Induction learning-based spatio-temporal data interpolation method, system and device

Abstract

The invention relates to a spatio-temporal data interpolation method, system and device based on inductive learning, and belongs to the field of data processing. Corresponding instruments are used for collecting spatio-temporal data, and then a spatio-temporal data set is preprocessed; constructing a training sample of a spatio-temporal data interpolation model by using the data set to generate a training sample capable of generalizing the model to unknown nodes and graph structures; constructing a spatial aggregation network belonging to the graph neural network; constructing a time encoder; training a spatio-temporal data interpolation model; the target model obtained by training is used for simulating generation of new sensor data and generation of data of unsampled nodes; a data set needing interpolation serves as the basis of a training model, data is processed into input capable of being accepted by the interpolation model, and the trained interpolation model is used for interpolation. The method provided by the invention not only improves the precision of space-time interpolation, but also has better adaptability and universality. And under the condition of data scarcity, accurate interpolation of the unobserved points is realized.

Description

Technical Field

[0001] The present invention belongs to the field of data processing, and specifically relates to an interpolation method, system and device for spatiotemporal data based on inductive learning. Background Art

[0002] With the development of global climate change and urbanization, the monitoring, analysis and prediction of spatiotemporal data have gradually become important research areas. Spatiotemporal data plays a vital role in many fields, such as air and water pollution in environmental monitoring, congestion prediction in traffic management, the spread of infectious diseases in public health, resource distribution in geographic information systems, and crowd flow in smart city planning. The richness and diversity of spatiotemporal data make it have irreplaceable application value in decision-making and management processes in various fields.

[0003] However, due to the complexity of data collection, spatiotemporal data often present the characteristics of sparseness and uneven distribution. Especially in complex or vast environments, such as large-scale oceans and atmospheres, data gaps are more significant. Although traditional interpolation methods (such as Kriging, inverse distance weighted method, etc.) can fill some missing data, they have limited ability to capture complex dependent features in spatiotemporal data, so there are obvious deficiencies in accuracy. These methods are usually based on preset assumptions and cannot flexibly adapt to the nonlinear and non-stationary features in the data. Especially in areas with significant spatiotemporal changes, the interpolation effect is often not ideal. Summary of the invention

[0004] In view of the above technical problems, the present invention provides a spatiotemporal data interpolation method based on inductive learning. The method constructs a more complex neural network model and uses deep learning to capture the nonlinear relationship in spatiotemporal data, thereby achieving accurate prediction of unsampled positions.

[0005] The present invention is achieved through the following technical solutions: A spatiotemporal data interpolation method based on inductive learning includes the following steps: Step 1: Use the corresponding instruments to collect spatiotemporal data, and then preprocess the spatiotemporal data set; Furthermore, the data set must cover the necessary timestamps and spatial information, and then perform data cleaning and normalization. The processed data is organized into a historical data matrix. At the same time, an initial all-zero mask matrix is ​​constructed for the subsequent marking of missing values ​​in the data and simulating unsampled nodes. According to the missing data in the historical data matrix, the data missing matrix is ​​updated, and the historical data matrix is ​​divided into training set, validation set and test set according to the proportion.

[0006] Step 2: Use the data set in step 1 to construct training samples for the spatiotemporal data interpolation model to generate training samples that can generalize the model to unknown nodes and graph structures; Furthermore, the method of step 2 is as follows: first, randomly select a time point within the time range of the historical data matrix, and extract a submatrix from the complete historical data matrix according to the selected time node; the submatrix contains the observation data of all nodes at a specific time point; randomly select 10%-20% of the nodes in the submatrix to simulate unsampled point nodes; set the positions corresponding to the set unsampled point nodes in the mask matrix to 1, and reconstruct the data of these unsampled nodes through model training.

[0007] Step 3: Use the training samples of the spatiotemporal data interpolation model constructed in step 2 to build a spatial aggregation network belonging to the graph neural network; Furthermore, the spatial location in the spatiotemporal data is regarded as a node in the graph, and the reachability and distance relationship are regarded as the connection relationship in the graph. The spatial dependency of the spatiotemporal data is extracted through the spatial aggregation network, and the aggregation function is used to integrate the features of neighboring nodes, and the features of the nodes are learned and updated. Furthermore, based on graph neural networks, spatial aggregation networks use aggregation functions and distance information in the same layer to capture complex spatial dependencies.

[0008] The aggregation functions include average aggregation, weighted average aggregation, Softmax aggregation, Softmin aggregation, standard deviation aggregation, maximum pooling, minimum pooling, mean distance aggregation, standard distance deviation aggregation or self-attention aggregation; Furthermore, the spatial aggregation network uses a scaler to consider the impact of different features, adjust the feature value range or distribution, and use the tensor product to combine the aggregation function and the scaler to enhance the learning ability of the model.

[0009] Step 4: Build the time encoder; Furthermore, the step 4 constructs a time encoder: use more than one one-dimensional convolution kernels of different sizes to perform convolution operations on the time series data of a single node in parallel, extract local and long-term temporal features, and perform zero padding before the convolution operation; splice all feature channels generated by the convolution together, and use a gating mechanism to pass information that is critical to the task. At the same time, the time encoder uses different activation functions, residual connections, and jump connections to enhance the learning ability of the network and avoid the gradient disappearance problem.

[0010] Step 5: Train the spatiotemporal data interpolation model; Furthermore, the hyperparameter settings of the model are determined. At the beginning of training, the spatial aggregation network layer and the temporal encoder layer are alternately stacked to learn the spatial and temporal features of spatiotemporal data. In each layer, the spatial aggregation network layer uses more than one aggregation function to integrate the information of neighboring nodes, while the temporal encoder captures the dynamic changes of the time series through multi-scale convolution operations. Residual connections are introduced into the model. In each iteration, training samples are randomly selected from historical data according to the number of samples determined by the training batch parameter, and a masking strategy is applied to simulate data missing conditions. The model parameters are adjusted by minimizing the root mean square error or mean absolute error of the loss function. The Adam optimizer gradient descent method is used to update the learnable parameters of the model according to the gradient calculated by the back-propagation algorithm. During the training process, an early stopping mechanism is used to monitor the loss on the validation set. When the loss does not decrease significantly after multiple consecutive iterations, the training is terminated early to avoid overfitting. When the performance of the model on the validation set reaches stability or meets the preset training conditions, the final target model is obtained.

[0011] Furthermore, the hyperparameters include the number of network layers, the training batch size and the maximum training cycle, as well as the ratio of missing nodes, the input sequence length of the training data, the length of the temporal convolution kernel in the temporal encoder, and the number of neighbor nodes.

[0012] Step 6: The target model trained in step 5 is used to simulate the generation of new sensor data and the data of unsampled nodes; the data set to be interpolated is used as the basis for training the model, the area to be interpolated is determined, including the location and time period of the unsampled nodes, and the data is processed into input acceptable to the interpolation model described in step 5. The adjacency matrix needs to contain the unsampled node information, and the mask matrix is ​​set to zero to identify the unsampled nodes. The interpolation model described in step 5 that has been trained is used for interpolation; Furthermore, in the fields of meteorology or oceanography, virtual data is generated to fill the gaps in the monitoring network and improve the spatial coverage of data; in traffic monitoring, traffic flow data of unsampled sections is generated to help conduct more comprehensive traffic analysis and decision-making; in natural disaster monitoring, data of unsampled areas is generated to help better assess risks and formulate response measures.

[0013] A spatiotemporal data interpolation system based on inductive learning, the system comprising a data input and processing module, a training sample module for constructing a spatiotemporal data interpolation model, a module for constructing a spatial aggregation network, a module for constructing a time encoder, a module for training a spatiotemporal data interpolation model, and a module for interpolating data; The data input and processing module is used to acquire data and pre-process the data, and the module runs the step (1); The training sample module for constructing a spatiotemporal data interpolation model runs step (2) of the method; The spatial aggregation network building module executes step (3) of the method; The construction time encoder module executes step (4) of the method; The training spatiotemporal data interpolation model module executes step (5) of the method; The data interpolation module executes step (6) of the method.

[0014] The present invention also provides a spatiotemporal data interpolation device based on inductive learning, wherein the device is equipped with the system.

[0015] Compared with the prior art, the present invention has the following beneficial effects: The method of the present invention not only improves the accuracy of spatiotemporal interpolation, but also has better adaptability and versatility. The model of high-precision interpolation that can make full use of spatiotemporal dependent features can realize accurate interpolation of unobserved points in the case of scarce data, which has important application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a flowchart of a spatiotemporal data interpolation method based on inductive learning provided by an embodiment of the present invention; Figure 2 It is a model structure diagram of a spatiotemporal data interpolation method based on inductive learning provided in an embodiment of the present invention; Figure 3 It is a spatial aggregation network structure diagram of a spatiotemporal data interpolation method based on inductive learning provided by an embodiment of the present invention; Figure 4 It is a structural diagram of a time encoder of a spatiotemporal data interpolation method based on inductive learning provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0017] The present invention will be further described below in conjunction with specific embodiments.

[0018] Example 1 A spatiotemporal data interpolation method based on inductive learning includes the following steps: Step 1: Use the corresponding instruments to collect spatiotemporal data, and then preprocess the spatiotemporal data set; As a preferred implementation, it is first necessary to ensure that the collected data set covers the necessary timestamps and spatial information, and then perform data cleaning, identify and process outliers caused by measurement errors, equipment failures or data recording errors to improve data quality and ensure the accuracy of subsequent analysis. To ensure that all data points are on the same scale and eliminate the effects of different dimensions and magnitudes, the data is normalized. Normalization can be achieved through a variety of methods, such as minimum-maximum scaling or Z-score standardization. The cleaned and normalized data are organized into a historical data matrix, which is a multivariate time series matrix containing spatiotemporal data of multiple location nodes within a specific time range. At the same time, an initial all-zero mask matrix is ​​constructed for subsequent labeling of missing values ​​in the data and simulating unsampled nodes. According to the missing data in the historical data matrix, the missing data matrix is ​​updated, and the setting of the missing data matrix makes the model robust. The construction of the adjacency matrix can be based on geographic distance, network connectivity, accessibility or other correlation metrics, using appropriate formulas to quantify geographic location relationships, such as Gaussian kernel functions or other spatial weight functions. Divide the historical data matrix into training set, validation set and test set in proportion to ensure the continuity of data in time series and avoid time overlap to ensure the effectiveness of model training.

[0019] Step 2: Construct training samples for the spatiotemporal data interpolation model; in this step, the goal is to generate training samples that enable the model to generalize to unknown nodes and graph structures.

[0020] As a preferred embodiment, a time point is randomly selected within the time range of the historical data matrix, and a submatrix is ​​extracted from the complete historical data matrix according to the selected time node. The submatrix contains the observation data of all nodes at a specific time point. About 10%-20% of the nodes are randomly selected in the submatrix to simulate the unsampled point nodes. The positions corresponding to the set unsampled point nodes are set to 1 in the mask matrix, and the goal of model training is to reconstruct the data of these unsampled nodes. Since the time points and masked nodes selected each time are random, the model not only learns the spatiotemporal dependencies in the data, but also has good generalization and induction capabilities, so that the model can still accurately interpolate data when encountering new and unseen spatiotemporal configurations.

[0021] Step 3: Construct a spatial aggregation network; Figure 3 As shown in the figure, the spatial aggregation network is a deep learning model belonging to the graph neural network, which is a deep learning model specifically used to process graph structured data.

[0022] As one of the specific implementation methods, the spatial position in the spatiotemporal data is regarded as a node in the graph, and the reachability and distance relationship are regarded as the connection relationship in the graph. The spatial dependency of the spatiotemporal data is extracted through the graph neural network, and the aggregation function (such as average, sum, etc.) is used to integrate the features of neighbor nodes, and the feature representation of the node is learned and updated: ; in, represents the node feature matrix of the lth layer, represents the weight matrix of the lth layer, is the result of adding self-loops to the adjacency matrix. yes The degree matrix of .

[0023] Based on the graph neural network, the spatial aggregation network uses a variety of aggregation functions and distance information in the same layer to capture complex spatial dependencies, such as average aggregation, weighted average aggregation, Softmax aggregation, Softmin aggregation, standard deviation aggregation, maximum pooling, minimum pooling, mean distance aggregation, standard distance deviation aggregation, self-attention aggregation, etc., so that each node can collect information about neighboring nodes from different angles; at the same time, the spatial aggregation network uses a scaler to consider the influence of different features, adjust the range or distribution of feature values, and use tensor product to combine aggregation functions and scalers together to enhance the learning ability of the model.

[0024] Step 4: Build a time encoder; Figure 4 As shown in the figure, another major feature of spatiotemporal data is its temporal continuity. The data at the current time point of a node is related to the data in the past and future. Temporal feature extraction can help the model capture this dependency and perform interpolation and prediction more accurately. At the same time, there may be important information at different time scales in spatiotemporal data, and it is necessary to capture multi-scale information from short-term fluctuations to long-term trends. The designed temporal encoder uses multiple one-dimensional convolution kernels of different sizes to perform convolution operations on the time series data of a single node in parallel to extract local and long-term temporal features.

[0025] As one of the preferred implementations, zero padding is performed before the convolution operation to maintain the consistency of the input and output data dimensions. All feature channels generated by the convolution are spliced ​​together to form a richer feature representation, and a gating mechanism is used to selectively pass information that is critical to the task. At the same time, the temporal encoder uses different activation functions, residual connections, and skip connections to enhance the network's learning ability and avoid the gradient vanishing problem.

[0026] Step 5: Train the spatiotemporal data interpolation model; To train the spatiotemporal data interpolation model, we must first determine the model's hyperparameter settings, including the number of network layers, training batch size and maximum training cycle, as well as the ratio of missing nodes, the input sequence length of the training data, the length of the temporal convolution kernel in the temporal encoder, and the number of neighbor nodes.

[0027] As one of the specific implementation methods, at the beginning of training, multiple layers of spatial aggregation network layers and time encoder layers are alternately stacked to learn the spatial and temporal features of spatiotemporal data. In each layer, the spatial aggregation network layer uses a variety of aggregation functions to integrate the information of neighboring nodes, while the time encoder captures the dynamic changes of the time series through multi-scale convolution operations. Residual connections are introduced into the model to promote the flow of information in deep networks and prevent the problem of gradient disappearance or explosion during training. In each iteration, training samples are randomly selected from historical data according to the number of samples determined by the training batch parameter, and a masking strategy is applied to simulate data missing conditions. The model parameters are adjusted by minimizing the root mean square error or mean absolute error of the loss function. The Adam optimizer gradient descent method is used to update the learnable parameters of the model according to the gradient calculated by the back-propagation algorithm.

[0028] During the training process, an early stopping mechanism is used to monitor the loss on the validation set. When the loss does not decrease significantly after multiple consecutive iterations, the training is terminated early to avoid overfitting. When the performance of the model on the validation set reaches stability or meets the preset training conditions, the final target model is obtained.

[0029] Step 6: The trained target model can be used to simulate the generation of new sensor data and generate data for unsampled nodes.

[0030] As one of the specific implementation methods, the data set that needs to be interpolated is used as the basis for training the model, and the area that needs to be interpolated, including the location and time period of the unsampled nodes, is determined. The data is processed into input that the model can accept. The adjacency matrix needs to contain the information of the unsampled nodes, and the mask matrix is ​​set to zero to identify the unsampled nodes. The trained target model is used for interpolation. In the fields of meteorology and oceanography, virtual data can be generated to fill the gaps in the monitoring network and improve the spatial coverage of data; in traffic monitoring, traffic flow data of unsampled sections can be generated to help conduct more comprehensive traffic analysis and decision-making; in natural disaster monitoring, generating data in unsampled areas can help better assess risks and formulate response measures.

[0031] Example 2 An embodiment of the present invention provides a method for interpolating spatiotemporal data, which can be applied to the interpolation process of an ocean surface temperature dataset.

[0032] See also Figure 1 , Figure 2, is a flow chart of a method for interpolating spatiotemporal data provided by an embodiment of the present invention, wherein the method is used for the interpolation process of an ocean surface temperature dataset and comprises the following steps: Step 1: Normalize the collected spatiotemporal data as a historical data matrix, mark the missing values ​​in the historical matrix, generate a data missing matrix, identify the missing data of the historical data matrix according to the data missing matrix, and divide the training set and test set. Construct the adjacency matrix A, considering the geographical location relationship between location nodes or the accessibility between nodes. The specific formula for the geographical location relationship is as follows: ; ; Among them, the longitude and latitude information of location node i is (lat1, lon1), and the longitude and latitude information of location node j is (lat2, lon2). is a hyperparameter that controls the scale; In the specific implementation, the sea surface temperature dataset uses the OISST observation data dataset from different platforms including satellites, ships, buoys and Argo buoys with a time span of 2014 to 2023. The data has been processed and the valid data is used as historical data X. The maximum absolute value normalization method is used to scale the value range to the interval [-1, 1]. X contains n position nodes and the time range is [1, p]. It exists in the form of a univariate time series matrix and is divided into training and test sets in a ratio of 7:3. Define the all-1 data missing matrix, set the corresponding points to 0 according to the null value points in the historical data matrix, and construct an adjacency matrix according to the geographical location relationship of the nodes in X.

[0033] Step 2: Randomly select different time points in the historical data matrix to generate multiple training samples. In each sample subset, randomly select some nodes as the missing position set, define the all-zero mask matrix, set the shielding nodes with a ratio of 10%-20%, and shield the corresponding positions in the mask matrix; Based on the above embodiment, step 2 specifically includes: Step 2.1: Randomly select a time point v in the time range {1+s,ph}, and obtain the training sample submatrix X of the sea surface temperature based on the selected time node sample =X[:,V sample ]; Among them, X sample The size is n×(h+s), where s is the time length reduction due to time convolution, and h is the time length of the interpolation target, i.e., the input sequence length, which is set to 7; Step 2.2: Select about 10%-20% of the nodes in the training sample submatrix, generate a random set S as the masked node set, simulate the situation of unsampled nodes, define an all-zero mask matrix, and set the corresponding positions in the mask matrix to 1; In the specific implementation, multiple training samples X of sea surface temperature are generated by randomly selecting different time points in the historical data matrix X. sample In each sample subset, 20% of the nodes are randomly selected to simulate unsampled nodes, and the corresponding positions of the mask matrix are masked.

[0034] Step 3: Construct a spatial aggregation network. The spatial aggregation network is a deep learning model specifically designed for processing graph-structured data. It captures and utilizes complex dependencies in spatial data by effectively aggregating the features of nodes and their neighbors. The model can capture spatial dependencies at different scales from local to global. The spatial aggregation network uses multiple aggregation functions, combined with adjacency matrix and masking strategy, to collect diverse information from the k nearest neighbor nodes of each node. Based on the above embodiment, step 3 specifically includes: Step 3.1: At each layer, multiple aggregation functions are used based on the adjacency matrix to more comprehensively capture the impact of neighbor nodes on the current node. The aggregation operations include average, weighted average, Softmax, Softmin, standard deviation, and standard distance deviation. The specific explanations are as follows: Average aggregation treats all neighbors of a node equally, regardless of the distance. Node i uses the average value to aggregate the feature values ​​of all neighboring nodes j at layer l express: ; Weighted average aggregation considers the distance weights of neighboring nodes. Node i uses weighted average aggregation to aggregate the feature values ​​of all neighboring nodes j in layer l. express: ; Softmax and Softmin aggregation indirectly measure the maximum and minimum values ​​of the received messages, providing better generalization capabilities for graph neural networks. Node i uses Softmax to aggregate the feature values ​​of all neighbors j in layer l. express: ; Node i uses Softmax to aggregate the feature values ​​of all neighbors j in layer l express: ; The average distance and standard deviation distance deviation aggregation characterize the spatial distance distribution from the current node to the adjacent nodes. Node i uses the average distance to aggregate the feature values ​​of all neighbor nodes j in the lth layer. express: ; Node i uses the standard deviation distance deviation to aggregate the feature values ​​of all neighboring nodes j at layer l express ; in, represents the feature vector of node j in the lth layer, k is the number of neighbors of node i, is the adjacency matrix, represents the distance or weight or reachability measure from node j to node i in the adjacency matrix, is the measure of all nodes connected to i in the adjacency matrix, d is the distance or weight or reachability measure between nodes, (x) is defined as , used to ensure the squared difference, non-negative ϵ is a small positive number used to prevent division by zero; Step 3.2: The aggregated information is adjusted by the sampling scaler and the saturation scaler. The sampling scaler uses a logarithmic function to amplify smaller aggregate values ​​while compressing larger aggregate values, increasing the model's sensitivity to subtle changes. The saturation scaler uses an inverse logarithmic function to attenuate larger aggregate values ​​while amplifying smaller aggregate values, paying more attention to changes in small values. The scaler formula is expressed as: ; ; in, is the aggregate eigenvalue of the neighbors of node i, is the measure of all nodes connected to i in the adjacency matrix; Step 3.3: The spatial aggregation network combines the aggregation function and the scaler to integrate different aggregation results and scale adjustments through tensor product to form a comprehensive representation of neighbor information; ; where I is an identity matrix, is to multiply all scalers and aggregators and stack them on top of each other. They are the average aggregation, weighted average aggregation, Softmax and Softmin aggregation, average distance and standard deviation distance deviation aggregation result matrices respectively; Step 3.4: The spatial aggregation network introduces a masking strategy, which prevents unobserved nodes from transmitting information during the aggregation process through a masking matrix. The spatial aggregation network contains multiple spatial aggregation layers, each of which independently applies the above aggregation function and scaler, so that the model can capture spatial dependencies at different levels of abstraction and deepen the understanding of spatial structure layer by layer: ; in, is the node feature matrix of the lth layer at the tth time point, is the activation function, is the weight matrix of the lth layer, used for spatial aggregation, represents the bias vector of the lth layer; In the specific implementation, a spatial aggregation network is constructed, and the adjacency matrix and mask matrix obtained in step 1 and step 2 are combined. The aggregation functions of average, weighted average, Softmax, Softmin, standard deviation, and standard distance deviation are applied to aggregate the historical feature matrix X sample The diversified information of the five nearest neighbor nodes of each node in the model is obtained, and the sampling scaler and saturation scaler are further used to adjust these eigenvalues ​​to improve the sensitivity and robustness of the model. Finally, the spatial feature information of the node is updated through the spatial feature extraction and aggregation of the multi-aggregation function and scaler of the spatial aggregation network.

[0035] Step 4: Use a time encoder based on one-dimensional convolution to perform multi-scale convolution on the time series data of each spatial node to extract local and long-term dependency features in the time dimension; In specific implementation, the temporal encoder pads the input data with zeros before the convolution operation. Each block applies 1×2, 1×3, 1×5, and 1×7 convolution kernels to the time axis of the input data. After convolution operations of different scales, the outputs of all convolutional layers are concatenated along the channel dimension, and finally a gating mechanism is used to selectively pass information that is critical to the task: ; in It is the feature obtained by splicing multi-scale convolution. (·) represents the Sigmoid activation function, and tanh(·) represents the Tanh activation function.

[0036] Step 5: Alternately use the spatial aggregation network and the temporal encoder layer to capture the spatiotemporal dependency characteristics of the nodes layer by layer, train the model to minimize the error between the output estimate and the true label, and train the model until the learnable parameters in the network reach the preset conditions to obtain the target model; Based on the above embodiment, step 5 specifically includes: Step 5.1, set the model's hyperparameters, including the number of network layers, training batch size and maximum training cycle, as well as the ratio of missing nodes, the input sequence length of the training data, and the number of neighbor nodes. Define the loss function as the error between the estimated value of the model output and the true label, and use the root mean square error RMSE and the mean absolute error MAE as error metrics; Step 5.2, alternately use the spatial aggregation network and the temporal encoder layer, and introduce residual connections in the model to improve the stability during training and the effect of the deep network; Step 5.3: During the model training process, an early stopping mechanism is used. When the loss on the validation set no longer decreases significantly within the set number of iterations, the training is terminated early. Step 5.4: The calculated loss is passed to the learnable parameters of the model through the back-propagation algorithm, and the value of each learnable parameter is updated using the Adam optimizer. The training process continues until the learnable parameters in the network meet the preset training conditions, and the final target model is obtained. In the specific implementation, the model's hyperparameters and the number of spatial neighbor nodes are set, and the three-layer spatial aggregation network and time encoder layers constructed in step 3 and step 4 are used alternately to capture the spatiotemporal dependency characteristics of the nodes layer by layer. Residual connections are introduced to prevent the deep network from experiencing gradient vanishing or exploding problems during training. The model is trained to minimize the error between the output estimate and the true label. The model is trained until the learnable parameters in the network reach the preset conditions to obtain the target model.

[0037] Step 6: Use the target model to simulate and generate new sensor data, i.e., data of unsampled nodes. Use the data set to be interpolated as the basis for training the model, determine the area to be interpolated, and use the trained target model for spatiotemporal interpolation. In the specific implementation, in order to obtain a gridded sea surface temperature dataset with complete data, an iterative interpolation strategy is adopted, and the target model is used to interpolate and predict the sea surface temperature of unsampled points in the sea surface temperature dataset. The iterative interpolation strategy starts from the vicinity of the known nodes and gradually expands outward. The interpolation results initially generated can be used to expand the training set, and the interpolation accuracy of the model is further optimized through multiple iterations, and finally a gridded sea surface temperature dataset with a time resolution of daily and a spatial resolution of 0.25°×0.25° without missing data is obtained. The target interpolation model achieves high-precision interpolation of unobserved points in the case of scarce data, and achieves good technical results. Taking the sea temperature data in the Bohai Sea area on January 15, 2022 as an example, the data missing rate is 30%, and about 15% of the shielded nodes are set. The target model is used for prediction and interpolation. The root mean square error (RMSE) of the model prediction is 0.2021, and the mean absolute error (MAE) is 0.1794, indicating that the present invention can still provide accurate temperature prediction under limited data conditions, and has high applicability and practical value.

Claims

1. A spatiotemporal data interpolation method based on inductive learning, characterized in that: The method comprises the following steps: Step 1: Use the corresponding instruments to collect spatiotemporal data, and then preprocess the spatiotemporal data set; Step 2: Use the data set in step 1 to construct training samples for the spatiotemporal data interpolation model to generate training samples that can generalize the model to unknown nodes and graph structures; Step 3: Use the training samples of the spatiotemporal data interpolation model constructed in step 2 to build a spatial aggregation network belonging to the graph neural network; Step 4: Build the time encoder; Step 5: Train the spatiotemporal data interpolation model; Step 6: The trained target model is used to simulate the generation of new sensor data and the data of unsampled nodes; the data set to be interpolated is used as the basis for the training model, and the area to be interpolated is determined, including the location and time period of the unsampled nodes. The data is processed into input acceptable to the interpolation model described in step 5. The adjacency matrix needs to contain the unsampled node information, and the mask matrix is ​​set to zero to identify the unsampled nodes. The interpolation model described in step 5 is used for interpolation.

2. The spatiotemporal data interpolation method based on inductive learning according to claim 1, characterized in that: The data set described in step 1 must cover timestamp and spatial information, and then data cleaning and normalization are performed. The processed data is organized into a historical data matrix. At the same time, an initial all-zero mask matrix is ​​constructed for subsequent marking of missing values ​​in the data and simulating unsampled nodes. According to the missing data in the historical data matrix, the data missing matrix is ​​updated, and the historical data matrix is ​​divided into training set, validation set and test set according to the proportion.

3. The spatiotemporal data interpolation method based on inductive learning according to claim 2, characterized in that: The method of step 2 is as follows: randomly select a time point within the time range of the historical data matrix, and extract a submatrix from the complete historical data matrix according to the selected time node; the submatrix contains the observation data of all nodes at a specific time point; randomly select 10%-20% of the nodes in the submatrix to simulate unsampled point nodes; set the positions corresponding to the set unsampled point nodes in the mask matrix to 1, and reconstruct the data of these unsampled nodes through model training.

4. The spatiotemporal data interpolation method based on inductive learning according to claim 3, characterized in that: Step 3: Consider the spatial position in the spatiotemporal data as a node in the graph, and the reachability and distance relationship as the connection relationship in the graph, extract the spatial dependency of the spatiotemporal data through the spatial aggregation network, use the aggregation function to integrate the features of the neighboring nodes, and learn and update the features of the nodes; Based on graph neural networks, spatial aggregation networks use aggregation functions and distance information in the same layer to capture complex spatial dependencies.

5. The spatiotemporal data interpolation method based on inductive learning according to claim 4, characterized in that: The aggregation functions include average aggregation, weighted average aggregation, Softmax aggregation, Softmin aggregation, standard deviation aggregation, maximum pooling, minimum pooling, mean distance aggregation, standard distance deviation aggregation or self-attention aggregation. The spatial aggregation network uses a scaler to consider the influence of different features, adjust the feature value range or distribution, and use tensor product to combine the aggregation function and the scaler together to enhance the learning ability of the model.

6. The spatiotemporal data interpolation method based on inductive learning according to claim 5, characterized in that: The step 4 constructs a time encoder: use more than one one-dimensional convolution kernels of different sizes to perform convolution operations on the time series data of a single node in parallel, extract local and long-term time features, and perform zero padding before the convolution operation; splice all feature channels generated by the convolution together, and use a gating mechanism to pass information that is critical to the task. At the same time, the time encoder uses different activation functions, residual connections, and skip connections to enhance the learning ability of the network and avoid the gradient disappearance problem.

7. The spatiotemporal data interpolation method based on inductive learning according to claim 6, characterized in that: The step 5: determining the hyperparameter settings of the model, and at the beginning of training, using the spatial aggregation network layer and the time encoder layer to alternately stack to learn the spatial and temporal features of the spatiotemporal data; In each layer, the spatial aggregation network layer uses more than one aggregation function to integrate the information of neighboring nodes, while the temporal encoder captures the dynamic changes of the time series through multi-scale convolution operations; residual connections are introduced into the model; In each iteration, training samples are randomly drawn from historical data according to the number of samples determined by the training batch parameter, and a masking strategy is applied to simulate data missing conditions; model parameters are adjusted by minimizing the root mean square error or mean absolute error of the loss function; the Adam optimizer gradient descent method is used to update the learnable parameters of the model according to the gradient calculated by the back-propagation algorithm; During the training process, an early stopping mechanism is used to monitor the loss on the validation set. When the loss does not decrease significantly over multiple consecutive iterations, the training is terminated early to avoid overfitting. When the performance of the model on the validation set reaches stability or meets the preset training conditions, the final target model is obtained. The hyperparameters include the number of network layers, the training batch size and the maximum training cycle, as well as the ratio of missing nodes, the input sequence length of the training data, the length of the temporal convolution kernel in the temporal encoder, and the number of neighbor nodes.

8. The spatiotemporal data interpolation method based on inductive learning according to claim 1, characterized in that: Step 6: In the meteorological or oceanographic fields, virtual data is generated to fill the gaps in the monitoring network and improve the spatial coverage of the data; in traffic monitoring, traffic flow data of unsampled sections is generated to help conduct more comprehensive traffic analysis and decision-making; In natural hazard monitoring, generating data on unsampled areas helps better assess risks and develop response measures.

9. A spatiotemporal data interpolation system based on inductive learning, characterized in that: The system includes a data input and processing module, a training sample module for constructing a spatiotemporal data interpolation model, a module for constructing a spatial aggregation network, a module for constructing a time encoder, a module for training a spatiotemporal data interpolation model, and a module for interpolating data; The data input and processing module is used to acquire data and pre-process the data, and the module runs step 1 of the spatiotemporal data interpolation method based on inductive learning described in claim 1; The training sample module for constructing a spatiotemporal data interpolation model Execute step 2 of the spatiotemporal data interpolation method based on inductive learning described in claim 1; The spatial aggregation network building module runs step 3 of the spatiotemporal data interpolation method based on inductive learning described in claim 1; The construction time encoder module runs step 4 of the spatiotemporal data interpolation method based on inductive learning described in claim 1; The training spatiotemporal data interpolation model module executes step 5 of the spatiotemporal data interpolation method based on inductive learning described in claim 1; The data interpolation module runs step 6 of the spatiotemporal data interpolation method based on inductive learning described in claim 1.

10. A spatiotemporal data interpolation device based on inductive learning, characterized in that: The device is equipped with the system according to claim 9.

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