A spatiotemporal interpolation method for air temperature data based on a decomposition kriging network

Abstract

The application provides a temperature data spatio-temporal interpolation method based on a decomposition Kriging network, and belongs to the technical field of data processing, and specifically comprises the following steps: collecting spatial coordinates of all meteorological monitoring stations in a research area and temperature observation data of the stations at a plurality of continuous time stamps; calculating a spatial embedding vector corresponding to each station by using a spatial encoder; decomposing a temperature time series of each sampling point into low-dimensional sparse features by using a decomposer network; mapping all low-dimensional sparse features into feature embedding vectors by using a feature representation network; constructing a Kriging network, calculating a covariance matrix, and solving low-dimensional sparse feature estimates based on a Kriging equation; reconstructing the low-dimensional sparse feature estimates into temperature time series estimates by using a reconstructor network; training the model by minimizing the estimation error; and interpolating temperature data of a target area by using the target model. The scheme provided by the application improves the interpolation efficiency and accuracy.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a spatiotemporal interpolation method for temperature data based on decomposed Kriging networks. Background Technology

[0002] Currently, mainstream temperature data interpolation methods can be divided into deterministic interpolation and geostatistical interpolation. Deterministic interpolation methods, such as inverse distance weighting, radial basis function methods, and trend surface methods, fit the correlation or smoothness within the data using specific mathematical formulas. Geostatistical interpolation methods, such as ordinary kriging and universal kriging, model spatial dependencies using variograms to achieve the best linear unbiased estimate. However, these methods often rely on pre-defined functional forms or linear assumptions, making it difficult to capture the complex spatial dependencies and spatial heterogeneity in the actual spatiotemporal evolution of temperature. In recent years, deep learning methods such as recurrent neural networks, graph neural networks, and attention mechanisms have also been attempted for temperature data interpolation. These methods have shown advantages in capturing complex data structures, but they often suffer from low computational efficiency when dealing with large-scale spatiotemporal data.

[0003] It is evident that there is an urgent need for a spatiotemporal interpolation method for temperature data based on decomposed Kriging networks that offers high interpolation efficiency and accuracy. Summary of the Invention

[0004] In view of this, embodiments of the present invention provide a spatiotemporal interpolation method for temperature data based on decomposed Kriging networks, which at least partially solves the problems of poor interpolation efficiency and accuracy in the prior art.

[0005] This invention provides a spatiotemporal interpolation method for temperature data based on decomposed Kriging networks, comprising:

[0006] Step 1: Collect the spatial coordinates of all meteorological monitoring stations in the study area and their temperature observation data at multiple consecutive timestamps, and divide the stations into a set of sampling points containing observation data and a set of unsampled points that need interpolation;

[0007] Step 2: Based on the spatial coordinates of each station, calculate the spatial embedding vector corresponding to each station using a spatial encoder;

[0008] Step 3: Using a decomposer network, the temperature time series of each sampling point is decomposed into low-dimensional sparse features, and the mean of the low-dimensional sparse features of all sampling points is used as the prior information of the low-dimensional sparse features of unsampled points.

[0009] Step 4: Through the feature representation network, all low-dimensional sparse features are mapped into feature embedding vectors;

[0010] Step 5: Construct a Kriging network, fuse spatial embedding vectors and feature embedding vectors, calculate the covariance matrix between sampled points and between unsampled points and sampled points, and solve for the low-dimensional sparse feature estimates of unsampled points based on the Kriging equation.

[0011] Step 6: Using the reconstructor network, the low-dimensional sparse feature estimates of the unsampled points are reconstructed into the corresponding temperature time series estimates.

[0012] Step 7: Based on the temperature observation data of the sampling points and their corresponding model estimates, train the model with the goal of minimizing the estimation error until the preset conditions are met to obtain the target model;

[0013] Step 8: Use the target model to interpolate the temperature data of the target area.

[0014] According to a specific implementation of an embodiment of the present invention, step 2 specifically includes:

[0015] Step 2.1, based on spatial coordinates The corresponding spatial embedding sub-vectors are calculated by different combinations of sine and cosine functions. :

[0016] ;

[0017] in, The constraint term representing the spatial embedding subvector is... Indicates the index of the spatially embedded subvector. Indicates the dimension of the latent space;

[0018] Step 2.2, concatenate all spatial embedding subvectors The corresponding spatial embedding vector is obtained. :

[0019] ;

[0020] in, This represents the vector concatenation operator. This indicates the number of space stations.

[0021] According to a specific implementation of an embodiment of the present invention, the computation process of the decomposer network is as follows:

[0022] ;

[0023] ;

[0024] in, Represents low-dimensional sparse features. Represents a high-dimensional time series of temperature. , For network learnable parameters, This represents the dimensionality of low-dimensional sparse features. It is an intermediate variable that integrates temperature and location information, combined with the Hadamard product operator. With sigmoid activation function The model complexity can be adaptively adjusted according to the location.

[0025] According to a specific implementation of an embodiment of the present invention, step 5 specifically includes:

[0026] Step 5.1, fuse the location embedding vectors With feature embedding vector The vector is then projected onto the query space and key space to obtain the corresponding query vector. With key vector :

[0027] ;

[0028] ;

[0029] in, For network learnable parameters, This represents a vector concatenation operation. The weights represent the position embedding vectors and are used to control the importance of spatial dependencies in the covariance;

[0030] Step 5.2: Calculate the covariance between each pair of sampling points in the latent space. And construct the covariance matrix of the sampling points. :

[0031] ;

[0032] in, SP represents the number of sampling points;

[0033] Step 5.3: Calculate the covariance between unsampled points and sampled points in the latent space. And construct the covariance matrix of unsampled points :

[0034] , ;

[0035] in, This represents the number of unsampled points, and UP represents the set of unsampled points.

[0036] Step 5.4, for each unsampled point Construct the Kriging equation and solve for the interpolation weights corresponding to the unsampled point. :

[0037] ;

[0038] in, For the Lagrange coefficients, Represents the covariance matrix The Middle The vector consisting of row elements, i.e., unsampled points The corresponding covariance vector, Represents a vector whose elements are all 1s;

[0039] Step 5.5, based on interpolation weights The matrix is ​​based on the low-dimensional sparse features corresponding to all sampling points. Calculate unsampled points Low-dimensional sparse feature estimates :

[0040] .

[0041] According to a specific implementation of an embodiment of the present invention, the reconstructor network includes a fully connected neural network with at least one hidden layer, used to nonlinearly map low-dimensional sparse feature estimates back to high-dimensional temperature time series space to obtain corresponding temperature time series estimates.

[0042] According to a specific implementation of an embodiment of the present invention, step 7 specifically includes:

[0043] Step 7.1: Use mean squared error as the model training loss function.

[0044] ;

[0045] in, and Let represent the model estimates and actual values ​​of the temperature time series data within the training set, respectively. This indicates the number of sites in the training set. Represents the L2 norm;

[0046] Step 7.2: Calculate the loss function using the backpropagation algorithm. The gradients of all learnable parameters of the model are calculated, and the Adam optimizer is used to iteratively update the learnable parameters until the error of the model on the validation set is minimized, thus obtaining the target model.

[0047] The spatiotemporal interpolation scheme for temperature data based on decomposed kriging networks in this invention includes: Step 1, collecting the spatial coordinates of all meteorological monitoring stations within the study area and their temperature observation data at multiple consecutive timestamps, and dividing the stations into a set of sampling points containing observation data and a set of unsampled points requiring interpolation; Step 2, calculating the spatial embedding vector corresponding to each station using a spatial encoder based on the spatial coordinates of each station; Step 3, using a decomposer network to decompose the temperature time series of each sampling point into low-dimensional sparse features, and using the mean of the low-dimensional sparse features of all sampling points as prior information for the low-dimensional sparse features of unsampled points; Step 4, using a feature representation network... Step 5: Map all low-dimensional sparse features to feature embedding vectors; Step 6: Construct a Kriging network, fuse spatial embedding vectors and feature embedding vectors, calculate the covariance matrix between sampled points and between unsampled points and sampled points, and solve for the low-dimensional sparse feature estimates of unsampled points based on the Kriging equation; Step 7: Use a reconstructor network to reconstruct the low-dimensional sparse feature estimates of unsampled points into corresponding temperature time series estimates; Step 8: Based on the temperature observation data of sampled points and their corresponding model estimates, train the model with the goal of minimizing the estimation error until the preset conditions are met to obtain the target model; Step 9: Use the target model to interpolate the temperature data of the target area.

[0048] The beneficial effects of the embodiments of the present invention are as follows: Through the scheme of the present invention, a decomposer network is designed to adaptively decompose low-dimensional sparse features that can characterize the unique change pattern of each location from the high-dimensional temperature time series data of each monitoring station, thereby realizing the dimensionality reduction expression of high-dimensional data and effectively handling the spatial heterogeneity of temperature changes; a kriging network is designed specifically to capture the complex spatial dependencies between low-dimensional sparse features of different locations, and then accurately estimate the low-dimensional sparse features of unsampled locations based on the low-dimensional sparse features of known stations; a reconstructor network is designed to accurately reconstruct the estimated low-dimensional sparse features of unsampled locations into complete high-dimensional temperature time series data, thereby achieving efficient interpolation of the temperature at unsampled locations. Attached Figure Description

[0049] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments 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 these drawings without creative effort.

[0050] Figure 1 A flowchart illustrating a spatiotemporal interpolation method for temperature data based on decomposed Kriging networks, provided in an embodiment of the present invention;

[0051] Figure 2This is a schematic diagram illustrating the specific implementation process of a spatiotemporal interpolation method for temperature data based on decomposed Kriging networks, provided in an embodiment of the present invention.

[0052] Figure 3 The diagram shows the spatial distribution of the mean absolute error of different interpolation methods provided in the embodiments of the present invention, wherein (a) is the method of the present invention, (b) is the IDW method, (c) is the OK method, and (d) is the DKNN method. Detailed Implementation

[0053] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0054] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0055] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this invention, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0056] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. The illustrations only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0057] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0058] With the intensification of global climate change and the increasing frequency of extreme weather events, accurate and detailed monitoring and analysis of temperature are crucial for agricultural production, energy management, urban planning, and public health. Currently, temperature monitoring mainly relies on a network of ground-based meteorological monitoring stations. However, due to factors such as construction costs and geographical limitations, the spatial distribution of monitoring stations is often sparse and uneven, resulting in a lack of direct observational data in many areas. This data sparsity restricts the detailed perception of a comprehensive and continuous spatiotemporal temperature field. Therefore, designing an efficient and accurate spatiotemporal interpolation method for temperature data, utilizing the limited observational data from sampled stations to accurately infer temperature information at unsampled locations, is a key technological foundation for improving meteorological monitoring capabilities and service levels.

[0059] The spatiotemporal evolution of temperature exhibits complex characteristics and structures. On the one hand, temperature distribution shows significant spatial dependence, meaning that temperature values ​​in geographically close locations are highly similar. On the other hand, due to differences in factors such as topography, altitude, climate, and land cover type, temperature change patterns in different locations exhibit spatial heterogeneity, meaning that temperature change patterns may differ across spatial regions. Accurately capturing and modeling this complex spatial dependence and spatial heterogeneity is the core and challenge of achieving high-precision spatiotemporal interpolation of temperature data.

[0060] Current mainstream temperature data interpolation methods can be divided into deterministic interpolation and geostatistical interpolation. Deterministic interpolation methods, such as inverse distance weighting, radial basis function methods, and trend surface methods, fit the correlation or smoothness within the data using specific mathematical formulas. Geostatistical interpolation methods, such as ordinary kriging and universal kriging, model spatial dependencies using variograms to achieve the best linear unbiased estimate. However, these methods often rely on pre-defined functional forms or linear assumptions, making it difficult to capture the complex spatial dependencies and spatial heterogeneity in the actual spatiotemporal evolution of temperature. In recent years, deep learning methods such as recurrent neural networks, graph neural networks, and attention mechanisms have also been attempted for temperature data interpolation. These methods have shown advantages in capturing complex data structures, but they often suffer from low computational efficiency when dealing with large-scale spatiotemporal data.

[0061] It is evident that the shortcomings of existing technologies are:

[0062] 1.1) Insufficient spatial heterogeneity modeling capability: Traditional interpolation models usually adopt a globally uniform function form or prior assumptions, which makes it difficult to capture and express the local differences in temperature change patterns caused by different geographical environments, resulting in large deviations in interpolation results in local areas.

[0063] 1.2) Difficulty in capturing complex spatial dependencies: The interaction between temperature distribution and its variation patterns at different locations is highly complex and nonlinear. Traditional methods based on linear assumptions or predetermined function forms are difficult to effectively capture such complex spatial dependencies, which limits the overall interpolation accuracy.

[0064] 1.3) Low efficiency in processing large-scale spatiotemporal data: Existing methods fail to separate the complexity in the spatiotemporal dimension, resulting in an exponential increase in computational load when processing high-dimensional spatiotemporal data with the increase in the number of stations and timestamps, which seriously restricts its application potential in large-scale, long-term temperature monitoring scenarios.

[0065] This invention provides a spatiotemporal interpolation method for temperature data based on decomposed Kriging networks, which can be applied to the temperature data interpolation process in data processing scenarios.

[0066] See Figure 1 This is a flowchart illustrating a spatiotemporal interpolation method for temperature data based on decomposed Kriging networks, provided by an embodiment of the present invention. Figure 1 and Figure 2 As shown, the method mainly includes the following steps:

[0067] Step 1: Collect the spatial coordinates of all meteorological monitoring stations in the study area and their temperature observation data at multiple consecutive timestamps, and divide the stations into a set of sampling points containing observation data and a set of unsampled points that need interpolation;

[0068] The temperature data used in this implementation scheme comes from hourly monitoring data from 395 meteorological stations in a certain area from January 1, 2018 to July 31, 2018. After data cleaning, a total of 388 valid station data points are obtained, which serve as the actual dataset for this invention implementation scheme, and are used to illustrate the implementation process of this invention.

[0069] In practice, data is collected from the research area. Total Several meteorological monitoring stations in continuous Temperature observation data at each timestamp. This includes observation data... Each station is defined as a set of sampling points. Interpolation is required. Each site is defined as the set of unsampled points. ,in For any sampling point Its spatial coordinates are The corresponding temperature time series is The goal of this method is to utilize temperature observation data from all sampling points. Estimate the time series of temperature at unsampled points .

[0070] Step 2: Based on the spatial coordinates of each station, calculate the spatial embedding vector corresponding to each station using a spatial encoder;

[0071] In practice, the spatial coordinates of all stations are considered. A spatial encoder is designed to map spatial information to a latent space, resulting in spatial embedding vectors. The main steps include:

[0072] (2.1) Based on spatial coordinates The corresponding spatial embedding sub-vectors are calculated by different combinations of sine and cosine functions. :

[0073] ;

[0074] in, The constraint term representing the spatial embedding subvector is... Indicates the index of the spatially embedded subvector. This represents the dimension of the latent space.

[0075] (2.2) Then, concatenate all the spatial embedding subvectors. The corresponding spatial embedding vector is obtained. :

[0076] ;

[0077] in, This represents the vector concatenation operator. Due to the properties of the sine and cosine functions, the dot product of pairwise embedded vectors gradually decreases as the distance increases, thus introducing spatial dependencies during model learning.

[0078] Step 3: Using a decomposer network, the temperature time series of each sampling point is decomposed into low-dimensional sparse features, and the mean of the low-dimensional sparse features of all sampling points is used as the prior information of the low-dimensional sparse features of unsampled points.

[0079] In practical implementation, a decomposer network based on a position-aware gating mechanism can be designed to decompose each sampling point. High-dimensional time series of temperature attributes Decomposed into low-dimensional sparse features :

[0080] ;

[0081] ;

[0082] in, , For network learnable parameters, This represents the dimensionality of the low-dimensional sparse features. It is an intermediate variable that integrates temperature and location information, combined with the Hadamard product operator. With sigmoid activation function The model complexity can be adaptively adjusted based on location, thus effectively addressing the spatial heterogeneity of temperature changes. Since unsampled points lack time-series temperature observation data, the average of the low-dimensional sparse features corresponding to all sampled points is calculated. Treat it as an unsampled point Prior information corresponding to low-dimensional sparse features .

[0083] Step 4: Through the feature representation network, all low-dimensional sparse features are mapped into feature embedding vectors;

[0084] In practical implementation, a feature representation network with two hidden layers can be designed to represent all low-dimensional sparse features. Mapped to feature embedding vector To adapt to the subsequent online learning process:

[0085] ;

[0086] in, For network learnable parameters, It is a non-linear activation function.

[0087] Step 5: Construct a Kriging network, fuse spatial embedding vectors and feature embedding vectors, calculate the covariance matrix between sampled points and between unsampled points and sampled points, and solve for the low-dimensional sparse feature estimates of unsampled points based on the Kriging equation.

[0088] In specific implementation, the position embedding vector obtained in step 2 is used as the basis. With the feature embedding vector obtained in step 4 A kriging network is constructed to fit the covariance matrix of sampled and unsampled points. Based on the kriging equation in geostatistical theory, the low-dimensional sparsity characteristics of unsampled points are inferred. The main steps include:

[0089] (5.1) Fusing the position embedding vectors in step 2 With the feature embedding vector in step 4 The vector is then projected onto the query space and key space to obtain the corresponding query vector. With key vector The formula is as follows:

[0090] ;

[0091] ;

[0092] in, For network learnable parameters, This represents a vector concatenation operation. The weights represent the position embedding vectors and are used to control the importance of spatial dependencies in the covariance.

[0093] (5.2) Calculate the pairwise sampling points in the latent space. covariance between And construct the covariance matrix of the sampling points. The formula is as follows:

[0094] ;

[0095] (5.3) Calculate the unsampled points in the latent space. With sampling points Point to point covariance between And construct the covariance matrix of unsampled points The formula is as follows:

[0096] ;

[0097] (5.4) For each unsampled point Construct the Kriging equation and solve for the interpolation weights corresponding to the unsampled point. The specific formula is as follows:

[0098] ;

[0099] in, For the Lagrange coefficients, Represents the covariance matrix The Middle The vector consisting of row elements, i.e., unsampled points The corresponding covariance vector, This represents a vector whose elements are all 1s.

[0100] (5.5) Based on interpolation weights The matrix is ​​based on the low-dimensional sparse features corresponding to all sampling points. Calculate unsampled points Low-dimensional sparse feature estimates :

[0101] .

[0102] Step 6: Using the reconstructor network, the low-dimensional sparse feature estimates of the unsampled points are reconstructed into the corresponding temperature time series estimates.

[0103] In practice, the low-dimensional sparse feature estimates of the unsampled points obtained in step 5 are used as the basis for implementation. Design a reconstructor network to reconstruct the corresponding high-dimensional time series estimates of temperature. :

[0104] ;

[0105] in, These are the learnable parameters of the network.

[0106] Step 7: Based on the temperature observation data of the sampling points and their corresponding model estimates, train the model with the goal of minimizing the estimation error until the preset conditions are met to obtain the target model;

[0107] In practice, 80% of the sampling points can be used as the training set, and the remaining 20% ​​as the validation set. Supervised learning is employed to calculate the error between the actual temperature time series values ​​and the model estimates in the training set. The learnable parameters in the model are updated with the goal of minimizing this error, ultimately ensuring the model achieves the minimum interpolation error on the validation set. The specific steps include:

[0108] (7.1) The mean squared error is used as the loss function for model training. The specific formula is as follows:

[0109] ;

[0110] in, and Let represent the model estimates and actual values ​​of the temperature time series data within the training set, respectively. This indicates the number of sites in the training set. This represents the L2 norm.

[0111] (7.2) Calculate the loss using the backpropagation algorithm Gradients of all learnable parameters of the model are calculated, and the Adam optimizer is used to iteratively update the learnable parameters until the model's error on the validation set is minimized.

[0112] Step 8: Use the target model to interpolate the temperature data of the target area.

[0113] The spatiotemporal interpolation method for temperature data based on decomposed kriging networks provided in this embodiment adaptively decomposes low-dimensional sparse features that characterize the unique change patterns at each location from high-dimensional temperature time series data at each monitoring station by designing a decomposer network. This achieves dimensionality reduction representation of high-dimensional data and effectively handles the spatial heterogeneity of temperature changes. A kriging network is designed specifically to capture the complex spatial dependencies between low-dimensional sparse features at different locations. Based on the low-dimensional sparse features of known stations, the low-dimensional sparse features of unsampled locations are accurately estimated. A reconstructor network is designed to accurately reconstruct the estimated low-dimensional sparse features of unsampled locations into complete high-dimensional temperature time series data, achieving efficient interpolation of temperatures at unsampled locations.

[0114] The method of the present invention will be further described below with reference to a specific embodiment. Experiments will be conducted to compare the method with several existing interpolation methods to verify its effectiveness. The selected comparison methods include: Inverse Distance Weighted (IDW), Ordinary Kriging (OK), and Deep Kriging Neural Network (DKNN).

[0115] 20% of all monitoring stations within the dataset were randomly selected as the unsampled point set, and the remainder were included in the sampled point set. A model was built and trained based on the sampled point set to estimate the temperature values ​​at the unsampled points. Multiple accuracy evaluation metrics were used to quantitatively evaluate the interpolation results, including ① Mean Absolute Error (MAE); ② Root Mean Square Error (RMSE); ③ Coefficient of Determination (CDO). The calculation formula is as follows:

[0116] ;

[0117] ;

[0118] ;

[0119] in, and They represent the first The actual and model-estimated temperature time series values ​​for each unsampled point This represents the average of the actual temperature values ​​at unsampled points. Indicates the number of unsampled points. Describing the L1 norm, R² represents the L2 norm. For the first two evaluation metrics, a smaller value indicates higher accuracy of the interpolation method, while a larger value indicates higher accuracy of the interpolation method.

[0120] Table 1 shows the accuracy comparison results of the method of the present invention and the comparative method on the temperature dataset. It can be seen that the method of the present invention is superior to the comparative method in all three evaluation indicators, indicating that the method of the present invention achieves the best overall accuracy performance.

[0121] Table 1

[0122] ;

[0123] Based on the interpolation results of the method of this invention and the comparison method, the mean absolute error of the corresponding station is calculated according to the spatial location of the unsampled points, and spatial visualization is performed, such as... Figure 3 As shown, compared with the comparative method, the method of the present invention has a smaller mean absolute error and a more uniform spatial distribution, indicating that the interpolation results of the method of the present invention are more accurate and more stable.

[0124] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof.

[0125] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A spatiotemporal interpolation method for temperature data based on decomposed kriging networks, characterized in that, include: Step 1: Collect the spatial coordinates of all meteorological monitoring stations in the study area and their temperature observation data at multiple consecutive timestamps, and divide the stations into a set of sampling points containing observation data and a set of unsampled points that need interpolation; Step 2: Based on the spatial coordinates of each station, calculate the spatial embedding vector corresponding to each station using a spatial encoder; Step 3: Using a decomposer network, the temperature time series of each sampling point is decomposed into low-dimensional sparse features, and the mean of the low-dimensional sparse features of all sampling points is used as the prior information of the low-dimensional sparse features of unsampled points. Step 4: Through the feature representation network, all low-dimensional sparse features are mapped into feature embedding vectors; Step 5: Construct a Kriging network, fuse spatial embedding vectors and feature embedding vectors, calculate the covariance matrix between sampled points and between unsampled points and sampled points, and solve for the low-dimensional sparse feature estimates of unsampled points based on the Kriging equation. Step 6: Using the reconstructor network, the low-dimensional sparse feature estimates of the unsampled points are reconstructed into the corresponding temperature time series estimates. Step 7: Based on the temperature observation data of the sampling points and their corresponding model estimates, train the model with the goal of minimizing the estimation error until the preset conditions are met to obtain the target model; Step 8: Use the target model to interpolate the temperature data of the target area.

2. The method according to claim 1, characterized in that, Step 2 specifically includes: Step 2.1, based on spatial coordinates The corresponding spatial embedding sub-vectors are calculated by different combinations of sine and cosine functions. : ； in, The constraint term representing the spatial embedding subvector is... Indicates the index of the spatially embedded subvector. Indicates the dimension of the latent space; Step 2.2, concatenate all spatial embedding subvectors The corresponding spatial embedding vector is obtained. : ； in, This represents the vector concatenation operator. This indicates the number of space stations.

3. The method according to claim 2, characterized in that, The calculation process of the decomposer network is as follows: ； ； in, Represents low-dimensional sparse features. Represents a high-dimensional time series of temperature. , For network learnable parameters, This represents the dimensionality of low-dimensional sparse features. It is an intermediate variable that integrates temperature and location information, combined with the Hadamard product operator. With sigmoid activation function The model complexity can be adaptively adjusted according to the location.

4. The method according to claim 3, characterized in that, Step 5 specifically includes: Step 5.1, fuse the location embedding vectors With feature embedding vector The vector is then projected onto the query space and key space to obtain the corresponding query vector. With key vector : ； ； in, For network learnable parameters, This represents a vector concatenation operation. The weights represent the position embedding vectors and are used to control the importance of spatial dependencies in the covariance; Step 5.2: Calculate the covariance between each pair of sampling points in the latent space. And construct the covariance matrix of the sampling points. : ； in, SP represents the number of sampling points; Step 5.3: Calculate the covariance between unsampled points and sampled points in the latent space. And construct the covariance matrix of unsampled points : , , ； in, This represents the number of unsampled points, and UP represents the set of unsampled points. Step 5.4, for each unsampled point Construct the Kriging equation and solve for the interpolation weights corresponding to the unsampled point. : ； in, For the Lagrange coefficients, Represents the covariance matrix The Middle The vector consisting of row elements, i.e., unsampled points The corresponding covariance vector, Represents a vector whose elements are all 1s; Step 5.5, based on interpolation weights The matrix is ​​based on the low-dimensional sparse features corresponding to all sampling points. Calculate unsampled points Low-dimensional sparse feature estimates : 。 5. The method according to claim 4, characterized in that, The reconstructor network comprises a fully connected neural network with at least one hidden layer, used to nonlinearly map low-dimensional sparse feature estimates back to high-dimensional temperature time series space to obtain corresponding temperature time series estimates.

6. The method according to claim 5, characterized in that, Step 7 specifically includes: Step 7.1: Use mean squared error as the model training loss function. ； in, and Let represent the model estimates and actual values ​​of the temperature time series data within the training set, respectively. This indicates the number of sites in the training set. Represents the L2 norm; Step 7.2: Calculate the loss function using the backpropagation algorithm. The gradients of all learnable parameters of the model are calculated, and the Adam optimizer is used to iteratively update the learnable parameters until the error of the model on the validation set is minimized, thus obtaining the target model.

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