computing system bottlenecks in their underlying data architecture and computing power scheduling when dealing with cross-level, large-scale, and multi-source heterogeneous physical spatial data: (1) Data distortion and computational overhead caused by traditional physical projection grids: When processing large-scale or high-latitude spherical geographic data, existing GIS underlying layers mostly use traditional latitude and longitude grids or planar projections (such as Gauss-Kruger projection) for data storage and gridding mapping. This static underlying data structure cannot guarantee the consistency of the actual physical area of ​​the surface cells in different spatial locations, and will produce serious physical area distortion during memory conversion.

[0003] (2) Data structure conflicts and output drift caused by the Variable Surface Up (MAUP) problem: Feature extraction of spatial data is highly dependent on the aggregation units allocated in computer memory. When there is a lack of a grid dynamic adaptive reconstruction mechanism that is immune to scale effects, the calculation results at different resolution levels often produce serious logical conflicts and data inconsistencies.

[0004] (3) Matrix singularity and system computing power overload risk in extreme sparsity environment: In local data extreme sparsity regions (such as strictly controlled "ecological data vacuum" areas), traditional models are prone to matrix singularity (Ill-conditioned Matrix) when constructing local feature matrices due to the lack of cross-grid information regularization constraints, which leads to the explosion of underlying computational variance and in turn causes division by zero error, memory overflow (OOM) or abnormal program crash.

[0005] Therefore, the industry urgently needs to develop a spatial data processing and rendering early warning architecture that can start from the underlying physical data structure reconstruction, endogenously suppress data deformation and MAUP effect, significantly reduce the computing power overhead of processing massive feature data, and maintain stable system memory scheduling even under extremely sparse data distribution. Summary of the Invention

[0006] The purpose of this invention is to provide a town expansion early warning method and system based on hierarchical equal-area quadtree and Bayesian methods, so as to achieve high-efficiency, low-computational-cost, and robust physical space entity early warning rendering.

[0007] To achieve the above objectives, the present invention provides the following technical solution: In a first aspect, the present invention provides a town expansion early warning method based on hierarchical equal-area quadtrees and Bayesian methods, comprising: Acquire multi-source physical space data, unify the spatial alignment of the multi-source physical space data, and load it into the underlying memory coordinate system of the computer device; Based on the theory of hierarchical spherical coordinate system, the purity index of dominant features of basic surface elements in the bottom layer memory is calculated; when the purity index of dominant features is lower than the preset purity threshold, the hierarchical equal-area quadtree instruction is called in the computer memory for recursive segmentation, and the tree memory index of the hierarchical equal-area quadtree is managed by Z-order one-dimensional encoding path, the retrieval of adjacent surface elements in two-dimensional space is transformed into pointer offset of one-dimensional array, the reconstructed mesh is dynamically constructed and the recursive level feature tensor is extracted. The feature tensor and physical space driving factors are loaded into the multi-scale spatial regression model to quantify the local uncertainty of the input features to perform dynamic weight calibration; the model loss function is constructed, and the Hessian-vector product or approximate Hessian matrix of the loss function is obtained based on the computer automatic differentiation engine to avoid memory overflow, and the deloading optimization iteration is performed along the local curvature gradient direction to obtain the spatial regression parameters. The spatial regression parameters are used as a prior distribution, and the tree memory index of the hierarchical equal-area quadtree is directly reused as the parameter transfer topology of the Bayesian hierarchical model. The macroscopic parameter constraints are executed from top to bottom along the vertical pointer path of the tree topology, and data regularization shrinkage is provided to the local extreme sparse grid to block the system anomalies caused by the singularity of the underlying computation matrix. The risk probability distribution of breaching the extended red line within the reconstructed mesh is evaluated based on the constrained Bayesian hierarchical model. When the probability is greater than the warning threshold, a rendering control instruction carrying three-dimensional physical space coordinates is generated, and the graphics card rendering pipeline is dynamically scheduled to drive the terminal screen to display the highlighted risk layer.

[0008] Furthermore, the multi-source physical space data includes remote sensing image data of physical urban land use patch characteristics in the target study area, population density raster data calculated based on mobile terminal signaling, and a set of physical space driving factors including road network density and terrain slope.

[0009] Furthermore, the dynamic construction and reconstruction of the mesh and extraction of the recursive hierarchical feature tensor specifically includes: when the purity index of the dominant feature within the basic spherical element is lower than the preset purity threshold and the current subdivision resolution has not reached the preset maximum physical level, the basic spherical element is divided into 4 sub-elements with equal volume and this process is repeated cyclically; the recursive hierarchical feature tensor is a three-dimensional tensor. Where N is the number of facets, C is the number of feature channels, L is the mesh depth level of the current node, and the tensor contains the purity variance information of the child nodes.

[0010] Furthermore, the local uncertainty of the quantized input features is used to perform dynamic weight calibration, specifically including: For target element i in the reconstructed mesh, calculate the normalized information contribution of the k-th physical space driving factor in the local topological neighborhood. Using Shannon's information entropy formula Quantify the uncertainty of this factor in the local physical space; based on the Shannon information entropy. Perform feature recalibration: assign weight gain to factors with entropy values ​​below a preset deterministic threshold, and assign weight decay to factors with entropy values ​​above a preset noise threshold.

[0011] Furthermore, the construction of the model loss function, based on a computer automatic differentiation engine, obtains the Hessian-vector product or approximate Hessian matrix of the loss function to avoid memory overflow, and performs load reduction optimization iterations along the local curvature gradient direction, specifically including: Construct a model loss function with the goal of correcting the Akaike Information Criterion (AICC); The gradient vector of the AICC model loss function with respect to the spatial response bandwidth vector b is obtained by analytical differentiation. AICC and Hessian-vector product (HVP) or approximate Hessian matrix; Using the modified Newton's method iterative formula Perform load reduction iterative calculations, where t is the current iteration number, η is the preset learning step size, and Hess... 1 is the inverse of the approximate Hessian matrix.

[0012] Furthermore, the execution of top-down macroscopic parameter constraints specifically includes: Using hierarchical transfer distribution to expand the parameters of the lower high-resolution submesh Subject to the prior parameters of its upper-level macroscopic parent node The constraints follow a distribution , where τ 2 For prior variance; Through the expected formula Perform parameter updates, where These are parameter estimates based on local observation data. The weights are determined by the quality of the data within the grid. The weight Local observation sample size based on microgrid Or local estimation of variance Dynamic calculation, set as When local extreme values ​​are scarce, it leads to hour, This forces the underlying parameters to converge to the macroscopic first acceptance.

[0013] Secondly, the present invention provides a town expansion early warning system based on hierarchical quadtrees and Bayesian methods, used to implement the aforementioned town expansion early warning method based on hierarchical quadtrees and Bayesian methods, comprising: The multi-source data mapping and loading module is used to acquire multi-source physical space data and load the multi-source physical space data into the underlying memory coordinate system of the computer device with unified spatial alignment. The equal-area grid reconstruction and feature extraction module is used to calculate the dominant feature purity index of the basic spherical element based on the hierarchical spherical coordinate system theory. When the dominant feature purity index is lower than the preset purity threshold, the hierarchical equal-area quadtree instruction is called to perform recursive segmentation, and the tree memory index is managed by Z-order one-dimensional encoding path. The reconstructed grid with immune projection deformation and physical area equivalence is dynamically constructed and the recursive hierarchical feature tensor is extracted. The multi-scale response optimization and deloading module is used to load the recursive hierarchical feature tensor and physical space driving factors into the multi-scale spatial regression model, quantify the local uncertainty of the input features to perform dynamic weight calibration, obtain the Hessian-vector product or approximate Hessian matrix based on the automatic differentiation engine, and perform deloading optimization iteration along the local curvature direction to obtain spatial regression parameters. The nested tree-structured prior anomaly prevention module is used to take the spatial regression parameters as the initial prior distribution, reuse the tree memory index of the hierarchical equal-area quadtree as the parameter transfer topology of the Bayesian hierarchical model, execute macroscopic parameter constraints from top to bottom along the vertical pointer path, provide data regularization shrinkage to the local extreme sparse grid, and prevent the singularity and division-by-zero anomaly of the underlying computation matrix. The terminal rendering and output module is used to evaluate the risk probability distribution of breaching the urban expansion red line based on the constrained model. When the risk probability is greater than the preset risk warning threshold, it generates rendering control instructions with three-dimensional physical space coordinates and dynamically schedules the graphics card rendering pipeline to drive the terminal screen to display the highlighted risk layer.

[0014] Thirdly, the present invention provides an electronic device, including a processor and a memory, wherein computer instructions are stored in the memory, and the processor is used to execute the computer instructions stored in the memory to implement the steps of the town expansion early warning method based on hierarchical equal-area quadtree and Bayesian.

[0015] Fourthly, the present invention provides a computer-readable storage medium storing computer instructions for causing a computer to perform the steps of the town expansion early warning method based on hierarchical equal-area quadtrees and Bayesian methods.

[0016] Based on the above technical solution, the embodiments of the present invention can produce at least the following technical effects: (1) Reconstructing the underlying data structure to eliminate projection distortion and compensate for computational power loss. This invention improves upon traditional static two-dimensional planar meshes such as Gauss-Kruger and innovatively constructs a dynamic underlying data structure based on the HEALPix basis and hierarchical equal-area quadtree (HPQT) in computer memory. This structure fundamentally achieves absolute physical area equivalence ("shape-based") during large-scale cross-region mapping, completely avoiding the massive CPU nonlinear error compensation calculations and resampling I / O operations frequently invoked by the computer to correct distortion during subsequent spatial feature extraction and aggregation. This significantly improves the reading, writing, and processing efficiency of the underlying data and endogenously overcomes the MAUP effect.

[0017] (2) Introducing Hessian matrix to perceive curvature, achieving optimization load reduction and superlinear convergence. Addressing the bottleneck of traditional spatial regression models (such as standard MGWR) in large-scale multidimensional feature analysis, which easily leads to an exponential increase in server computational load due to reliance on first-order step blind search (such as the golden section method), this invention introduces analytical second-order Hessian matrix technology at the system level. The algorithm enables the computer to accurately perceive the local curvature of the hypersurface of the high-dimensional objective function, guiding the optimization path along the optimal gradient descent, achieving superlinear convergence of multi-scale bandwidth optimization while ensuring the accuracy of heterogeneous feature decoupling. This significantly reduces the optimization time of the million-level surface model by approximately 40%, greatly reducing the hardware computational load under high-concurrency geospatial computing.

[0018] (3) Constructing endogenous regularization fault tolerance to effectively prevent memory crashes in extreme value regions. When dealing with extremely sparse data distributions in strictly restricted areas (such as the edge of ecological red lines), traditional regression matrix operations often result in the phenomenon of "data vacuum" leading to the invertibility of the design matrix (Ill-conditioned Matrix), causing variance explosion, division by zero anomalies, or even system crashes (OOM). This invention creatively binds the "contraction effect" of Bayesian inference to the underlying logic of the HPQT pure mathematical tree topology of the physical grid. When the bottom-level nodes encounter extreme sparsity, the vertical and horizontal "information borrowing" mechanism constructed by the system is like equipping them with a powerful earthquake-resistant "hydraulic damper," automatically retrieving stable priors from the parent node or neighborhood for smooth constraints. This constitutes a powerful algorithm-level fault tolerance backstop mechanism, ensuring the absolute stability of system memory scheduling and the robustness of early warning output under extreme input distributions.

[0019] (4) Breaking away from pure data inference, achieving end-to-end physical rendering closed-loop control. This invention breaks through the limitations of traditional monitoring algorithms that only output isolated, rigid values ​​that are prone to scale contradictions. The system directly converts the noise-reduced full probability posterior inference results into computer-level UI control signals with spatial coordinate orientation. When the evaluated probability exceeds the safety threshold, the system automatically triggers hard instructions to drive the screen rendering module of the terminal physical display device, outputting a high-resolution intuitive early warning layer, forming a complete data control link from "bottom-level massive data intake" to "hardware efficient load reduction processing" and then to "terminal physical visual output", thus opening up the machine collaborative decision-making closed loop of smart land management. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, 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 the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0021] Figure 1 This is a flowchart illustrating the system architecture and physical hardware interaction provided in the embodiments of the present invention. Figure 2 This is a schematic diagram illustrating the underlying data structure mapping principle of the physical reconstruction mesh, one-dimensional memory addressing, and nested anomaly prevention topology of this invention. Detailed Implementation

[0022] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. In addition, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0023] Example 1 like Figure 1 and Figure 2 As shown, this embodiment provides a town expansion early warning method based on hierarchical equal-area quadtree and Bayesian methods, executed by a computer device. The method includes the following steps: Step S1: Obtain multi-source physical space data, map the multi-source physical space data in a unified manner, and load it into the underlying memory coordinate system of the computer system.

[0024] In this embodiment, the multi-source physical space data includes remote sensing image data of physical urban land patch characteristics of the target study area, population density raster data calculated based on mobile terminal signaling, and a set of physical space driving factors including road network density, terrain slope, etc.

[0025] It should be noted that the underlying computer hardware environment relied upon in this embodiment can be configured as a hardware and software collaborative system including a multi-core CPU, a high-performance graphics card, a large-capacity high-speed running memory (RAM), and a graphics display terminal device. First, the data acquisition module acquires 30-meter resolution full-coverage remote sensing image data of land cover entities in the target study area for the planning base year and the current monitoring year. The computer equipment loads the multi-source physical data into the underlying running memory of the computing nodes through the underlying geocoding engine.

[0026] Step S2: Based on the theory of hierarchical spherical coordinate system, calculate the dominant feature purity index of the basic surface elements in the bottom layer memory; when the dominant feature purity index is lower than the preset purity threshold, call the hierarchical equal-area quadtree HPQT instruction in the computer memory for recursive segmentation, and use Z-order one-dimensional encoding path to manage the tree memory index of the HPQT, transforming the retrieval of adjacent surface elements in two-dimensional space into pointer offset of one-dimensional array, dynamically constructing a reconstructed mesh that is immune to projection deformation and physically equivalent in area; simultaneously, based on the hierarchical depth and spatial topology of the recursive segmentation nodes, extract the recursive hierarchical feature tensor representing the local physical spatial distribution pattern. The recursive hierarchical feature tensor is a three-dimensional tensor. Where N is the number of facets, C is the number of feature channels, L is the mesh depth level of the current node, and the tensor contains the purity variance information of the child nodes.

[0027] It should be noted that, in order to completely eliminate the large-scale grid area distortion and error compensation computational power loss caused by traditional planar 2D projection, this embodiment uses a hierarchical equal-area equal-dimensional pixelation (HEALPix) substrate for reconstruction. The initial spatial resolution is set as the base spherical element (e.g., Nside=16). The computer's low-level processor traverses each base element and calculates the dominant feature purity index. When the feature purity index is lower than a preset purity threshold (e.g., P<0.85) and has not reached the maximum hardware memory partitioning level (e.g., Nside=1024), the system sends a dynamic allocation partitioning instruction to memory, precisely subdividing it into four absolutely equal-area physical sub-elements.

[0028] It should be noted that during the dynamic mesh reconstruction process, the system employs NESTED (Z-order) one-dimensional encoded path management for HPQT's tree-structured memory index. This mechanism transforms the complex mesh retrieval of adjacent facets in two-dimensional space into pointer offsets in a one-dimensional array, significantly reducing the time complexity of computer memory addressing. The extracted feature tensors are pushed into a high-speed video memory queue for downstream use.

[0029] Step S3: Load the recursive hierarchical feature tensor and physical space driving factor set extracted in step S2 into a multi-scale spatial regression model (such as an adaptive information entropy multi-scale geographic weighted model), quantify the local uncertainty of the input features to perform dynamic weight calibration; construct the model loss function, obtain the Hessian-vector product (HVP) or approximate Hessian matrix of the loss function based on the computer automatic differentiation engine to avoid memory overflow, and perform deloading optimization iteration along the local curvature gradient direction to obtain the optimal spatial response bandwidth and corresponding spatial regression parameters of each factor.

[0030] It should be noted that, for each HPQT reconstructed surface element i, the normalized information contribution of the k-th physical space driving factor in the local topological neighborhood is calculated. And strictly apply Shannon's information entropy formula. To measure the uncertainty of features, weight gain is assigned to deterministic factors with low entropy. A model loss function targeting AICC is constructed. To address the risk of memory explosion (OOM) caused by the Hessian matrix in high-dimensional arrays with millions of surface elements, the GPU utilizes the Hessian-Vector Product (HVP) technique based on automatic differentiation or the L-BFGS quasi-Newton method to approximate the inversion of the Hessian matrix. 1 We utilize the modified Newton's method iterative formula to optimize the load reduction of the underlying hardware. This enables the optimization path to achieve superlinear convergence along the local curvature of the hypersurface of the objective function.

[0031] Step S4: Using the spatial regression parameters output in step S3 as the initial prior distribution, directly reuse the tree-shaped memory index of HPQT as the parameter transfer topology of the Bayesian hierarchical model (BHM); along the vertical pointer path of the tree topology, perform top-down macroscopic parameter constraints, and provide data regularization shrinkage to the local extreme sparse grid to block system anomalies caused by the singularity of the underlying computation matrix.

[0032] It should be noted that, in response to the design matrix singularity (Ill-conditioned Matrix) and the risk of division-by-zero errors caused by extreme sparse regions (data vacuum areas) such as ecological edges, the system executes the underlying spatial regularization mechanism and calls the expected shrinkage formula: Through weight This forces the parameters of the lower-level micro-units to be forced to conform to the macroscopic prior parameters of the parent node under extreme conditions. Contraction. The weight wi mentioned here is based on the local observation sample size of the microgrid. Or local estimation of variance Dynamic calculation, for example, specifically set as (where τ) 2 (For prior variance). When local extrema are sparse, leading to... hour, This approach forces the underlying parameters to converge to macroscopic priors, preventing division-by-zero overflow at the algorithm level. At the computer's underlying implementation, each HPQT node is allocated a structure in memory containing a `parent_ptr` (a pointer to the parent node). Step S4 does not require rebuilding the time-complexity spatial adjacency network; the underlying algorithm simply calls the prior parameters in the parent register directly along the `parent_ptr` address pointer. This hard binding of the algorithm's topology to the memory index achieves extremely low-latency information borrowing.

[0033] Step S5: The computer invokes a parallel Hamiltonian Monte Carlo (HMC) sampler to evaluate the joint posterior probability of each reconstructed surface element breaking through the preset red line. When the evaluation shows that the probability of a certain reconstructed surface element breaking through is greater than the preset risk warning threshold, the system generates a hardware interrupt control instruction to drive the external physical display screen to render a risk layer with a bright red flashing effect.

[0034] In a comparative verification process involving 15-megapixel pixels in a certain city, the traditional blind search MGWR system crashed and malfunctioned (OOM) at step 4 due to memory peaks (>64GB) triggered by calculating the Hessian matrix. By employing the HVP load reduction combined with BHM topology nesting introduced in this invention, the CPU's single-round optimization time was reduced by 82%, the system's peak memory usage remained stable within 14.2GB, and there were no abnormal crashes throughout the process. Simultaneously, thanks to Z-order one-dimensional addressing, memory I / O retrieval time decreased by approximately 75%.

[0035] Example 2 This embodiment provides a town expansion early warning system based on hierarchical equal-area quadtrees and Bayesian methods, including: The multi-source data mapping and loading module is used to acquire multi-source physical space data and load the multi-source physical space data into the underlying memory coordinate system of the computer device with unified spatial alignment. The equal-area grid reconstruction and feature extraction module is used to calculate the dominant feature purity index of the basic surface element based on the hierarchical spherical coordinate system theory. When the dominant feature purity index is lower than the preset purity threshold, the HPQT instruction is called to perform recursive segmentation, and the Z-order one-dimensional encoding path is used to manage the tree memory index, dynamically construct the reconstructed grid and extract the recursive level feature tensor. The multi-scale response optimization and deloading module is used to load the feature tensor and physical space driving factors into the multi-scale spatial regression model, quantify the local uncertainty of the input features to perform dynamic weight calibration, obtain the Hessian-vector product (HVP) or approximate Hessian matrix based on the automatic differentiation engine, and perform deloading optimization iteration along the local curvature direction to obtain spatial regression parameters. The nested tree-structured prior anomaly prevention module is used to take the spatial regression parameters as the prior distribution, reuse the tree-structured memory index of HPQT as the parameter transfer topology of the Bayesian hierarchical model, execute top-down macroscopic parameter constraints along the vertical pointer path, provide data regularization shrinkage to the local extreme sparse grid, and prevent the singularity and division-by-zero anomaly of the underlying computation matrix. The terminal rendering and output module is used to evaluate the risk probability distribution of exceeding the extended red line based on the constrained model; when the probability is greater than the preset risk warning threshold, it generates rendering control instructions with three-dimensional physical space coordinates and dynamically schedules the graphics card rendering pipeline to drive the terminal screen to perform visualization output of the highlighted risk layer.

[0036] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A town expansion early warning method based on hierarchical equal-area quadtree and Bayesian methods, characterized in that, include: Acquire multi-source physical space data, unify the spatial alignment of the multi-source physical space data, and load it into the underlying memory coordinate system of the computer device; Based on the theory of hierarchical spherical coordinate system, the purity index of dominant features of basic surface elements in the bottom layer memory is calculated; when the purity index of dominant features is lower than the preset purity threshold, the hierarchical equal-area quadtree instruction is called in the computer memory for recursive segmentation, and the tree memory index of the hierarchical equal-area quadtree is managed by Z-order one-dimensional encoding path, the retrieval of adjacent surface elements in two-dimensional space is transformed into pointer offset of one-dimensional array, the reconstructed mesh is dynamically constructed and the recursive level feature tensor is extracted. The feature tensor and physical space driving factors are loaded into the multi-scale spatial regression model to quantify the local uncertainty of the input features to perform dynamic weight calibration; the model loss function is constructed, and the Hessian-vector product or approximate Hessian matrix of the loss function is obtained based on the computer automatic differentiation engine to avoid memory overflow, and the deloading optimization iteration is performed along the local curvature gradient direction to obtain the spatial regression parameters. The spatial regression parameters are used as a prior distribution, and the tree memory index of the hierarchical equal-area quadtree is directly reused as the parameter transfer topology of the Bayesian hierarchical model. The macroscopic parameter constraints are executed from top to bottom along the vertical pointer path of the tree topology, and data regularization shrinkage is provided to the local extreme sparse grid to block the system anomalies caused by the singularity of the underlying computation matrix. The risk probability distribution of breaching the extended red line within the reconstructed grid is evaluated based on the constrained Bayesian hierarchical model. When the probability exceeds the warning threshold, a rendering control command carrying three-dimensional physical space coordinates is generated, and the graphics card rendering pipeline is dynamically scheduled to drive the terminal screen to display the high-risk layer.

2. The town expansion early warning method based on hierarchical equal-area quadtree and Bayesian methods according to claim 1, characterized in that, The multi-source physical space data includes remote sensing image data of urban land patch characteristics in the target study area, population density raster data calculated based on mobile terminal signaling, and a set of physical space driving factors including road network density and terrain slope.

3. The town expansion early warning method based on hierarchical equal-area quadtree and Bayesian method according to claim 1, characterized in that, The dynamic construction and reconstruction of the mesh and extraction of recursive hierarchical feature tensors specifically includes: When the purity index of the dominant feature within the basic spherical element is lower than the preset purity threshold and the current subdivision resolution has not reached the preset maximum physical level, the basic spherical element is divided into 4 sub-elements with equal volume and the process is repeated cyclically; the recursive hierarchical feature tensor is a three-dimensional tensor. Where N is the number of facets, C is the number of feature channels, L is the mesh depth level of the current node, and the tensor contains the purity variance information of the child nodes.

4. The town expansion early warning method based on hierarchical equal-area quadtree and Bayesian method according to claim 1, characterized in that, The local uncertainty of the quantized input features is used to perform dynamic weight calibration, specifically including: For target element i in the reconstructed mesh, calculate the normalized information contribution of the k-th physical space driving factor in the local topological neighborhood. Using Shannon's information entropy formula Quantify the uncertainty of this factor in the local physical space; based on the Shannon information entropy. Perform feature recalibration: assign weight gain to factors with entropy values ​​below a preset deterministic threshold, and assign weight decay to factors with entropy values ​​above a preset noise threshold.

5. The urban expansion early warning method based on hierarchical equal-area quadtree and Bayesian methods according to claim 1, characterized in that, The construction of the model loss function, based on a computer automatic differentiation engine, obtains the Hessian-vector product or approximate Hessian matrix of the loss function to avoid memory overflow, and performs load reduction optimization iterations along the local curvature gradient direction, specifically including: Construct a model loss function with the goal of correcting the Akaike Information Criterion (AICC); The gradient vector of the AICC model loss function with respect to the spatial response bandwidth vector b is obtained by analytical differentiation. AICC and Hessian-vector product (HVP) or approximate Hessian matrix; Using the modified Newton's method iterative formula Perform load reduction iterative calculations, where t is the current iteration number, η is the preset learning step size, and Hess... 1 is the inverse of the approximate Hessian matrix.

6. The town expansion early warning method based on hierarchical equal-area quadtree and Bayesian method according to claim 1, characterized in that, The execution of top-down macroscopic parameter constraints specifically includes: Using hierarchical transfer distribution to expand the parameters of the lower high-resolution submesh Subject to the prior parameters of its upper-level macroscopic parent node The constraints follow a distribution , where τ 2 For prior variance; Through the expected formula Perform parameter updates, where These are parameter estimates based on local observation data. The weights are determined by the quality of the data within the grid. The weight Local observation sample size based on microgrid Or local estimation of variance Dynamic calculation, set as When local extreme values ​​are scarce, it leads to hour, This forces the underlying parameters to converge to the macroscopic first acceptance.

7. A town expansion early warning system based on hierarchical quadtrees and Bayesian methods, used to implement the town expansion early warning method based on hierarchical quadtrees and Bayesian methods as described in any one of claims 1-6, characterized in that, include: The multi-source data mapping and loading module is used to acquire multi-source physical space data and load the multi-source physical space data into the underlying memory coordinate system of the computer device with unified spatial alignment. The equal-area grid reconstruction and feature extraction module is used to calculate the dominant feature purity index of the basic spherical element based on the hierarchical spherical coordinate system theory. When the dominant feature purity index is lower than the preset purity threshold, the hierarchical equal-area quadtree instruction is called to perform recursive segmentation, and the tree memory index is managed by Z-order one-dimensional encoding path. The reconstructed grid with immune projection deformation and physical area equivalence is dynamically constructed and the recursive hierarchical feature tensor is extracted. The multi-scale response optimization and deloading module is used to load the recursive hierarchical feature tensor and physical space driving factors into the multi-scale spatial regression model, quantify the local uncertainty of the input features to perform dynamic weight calibration, obtain the Hessian-vector product or approximate Hessian matrix based on the automatic differentiation engine, and perform deloading optimization iteration along the local curvature direction to obtain spatial regression parameters. The nested tree-structured prior anomaly prevention module is used to take the spatial regression parameters as the initial prior distribution, reuse the tree memory index of the hierarchical equal-area quadtree as the parameter transfer topology of the Bayesian hierarchical model, execute macroscopic parameter constraints from top to bottom along the vertical pointer path, provide data regularization shrinkage to the local extreme sparse grid, and prevent the singularity and division-by-zero anomaly of the underlying computation matrix. The terminal rendering and output module is used to evaluate the risk probability distribution of breaching the urban expansion red line based on the constrained model. When the risk probability is greater than the preset risk warning threshold, it generates rendering control instructions with three-dimensional physical space coordinates and dynamically schedules the graphics card rendering pipeline to drive the terminal screen to display the highlighted risk layer.

8. An electronic device comprising a processor and a memory, characterized in that, The memory stores computer instructions, and the processor executes the computer instructions stored in the memory to implement the steps of the town expansion early warning method based on hierarchical equal-area quadtree and Bayes as described in any one of claims 1-6.

9. A computer-readable storage medium storing computer instructions, characterized in that, Computer instructions are used to cause a computer to perform the steps of the town expansion early warning method based on hierarchical equal-area quadtrees and Bayes as described in any one of claims 1-6.

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