Twsa data recovery method, device, equipment, storage medium and computer program product

Abstract

The application relates to the technical field of time-varying gravity data processing, in particular to a TWSA data recovery method and device, equipment, a storage medium and a computer program product. The method comprises the following steps: acquiring original gravity field coefficient data, and converting the original gravity field coefficient data into grid data sequences under a target resolution based on a preset conversion rule; performing normalization processing on the grid data sequences to obtain standardized input data; based on the standardized input data, a training sample set and a target label set of an initial neural network model are constructed, and the initial neural network model is trained based on the training sample set and the target label set to obtain a target neural network model; based on the target neural network model, inference is performed on the current standardized input data to obtain standardized prediction data; and the standardized prediction data is subjected to inverse normalization processing to obtain target TWSA recovery data, thereby improving the efficiency of TWSA data recovery.

Description

Technical Field

[0001] This application relates to the field of time-varying gravity data processing technology, and in particular to a TWSA data recovery method, apparatus, device, storage medium, and computer program product. Background Technology

[0002] The GRACE / GRACE-FO satellite mission provides high-precision, globally covered Level-2 time-varying gravity field data, widely used in Earth system science research on land water storage changes, ice sheet mass changes, and crustal deformation. However, Level-2 data is expressed in spherical harmonic coefficients, exhibiting significant "striping" errors and high-frequency noise, which often mask the true time-varying signals of Earth's mass. Therefore, complex post-processing steps such as filtering and restoration are necessary to obtain Level-3 Surface Water Storage Anomaly (TWSA) data with clear physical meaning and spatial structure. Currently, mainstream filtering methods include DDK series filters (such as DDK4) and Gaussian filters (such as the 300 km Gaussian filter), which improve data quality by suppressing high-frequency noise in the spherical harmonic coefficients. However, these methods generally rely on preset filtering parameters or window widths, which are usually determined empirically and lack data-driven optimality analysis. This can easily lead to over-smoothing of the target signal or information loss, thus affecting the physical interpretability and regional adaptability of the final results. After filtering, techniques such as scale factor correction, forward modeling, and Mascon inversion are typically applied to recover the signal attenuation caused by filtering and further approximate the true TWSA. However, these recovery techniques rely heavily on domain knowledge, geodetic theory, and empirical models, resulting in high computational complexity and tedious parameter tuning, leading to poor efficiency in TWSA data recovery. Therefore, improving the efficiency of TWSA data recovery has become an urgent technical problem to be solved. Summary of the Invention

[0003] The main objective of this application is to provide a TWSA data recovery method, apparatus, device, storage medium, and computer program product, aiming to solve the technical problem of how to improve the efficiency of TWSA data recovery.

[0004] To achieve the above objectives, this application provides a TWSA data recovery method, which includes the following steps: The original gravity field coefficient data is acquired and converted into a gridded data sequence at the target resolution based on a preset conversion rule. The gridded data sequence is normalized to obtain standardized input data; Based on the standardized input data, a training sample set and a target label set for an initial neural network model are constructed, and the initial neural network model is trained based on the training sample set and the target label set to obtain the target neural network model; Based on the target neural network model, reasoning is performed on the current standardized input data to obtain standardized prediction data; The standardized prediction data is denormalized to obtain the target TWSA recovery data.

[0005] In one embodiment, the step of acquiring the original gravity field coefficient data and converting the original gravity field coefficient data into a gridded data sequence at the target resolution based on a preset conversion rule includes: Obtain the raw gravity field coefficient data; The original gravity field coefficient data is converted into physical quantity data in grid form according to the spherical harmonic representation format; Based on the target resolution, the physical quantity data is rearranged in chronological order to obtain the gridded data sequence.

[0006] In one embodiment, the step of constructing a training sample set and a target label set for an initial neural network model based on the standardized input data, and training the initial neural network model based on the training sample set and the target label set to obtain a target neural network model, includes: Based on the standardized input data, a training sample set and a target label set for the initial neural network model are constructed; The initial neural network model is trained based on the training sample set and the target label set; Based on the training results, the hyperparameters in the initial neural network model are adjusted using a Bayesian optimization algorithm. The hyperparameters include at least one of the following: number of convolutional kernels, learning rate, and training batch size. Based on the adjustment results, the target neural network model is obtained.

[0007] In one embodiment, the step of inferring from the current standardized input data based on the target neural network model to obtain standardized prediction data includes: Feature extraction is performed on the current standardized input data by inputting it into the convolutional layer of the target neural network model; Spatial attention processing is applied to the feature extraction results to obtain a weighted feature map; By performing a deconvolution operation on the weighted feature map, the weighted feature map is restored to the spatial dimension of the current standardized input data; The recovered weighted feature map is input into the output convolutional layer to obtain the standardized prediction data.

[0008] In one embodiment, the step of performing spatial attention processing on the feature extraction results to obtain a weighted feature map includes: Based on the feature extraction results, a spatial mask matrix is ​​obtained; The spatial regions of the feature extraction results are weighted based on the spatial mask matrix. The weighted feature extraction results are output to obtain the weighted feature map.

[0009] In one embodiment, the step of performing inverse normalization on the standardized prediction data to obtain the target TWSA recovery data includes: Obtain the mean and standard deviation parameters of the standardized prediction data for the corresponding time period; Based on the standardized prediction data, the mean parameter, and the standard deviation parameter, the standardized prediction data is denormalized to obtain unstandardized prediction data. The unstandardized prediction data is output and used as the target TWSA recovery data.

[0010] Furthermore, to achieve the above objectives, this application also proposes a TWSA data recovery device, which includes: The data conversion module is used to acquire the original gravity field coefficient data and convert the original gravity field coefficient data into a gridded data sequence at the target resolution based on a preset conversion rule. The standardization module is used to normalize the gridded data sequence to obtain standardized input data; The training module is used to construct a training sample set and a target label set for an initial neural network model based on the standardized input data; train the initial neural network model based on the training sample set and the target label set; adjust the hyperparameters in the initial neural network model using a Bayesian optimization algorithm based on the training results, wherein the hyperparameters include at least one of the following: number of convolutional kernels, learning rate, and training batch size; and obtain the target neural network model based on the adjustment results. The inference module is used to extract features from the current standardized input data by inputting it into the convolutional layer of the target neural network model; obtain a spatial mask matrix based on the feature extraction results; perform weighted processing on the spatial regions of the feature extraction results based on the spatial mask matrix; output the weighted feature extraction results to obtain a weighted feature map; restore the weighted feature map to the spatial dimension of the current standardized input data by performing a deconvolution operation on the weighted feature map; and input the restored weighted feature map into the output convolutional layer to obtain standardized prediction data. The target module is used to perform inverse normalization processing on the standardized prediction data to obtain the target TWSA recovery data.

[0011] In addition, to achieve the above objectives, this application also proposes a TWSA data recovery device, the device comprising: a memory, a processor, and a TWSA data recovery program stored in the memory and executable on the processor, the TWSA data recovery program being configured to implement the steps of the TWSA data recovery method as described above.

[0012] In addition, to achieve the above objectives, this application also proposes a storage medium storing a TWSA data recovery program, which, when executed by a processor, implements the steps of the TWSA data recovery method as described above.

[0013] In addition, to achieve the above objectives, this application also proposes a computer program product comprising a computer program that, when executed by a processor, implements the steps of the TWSA data recovery method as described above.

[0014] This application acquires raw gravity field coefficient data and converts it into a gridded data sequence at the target resolution based on a preset conversion rule. The gridded data sequence is then normalized to obtain standardized input data. Based on the standardized input data, a training sample set and a target label set for an initial neural network model are constructed. The initial neural network model is then trained using the training sample set and the target label set to obtain the target neural network model. Based on the target neural network model, inference is performed on the current standardized input data to obtain standardized prediction data. Finally, the standardized prediction data is denormalized to obtain the target TWSA recovery data. This application acquires raw gravity field coefficient data and converts it into a gridded data sequence to ensure the spatial tractability of the raw data. Then, normalization is applied to standardize the data to meet model training requirements and improve training stability. Next, by constructing a training sample set and a target label set, the initial neural network model is trained, forming a target neural network model with specific mapping capabilities. This model is then used to infer from the current standardized input data, enabling rapid generation of standardized prediction data. Finally, denormalization is used to recover the physical-scale TWSA results. This structured approach encapsulates the complete path from data preprocessing to model prediction to result restoration, avoiding the multi-step manual calibration involved in traditional methods and improving the automation and efficiency of the TWSA data recovery process. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating the first embodiment of the TWSA data recovery method of this application; Figure 2 This is a schematic diagram of a sub-process in the second embodiment of the TWSA data recovery method of this application; Figure 3 This is a schematic diagram of a sub-process in the third embodiment of the TWSA data recovery method of this application; Figure 4 This is a schematic diagram of the data recovery process in one embodiment of the TWSA data recovery method of this application; Figure 5 This is a schematic diagram of the module structure of the TWSA data recovery device according to an embodiment of this application; Figure 6 This is a schematic diagram of the device structure of the hardware operating environment involved in the TWSA data recovery method in the embodiments of this application.

[0016] The realization of the purpose, functional features and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0017] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of this application.

[0018] To better understand the technical solution of this application, a detailed description will be provided below in conjunction with the accompanying drawings and specific implementation methods.

[0019] It should be noted that the GRACE / GRACE-FO satellite mission provides high-precision, globally covered Level-2 time-varying gravity field data, widely used in Earth system science research on land water storage changes, ice sheet mass changes, and crustal deformation. However, Level-2 data is expressed in spherical harmonic coefficients, exhibiting significant "striping" errors and high-frequency noise. These errors often mask the true time-varying signals of Earth's mass. Therefore, complex post-processing steps such as filtering and restoration are necessary to obtain Level-3 Surface Water Storage Anomaly (TWSA) data with clear physical meaning and spatial structure. Currently, mainstream filtering methods include DDK series filters (such as DDK4) and Gaussian filters (such as the 300 km Gaussian filter), which improve data quality by suppressing high-frequency noise in the spherical harmonic coefficients. However, these methods generally rely on preset filtering parameters or window widths, which are usually determined empirically and lack data-driven optimality analysis. This can easily lead to over-smoothing of the target signal or information loss, thus affecting the physical interpretability and regional adaptability of the final results. After filtering, techniques such as scale factor correction, forward modeling, and Mascon inversion are typically applied to recover the signal attenuation caused by filtering and further approximate the true TWSA. However, these recovery techniques rely heavily on domain knowledge, geodetic theory, and empirical models, resulting in high computational complexity and tedious parameter tuning, leading to poor efficiency in TWSA data recovery. Therefore, improving the efficiency of TWSA data recovery has become an urgent technical problem to be solved.

[0020] The main solution of this application is as follows: First, acquire the original gravity field coefficient data and convert it into a gridded data sequence at the target resolution based on a preset conversion rule. Second, normalize the gridded data sequence to obtain standardized input data. Third, construct a training sample set and a target label set for an initial neural network model based on the standardized input data. Fourth, train the initial neural network model based on the training sample set and the target label set to obtain the target neural network model. Fifth, perform inference on the current standardized input data based on the target neural network model to obtain standardized prediction data. Sixth, perform inverse normalization on the standardized prediction data to obtain the target TWSA recovery data.

[0021] This application acquires raw gravity field coefficient data and converts it into a gridded data sequence to ensure the spatial tractability of the raw data. Then, normalization is applied to standardize the data to meet model training requirements and improve training stability. Next, by constructing a training sample set and a target label set, the initial neural network model is trained, forming a target neural network model with specific mapping capabilities. This model is then used to infer from the current standardized input data, enabling rapid generation of standardized prediction data. Finally, denormalization is used to recover the physical-scale TWSA results. This structured approach encapsulates the complete path from data preprocessing to model prediction to result restoration, avoiding the multi-step manual calibration involved in traditional methods and improving the automation and efficiency of the TWSA data recovery process.

[0022] It should be noted that the executing entity of the method in this embodiment can be a computing service device with data processing, network communication, and program execution functions, or it can be the aforementioned TWSA data recovery device with the same or similar functions. This embodiment and the following embodiments will be described using a TWSA data recovery device as an example.

[0023] Based on this, a first embodiment of the TWSA data recovery method of this application is proposed. Please refer to... Figure 1 , Figure 1 This is a flowchart illustrating the first embodiment of the TWSA data recovery method of this application.

[0024] In this embodiment, the TWSA data recovery method includes the following steps: S1: Obtain the original gravity field coefficient data and convert the original gravity field coefficient data into a gridded data sequence at the target resolution based on a preset conversion rule; It should be noted that the raw gravity field coefficient data refers to Level-2 time-varying gravity field observation data, expressed in the form of spherical harmonic coefficients, provided by the GRACE or GRACE-FO satellite missions. The preset conversion rules refer to the pre-defined mathematical mapping methods and parameter settings used when converting gravity field data in spherical harmonic coefficient form into a spatially gridded representation. The target resolution refers to the desired accuracy or unit area scale of the final gridded data in geographic space. The gridded data sequence refers to a series of data sets that have been spatially divided according to a uniform latitude and longitude grid and arranged in chronological order after processing the Earth's gravity field data. TWSA (Terrestrial Water Storage Anomaly) refers to terrestrial water storage anomalies.

[0025] Specifically, the first step is to obtain raw gravity field coefficient data. This data typically comes from the data release agencies of the GRACE or GRACE-FO satellite missions (such as CSR, GFZ, etc.), and is provided in the form of time-series spherical harmonic coefficient files. These spherical harmonic coefficients contain components of multiple orders and degrees, encoding the variation patterns of the Earth's gravitational field at different points in time. This raw data does not have intuitive spatial visualization and requires further processing before it can be used for space analysis.

[0026] Furthermore, according to preset transformation rules, the spherical harmonic coefficient data undergoes spatial transformation to obtain a gridded data sequence at the target resolution. This transformation process mainly converts the coefficient form of the gravity field representation into raster values ​​in geographic coordinates (such as the change in surface water storage at each latitude and longitude grid point) through spherical harmonic function expansion. During this process, the maximum order, truncation range, grid size, and reference ellipsoid parameters need to be set to ensure that the generated gridded data has a uniform spatial structure and the desired accuracy. Finally, the processed gridded data is organized chronologically to form a time series structure for use in subsequent models.

[0027] This step transforms the raw spherical harmonic coefficient data into a gridded data sequence with a well-defined spatial distribution structure and a uniform scale, giving the original gravity field observations good spatial representation capabilities and an input format acceptable to machine learning models. Without relying on traditional filtering and manual modeling, the high-dimensional and complex gravity field information is standardized and structured using unified transformation rules. This reduces the complexity of subsequent processing and improves the standardization and processing efficiency of the TWSA data recovery task, laying a solid foundation for the training and inference of deep learning models.

[0028] S2: Normalize the gridded data sequence to obtain standardized input data; It should be noted that normalization refers to the process of converting raw data into data with a uniform distribution range or numerical scale. Standardized input data refers to the data used as input to neural networks after normalization.

[0029] Specifically, firstly, based on the entire gridded data sequence, its statistical parameters in the time or spatial dimensions are calculated, such as the mean and standard deviation, or the maximum and minimum values. To ensure that the data performs stably and is comparable in the model, the data values ​​at each time step or at each grid point need to be normalized to eliminate scale differences present in the original data.

[0030] Furthermore, normalization is typically performed on a grid matrix at different time steps, converting each data value into a dimensionless standard value relative to the overall distribution. For example, if Z-score normalization is used, the value of each grid point is processed by subtracting the mean and then dividing by the standard deviation. This process maintains consistency across all training samples and reuses the same normalization parameters during the model inference phase to ensure data consistency.

[0031] By normalizing the gridded data sequence, the input data is kept stable on a numerical scale, avoiding problems such as model training non-convergence or gradient imbalance caused by numerical differences across different regions or time scales. The standardized input data not only facilitates the extraction of key features by the model but also effectively improves training efficiency and accuracy, and ensures repeatability and stability when applied to different data batches or at different times, providing a fundamental guarantee for efficient training and accurate prediction of neural network models.

[0032] S3: Based on the standardized input data, construct a training sample set and a target label set for the initial neural network model, and train the initial neural network model based on the training sample set and the target label set to obtain the target neural network model; It should be noted that the training sample set refers to the input dataset used in the neural network training process. The target label set refers to the target output dataset that corresponds one-to-one with the training sample set. The initial neural network model refers to the neural network structure that has not yet been trained or has only had its weight parameters initialized. The target neural network model refers to the neural network model with fitting ability obtained after iterative training using the training sample set and the target label set, which can be used for subsequent inference tasks.

[0033] Specifically, the training sample set and target label set are first constructed based on the normalized gridded data sequence. Typically, the training sample set comes from slices of the original Level-2 gridded TWSA data at specific time points, while the target label set comes from the standardized values ​​of a known Level-3 reference product (such as CSR_L3 data) at the corresponding time points. The two sets are then paired and arranged chronologically to form complete training data pairs.

[0034] Furthermore, an initial neural network model with a multi-layered structure is constructed, which may include convolutional layers, deconvolutional layers, and non-linear activation function layers. By inputting training samples into the model and using the target label set as supervision, gradient descent-like optimization algorithms are employed to iteratively iterate the model parameters, minimizing the error between the predicted and target values, thus obtaining the converged target neural network model. The training process is typically performed alternately on the training and validation sets to ensure the model possesses generalization ability.

[0035] By constructing a training sample set and a target label set, and training a neural network model based on these, the model can automatically learn the nonlinear mapping relationship between standardized input data and target TWSA data, replacing the traditional method of relying on empirical rules or complex physical models for inversion. The trained target neural network model has stable feature extraction and prediction capabilities, and can be used for subsequent multi-time-period and multi-regional automatic inference tasks, thereby significantly improving the intelligence and processing efficiency of TWSA data recovery.

[0036] S4: Based on the target neural network model, reason about the current standardized input data to obtain standardized prediction data; It should be noted that the standardized input data refers to the normalized gridded TWSA data that needs to be predicted. Inference refers to the process of using a trained neural network model to perform forward propagation calculations on new input data and obtain the output results. Standardized prediction data refers to the prediction results that are still within the normalized numerical range of the model's inference results.

[0037] Specifically, the standardized input data corresponding to the current moment is first fed into the trained target neural network model. This input data structure must be consistent with that of the training phase to ensure the model can correctly identify feature dimensions and spatial structure. Subsequently, the target neural network model sequentially executes the forward propagation process. The input data is processed layer by layer through convolutional layers, nonlinear activation layers, and deconvolutional layers. The model uses its learned weight parameters to analyze and transform the spatial features of the input data, ultimately generating a predicted value at the output layer that corresponds to the spatial structure of the input, forming standardized prediction data. This prediction result is still at a normalized scale and requires further denormalization to obtain the physical quantity.

[0038] This step involves feeding the current standardized input data into a pre-trained neural network model and performing a one-time inference operation to quickly output the corresponding prediction result, avoiding the cumbersome process of multiple rounds of filtering, scaling, and model building required in traditional methods. The neural network model has learned deep mapping relationships between data through historical samples and can directly generalize to new input data, achieving efficient and automatic TWSA data prediction. This inference process does not require retraining, greatly improving the real-time performance and processing efficiency of data recovery.

[0039] S5: Perform inverse normalization on the standardized prediction data to obtain the target TWSA recovery data.

[0040] It should be noted that denormalization refers to the process of restoring standardized data to its original physical quantity scale. TWSA restored data, namely the Terrestrial Water Storage Anomaly restoration results, represent the predicted actual physical quantities.

[0041] Specifically, the mean and standard deviation parameters saved during the normalization process are first invoked. These parameters were calculated on the training dataset to ensure consistency between the input and output data. For each value in the standardized prediction data, numerical restoration is performed according to the "inverse normalization rule".

[0042] Furthermore, for each grid point in the standardized prediction results, the value is first multiplied by the standard deviation of the corresponding location, and then the corresponding mean is added to obtain the predicted value of the physical quantity at that location. This process is executed in parallel across the entire prediction grid to ensure that the spatiotemporal distribution structure is consistent with the input data. The final processing result constitutes a geographic layer representing changes in surface water storage, namely the target TWSA restored data, which can be used for scientific research or decision support.

[0043] By performing inverse normalization on standardized prediction data, the relative values ​​of the model output can be restored to absolute values ​​with physical quantity attributes, thereby giving the model prediction results practical interpretability and facilitating scientific analysis and engineering applications. This process ensures data scale consistency between model training and inference phases, eliminates the dimensionless influence introduced by the standardization process, helps maintain data comparability and accuracy, and further enhances the reliability and practicality of the TWSA data recovery method.

[0044] This embodiment acquires raw gravity field coefficient data and converts it into a gridded data sequence at the target resolution based on a preset conversion rule. The gridded data sequence is then normalized to obtain standardized input data. Based on the standardized input data, a training sample set and a target label set for an initial neural network model are constructed. The initial neural network model is then trained using these two sets to obtain the target neural network model. Based on the target neural network model, inference is performed on the current standardized input data to obtain standardized prediction data. Finally, the standardized prediction data is denormalized to obtain the target TWSA recovery data. This embodiment acquires the original gravity field coefficient data and converts it into a gridded data sequence to ensure the spatial tractability of the original data. Then, normalization is applied to standardize the data to meet model training requirements and improve training stability. Next, by constructing a training sample set and a target label set, the initial neural network model is trained, forming a target neural network model with specific mapping capabilities. This model is then used to infer from the current standardized input data, enabling rapid generation of standardized prediction data. Finally, denormalization is used to recover the physical-scale TWSA results. This structured approach encapsulates the complete path from data preprocessing to model prediction to result restoration, avoiding the multi-step manual intervention and correction operations involved in traditional methods, thus improving the automation and processing efficiency of the TWSA data recovery process.

[0045] Based on the first embodiment described above, a second embodiment of the TWSA data recovery method of this application is proposed. Please refer to... Figure 2 , Figure 2 This is a schematic diagram of a sub-process in the second embodiment of the TWSA data recovery method of this application.

[0046] like Figure 2 As shown, in this embodiment, step S1 includes: S11: Obtain raw gravity field coefficient data; S12: Convert the original gravity field coefficient data into physical quantity data in grid form according to the spherical harmonic representation format; S13: Based on the target resolution, the physical quantity data is rearranged in chronological order to obtain the gridded data sequence.

[0047] It should be noted that the spherical harmonic representation refers to representing the global gravitational field as a linear combination of harmonic functions on a sphere, with each coefficient corresponding to information about different spatial frequencies. A gridded data sequence refers to arranging gridded data from multiple time points in chronological order to form an input dataset with a time-dimensional structure.

[0048] Specifically, raw gravity field coefficient data is obtained, typically downloaded from GRACE or GRACE-FO official data centers (such as CSR, GFZ). The data is in the form of a series of spherical harmonic coefficient files containing different orders and degrees. These spherical harmonic coefficients constitute a complete mathematical description of the Earth's gravitational field at a specific point in time and are the standard output format for Level-2 products. Subsequently, the spherical harmonic coefficient data is projected onto a grid location in a geographic coordinate system according to the spherical harmonic function expansion rules, resulting in gridded physical quantity data. This process involves setting parameters such as the maximum expansion order and selecting a coordinate reference (e.g., the WGS84 ellipsoid). After conversion, each grid point represents a physical change at a corresponding location on the Earth's surface, such as water storage anomalies. After conversion, based on the target resolution (e.g., dividing the globe into 1×1 sections), the gridded data from multiple time points are uniformly rearranged and organized into a sequence according to time order, forming a spatially consistent and temporally continuous gridded data sequence. This data structure is suitable for subsequent model training and prediction tasks.

[0049] By transforming spherical harmonic coefficient data into a gridded sequence of physical quantities at a uniform resolution, not only was the raw gravity field data converted into a spatially intuitive structure, but the originally abstract, high-dimensional coefficient data also acquired a spatial organization form that could be directly used as input for neural networks. This preprocessing step solves the problem that raw observation data cannot be directly used, providing standardized and structured basic inputs for subsequent normalization, modeling, and inference processes, thereby significantly improving the automation and efficiency of the entire TWSA data recovery process.

[0050] Based on the first embodiment described above, in this embodiment, step S3 includes: S31: Based on the standardized input data, construct the training sample set and target label set of the initial neural network model; S32: Train the initial neural network model based on the training sample set and the target label set; S33: Based on the training results, the hyperparameters in the initial neural network model are adjusted using the Bayesian optimization algorithm. The hyperparameters include at least one of the following: number of convolutional kernels, learning rate, and training batch size. S34: Based on the adjustment results, the target neural network model is obtained.

[0051] It should be noted that the training sample set refers to the set of input data used for training the neural network model. The target label set refers to the set of output data corresponding to the training samples, used to supervise the model training. The initial neural network model refers to the neural network structure that has not been trained or only contains randomly initialized parameters. Hyperparameters refer to parameters that affect the model training process but are not automatically learned by training. The Bayesian optimization algorithm is a global optimization method based on a probabilistic model. The target neural network model refers to the final neural network model with optimal performance and suitable for inference after training and hyperparameter optimization.

[0052] Specifically, standardized input data is paired with its corresponding target output (referencing TWSA data) to construct a training sample set and a target label set. This process typically involves dividing the data into training, validation, and test sets, ensuring that the spatial structure, temporal order, and numerical format are consistent with the model's input and output requirements. Based on this, an initial neural network model with convolutional layers, activation layers, and deconvolutional layers is constructed. Using the training sample set as input and the target label set as supervision, a parameter learning process is performed. The model continuously updates its internal weights through forward and backward propagation mechanisms to minimize the error between the output and the label.

[0053] Furthermore, after the initial model training is complete, a Bayesian optimization algorithm is introduced to adjust the hyperparameters in the neural network. By constructing a performance evaluation function (such as the validation set RMSE), the optimal combination of parameters, including the number of convolutional kernels, learning rate, and training batch size, is searched using the Bayesian optimization strategy. In each round of optimization, the algorithm constructs a probabilistic model based on historical evaluation results, predicts the most promising hyperparameter combinations, and conducts experimental evaluations until it converges to the optimal performance point. Finally, the trained and optimized model is selected as the target neural network model for subsequent inference and data recovery tasks.

[0054] By introducing three stages—training sample construction, model training, and hyperparameter optimization—a highly efficient mapping model from input data to target output is systematically established. Based on the completion of basic training, the key hyperparameters of the neural network are automatically adjusted using a Bayesian optimization algorithm. This not only avoids the inefficiency and uncertainty of traditional manual parameter tuning but also significantly improves the model's stability and generalization performance. The resulting target neural network model possesses superior predictive ability and convergence speed, providing core support for high-quality recovery of TWSA data.

[0055] This embodiment acquires raw gravity field coefficient data and converts it into a gridded data sequence at the target resolution based on a preset conversion rule. The gridded data sequence is then normalized to obtain standardized input data. Based on the standardized input data, a training sample set and a target label set for an initial neural network model are constructed. The initial neural network model is then trained using these two sets to obtain the target neural network model. Based on the target neural network model, inference is performed on the current standardized input data to obtain standardized prediction data. Finally, the standardized prediction data is denormalized to obtain the target TWSA recovery data. This embodiment acquires the original gravity field coefficient data and converts it into a gridded data sequence to ensure the spatial tractability of the original data. Then, normalization is applied to standardize the data to meet model training requirements and improve training stability. Next, by constructing a training sample set and a target label set, the initial neural network model is trained, forming a target neural network model with specific mapping capabilities. This model is then used to infer from the current standardized input data, enabling rapid generation of standardized prediction data. Finally, denormalization is used to recover the physical-scale TWSA results. This structured approach encapsulates the complete path from data preprocessing to model prediction to result restoration, avoiding the multi-step manual intervention and correction operations involved in traditional methods, thus improving the automation and processing efficiency of the TWSA data recovery process.

[0056] Based on the second embodiment described above, a third embodiment of the TWSA data recovery method of this application is proposed. Please refer to... Figure 3 , Figure 3 This is a schematic diagram of a sub-process in the third embodiment of the TWSA data recovery method of this application.

[0057] In this embodiment, step S4 includes: S41: By inputting the current standardized input data into the convolutional layer of the target neural network model, feature extraction is performed on the current standardized input data; S42: Perform spatial attention processing on the feature extraction results to obtain a weighted feature map; S43: By performing a deconvolution operation on the weighted feature map, the weighted feature map is restored to the spatial dimension of the current standardized input data; S44: Input the recovered weighted feature map into the output convolutional layer to obtain the standardized prediction data.

[0058] It's important to note that convolutional layers are one of the fundamental structures in neural networks, used to extract local spatial features from input data. Feature extraction refers to processing input data using a neural network. Spatial attention is a weighting mechanism that identifies salient regions in the input feature map and adjusts their response intensity, thereby enhancing the feature representation of key regions. The weighted feature map refers to the feature map formed after processing by the spatial attention mechanism. Deconvolution, also known as transposed convolution, is used to restore the downsampled feature map to its original input resolution. The output convolutional layer is the final convolutional layer in the model structure. Standardized prediction data refers to the model's output prediction results that are still at a normalized scale.

[0059] Specifically, the current standardized input data is fed into the trained target neural network model. The convolutional layers in the model sequentially perform multiple convolution operations on the input data. Each convolutional kernel scans a local region of the input, extracting spatial feature information and progressively forming increasingly abstract intermediate feature maps. This process extracts representative and distinguishable structural features from the input data, resulting in feature extraction results.

[0060] Furthermore, the feature extraction results are input into the spatial attention processing module. This module calculates attention weights for each spatial location, identifies key regions based on prior information (such as geographic masks), and adjusts the response values ​​of the corresponding regions to generate a weighted feature map. Next, a deconvolution operation is performed on the weighted feature map, gradually restoring its spatial resolution through a series of upsampling steps to ensure it matches the spatial dimension of the original input data. Finally, the restored weighted feature map is input into the output convolutional layer to perform the final mapping operation, outputting standardized prediction data with a structure corresponding to the input, which serves as the model's inference result.

[0061] By sequentially processing the standardized input data through convolutional feature extraction, spatial attention weighting, deconvolutional reconstruction, and output mapping, a complete forward inference path is formed. This not only achieves efficient spatial feature modeling but also effectively enhances the model's ability to express change patterns in key regions (such as land and water reservoirs). This process accurately maintains spatial structure consistency, ensuring that the model output has both good resolution and interpretability, laying the foundation for subsequent generation of high-precision TWSA reconstruction data, thereby significantly improving the accuracy and practicality of the inference stage.

[0062] Based on the second embodiment described above, in this embodiment, step S42 includes: S421: Based on the feature extraction results, obtain the spatial mask matrix; S422: Weight the spatial regions of the feature extraction results based on the spatial mask matrix; S423: Output the weighted feature extraction results to obtain the weighted feature map.

[0063] It should be noted that the feature extraction result refers to the intermediate feature map obtained after processing the input data through the convolutional layers of a neural network. The spatial mask matrix is ​​a two-dimensional matrix with the same spatial dimensions as the feature map. Spatial region weighting refers to amplifying or suppressing the response values ​​at different locations in the feature map based on the mask matrix, making the model focus more on key regional features.

[0064] Specifically, based on the spatial dimensions of the feature extraction results and their relationship to geographical location, a spatial mask matrix is ​​generated or loaded. The spatial dimensions of this matrix are related to the features... Figure 1 Each element of the mask identifies the region type for its corresponding location. For example, it can be set to 1 for land regions and 0 for ocean regions, or set to different weight values ​​to express the degree of attention to the region. This mask can be a static preset or dynamically generated based on input data.

[0065] Furthermore, the feature extraction results are weighted element-wise using a spatial mask matrix. Specifically, the mask matrix and the feature map are multiplied correspondingly in the spatial dimension, and the feature values ​​at corresponding positions are enhanced or suppressed according to the mask weights. This weighting process can be applied to each channel of the feature map, preserving its structure. After the weighting operation, the processed result is the weighted feature map, which serves as the input for subsequent deconvolution and output mapping.

[0066] By introducing a spatial mask matrix and weighting the feature extraction results, the neural network model can focus on key spatial regions during inference, improving its ability to perceive geographically heterogeneous areas (such as land and water system distribution areas). This weighting mechanism can enhance the expression of specific regional features without increasing the number of model parameters, thereby improving the model's accuracy in capturing change patterns in the target region. This provides more accurate and spatially sensitive feature inputs for subsequent TWSA recovery, contributing to improved overall recovery quality and regional adaptability.

[0067] Based on the second embodiment described above, in this embodiment, step S5 includes: S51: Obtain the mean and standard deviation parameters of the time period corresponding to the standardized prediction data; S52: Based on the standardized prediction data, the mean parameter and the standard deviation parameter, the standardized prediction data is denormalized to obtain unstandardized prediction data; S53: Output the unstandardized prediction data and use it as the target TWSA recovery data.

[0068] It should be noted that the mean parameter and standard deviation parameter refer to the statistical parameters used during data normalization. They represent the average value and dispersion of the original data, respectively, and are used to inversely reconstruct the true physical values. Denormalization refers to the calculation process of restoring the standardized predicted values ​​to the scale of the original data. Unstandardized predicted data refers to the predicted results after denormalization, which have actual physical units. The target TWSA restored data is the final output, the surface water storage anomaly value restored to the form of a physical quantity.

[0069] Specifically, based on the time labels of the standardized forecast data, the normalization parameters corresponding to that time period are extracted, namely the mean parameter and the standard deviation parameter. These parameters are usually pre-calculated and saved in the normalization process to maintain the consistency of data processing at different stages.

[0070] Furthermore, for each value in the standardized prediction data, an inverse normalization operation is performed: multiplying it by the standard deviation parameter at the corresponding location and adding the mean parameter yields the unstandardized prediction data. This process can be executed in parallel across the entire spatial grid, maintaining consistency with the original data format. Finally, this unstandardized prediction data is output as the target TWSA recovery data with physical units, for subsequent analysis or system applications.

[0071] By performing denormalization at the inference output stage, the standardized prediction results can be restored to TWSA values ​​with actual physical meaning, thus making the model output results intuitive, interpretable, and scientifically valid. This step ensures the consistency between the model's predicted values ​​and the original data scale, avoiding the problem of relative quantity expression caused by normalization affecting subsequent analysis or visualization results. Overall, this processing step constitutes a key bridge from model inference results to practical applications, effectively improving the practicality and engineering adaptability of the TWSA data recovery method.

[0072] This embodiment acquires raw gravity field coefficient data and converts it into a gridded data sequence at the target resolution based on a preset conversion rule. The gridded data sequence is then normalized to obtain standardized input data. Based on the standardized input data, a training sample set and a target label set for an initial neural network model are constructed. The initial neural network model is then trained using these two sets to obtain the target neural network model. Based on the target neural network model, inference is performed on the current standardized input data to obtain standardized prediction data. Finally, the standardized prediction data is denormalized to obtain the target TWSA recovery data. This embodiment acquires the original gravity field coefficient data and converts it into a gridded data sequence to ensure the spatial tractability of the original data. Then, normalization is applied to standardize the data to meet model training requirements and improve training stability. Next, by constructing a training sample set and a target label set, the initial neural network model is trained, forming a target neural network model with specific mapping capabilities. This model is then used to infer from the current standardized input data, enabling rapid generation of standardized prediction data. Finally, denormalization is used to recover the physical-scale TWSA results. This structured approach encapsulates the complete path from data preprocessing to model prediction to result restoration, avoiding the multi-step manual intervention and correction operations involved in traditional methods, thus improving the automation and processing efficiency of the TWSA data recovery process.

[0073] Please see Figure 4 , Figure 4 This is a schematic diagram of the data recovery process in one embodiment of the TWSA data recovery method of this application. Figure 4 As shown, this embodiment discloses a method for directly recovering Level-3 data from GRACE / GRACE-FO Level-2 time-varying gravity data. In this embodiment, a mapping relationship between Level-2 spherical harmonic coefficients and reference Level-3 data is constructed, and training, validation, and testing datasets are built to achieve direct learning from spherical harmonic coefficients to observable surface water storage. Bayesian optimization is used to automatically search for hyperparameters (such as kernel size, learning rate, network depth, etc.) of the deep learning model, improving the model's stability and generalization performance, and avoiding the inefficiency and subjectivity of traditional empirical parameter tuning. A spatial attention module is introduced to effectively capture the spatial heterogeneity and key regional features of Level-2 data, enhancing the model's ability to perceive complex geophysical processes. Traditional complex steps such as filtering and scale factor correction are abandoned, directly outputting Level-3 data with clear physical meaning and faithful structure, improving application efficiency and lowering the professional threshold.

[0074] This application also provides a TWSA data recovery device. Please refer to... Figure 5 , Figure 5This is a schematic diagram of the module structure of the TWSA data recovery device according to an embodiment of this application. The TWSA data recovery device includes: The data conversion module 501 is used to acquire the original gravity field coefficient data and convert the original gravity field coefficient data into a gridded data sequence at the target resolution based on a preset conversion rule. Standardization module 502 is used to normalize the gridded data sequence to obtain standardized input data; Training module 503 is used to construct a training sample set and a target label set for an initial neural network model based on the standardized input data; train the initial neural network model based on the training sample set and the target label set; adjust the hyperparameters in the initial neural network model using a Bayesian optimization algorithm based on the training results, wherein the hyperparameters include at least one of the following: number of convolutional kernels, learning rate, and training batch size; and obtain the target neural network model based on the adjustment results. The inference module 504 is used to extract features from the current standardized input data by inputting it into the convolutional layer of the target neural network model; obtain a spatial mask matrix based on the feature extraction results; perform weighted processing on the spatial regions of the feature extraction results based on the spatial mask matrix; output the weighted feature extraction results to obtain a weighted feature map; restore the weighted feature map to the spatial dimension of the current standardized input data by performing a deconvolution operation on the weighted feature map; and input the restored weighted feature map into the output convolutional layer to obtain standardized prediction data. The target module 505 is used to perform inverse normalization processing on the standardized prediction data to obtain the target TWSA recovery data.

[0075] The TWSA data recovery device provided in this application, employing the TWSA data recovery method described in the above embodiments, can solve the technical problem of how to improve the efficiency of TWSA data recovery. Compared with the prior art, the beneficial effects of the TWSA data recovery device provided in this application are the same as those of the TWSA data recovery method provided in the above embodiments, and other technical features in the TWSA data recovery device are the same as those disclosed in the methods of the above embodiments, and will not be repeated here.

[0076] This application provides a TWSA data recovery device, which includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, which are executed by the at least one processor to enable the at least one processor to perform the TWSA data recovery method in the above embodiments.

[0077] The following is for reference. Figure 6 , Figure 6 This is a schematic diagram of the hardware operating environment involved in the TWSA data recovery method in the embodiments of this application, showing a schematic diagram of the structure of the TWSA data recovery device suitable for implementing the embodiments of this application. Figure 6 The TWSA data recovery device shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments of this application.

[0078] like Figure 6 As shown, the TWSA data recovery device may include a processing unit 1001 (e.g., a central processing unit, a graphics processing unit, etc.), which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 1002 or a program loaded from a storage device 1003 into a random access memory (RAM) 1004. The RAM 1004 also stores various programs and data required for the operation of the TWSA data recovery device. The processing unit 1001, ROM 1002, and RAM 1004 are interconnected via a bus 1005. An input / output (I / O) interface 1006 is also connected to the bus. Typically, the following systems can be connected to the I / O interface 1006: input devices 1007 including, for example, a touchscreen, touchpad, keyboard, mouse, image sensor, microphone, accelerometer, gyroscope, etc.; output devices 1008 including, for example, a liquid crystal display (LCD), speaker, vibrator, etc.; storage devices 1003 including, for example, magnetic tape, hard disk, etc.; and communication devices 1009. Communication device 1009 allows the TWSA data recovery device to communicate wirelessly or wiredly with other devices to exchange data. Although the figures show TWSA data recovery devices with various systems, it should be understood that implementing or having all of the systems shown is not required. More or fewer systems may be implemented alternatively.

[0079] In particular, according to the embodiments disclosed in this application, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, the embodiments disclosed in this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. When the computer program is executed by the processing device 1001, it performs the functions defined in the methods of the embodiments disclosed in this application.

[0080] The TWSA data recovery device provided in this application, employing the TWSA data recovery method described in the above embodiments, can solve the technical problem of how to improve the efficiency of TWSA data recovery. Compared with the prior art, the beneficial effects of the TWSA data recovery device provided in this application are the same as those of the TWSA data recovery method provided in the above embodiments, and other technical features of this TWSA data recovery device are the same as those disclosed in the previous embodiment method, and will not be repeated here.

[0081] It should be understood that the various parts disclosed in this application can be implemented using hardware, software, firmware, or a combination thereof. In the description of the above embodiments, specific features, structures, materials, or characteristics can be combined in any suitable manner in one or more embodiments or examples.

[0082] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0083] This application provides a computer-readable storage medium having computer-readable program instructions (i.e., a computer program) stored thereon, the computer-readable program instructions being used to execute the TWSA data recovery method in the above embodiments.

[0084] The aforementioned computer-readable storage medium carries one or more programs. When these programs are executed by the TWSA data recovery device, the TWSA data recovery device performs the following actions: acquires raw gravity field coefficient data and converts it into a gridded data sequence at the target resolution based on a preset conversion rule; normalizes the gridded data sequence to obtain standardized input data; constructs a training sample set and a target label set for an initial neural network model based on the standardized input data, and trains the initial neural network model based on the training sample set and the target label set to obtain a target neural network model; performs inference on the current standardized input data based on the target neural network model to obtain standardized prediction data; and performs denormalization on the standardized prediction data to obtain the target TWSA recovered data. Computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof. These programming languages ​​include object-oriented programming languages—such as Java, Smalltalk, and C++—and conventional procedural programming languages—such as the "C" language or similar programming languages. The program code can execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or it can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0085] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0086] The modules described in the embodiments of this application can be implemented in software or hardware. The names of the modules do not necessarily limit the functionality of the unit itself.

[0087] The readable storage medium provided in this application is a computer-readable storage medium that stores computer-readable program instructions (i.e., a computer program) for executing the above-described TWSA data recovery method, thereby solving the technical problem of how to improve the efficiency of TWSA data recovery. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided in this application are the same as those of the TWSA data recovery method provided in the above embodiments, and will not be repeated here.

[0088] This application provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the TWSA data recovery method described above.

[0089] The computer program product provided in this application can solve the technical problem of how to improve the efficiency of TWSA data recovery. Compared with the prior art, the beneficial effects of the computer program product provided in the embodiments of this application are the same as the beneficial effects of the TWSA data recovery method provided in the above embodiments, and will not be repeated here.

[0090] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent scope of this application.

Claims

1. A TWSA data recovery method, characterized in that, The method includes: The original gravity field coefficient data is acquired and converted into a gridded data sequence at the target resolution based on a preset conversion rule. The gridded data sequence is normalized to obtain standardized input data; Based on the standardized input data, a training sample set and a target label set for the initial neural network model are constructed; The initial neural network model is trained based on the training sample set and the target label set; Based on the training results, the hyperparameters in the initial neural network model are adjusted using a Bayesian optimization algorithm. The hyperparameters include at least one of the following: number of convolutional kernels, learning rate, and training batch size. Based on the adjustment results, the target neural network model is obtained; Feature extraction is performed on the current standardized input data by inputting it into the convolutional layer of the target neural network model; Based on the feature extraction results, obtain the spatial mask matrix; The spatial regions of the feature extraction results are weighted based on the spatial mask matrix. The weighted feature extraction results are output to obtain the weighted feature map; By performing a deconvolution operation on the weighted feature map, the weighted feature map is restored to the spatial dimension of the current standardized input data; The recovered weighted feature map is input into the output convolutional layer to obtain standardized prediction data; The standardized prediction data is denormalized to obtain the target TWSA recovery data.

2. The method as described in claim 1, characterized in that, The step of acquiring the original gravity field coefficient data and converting the original gravity field coefficient data into a gridded data sequence at the target resolution based on a preset conversion rule includes: Obtain the raw gravity field coefficient data; The original gravity field coefficient data is converted into physical quantity data in grid form according to the spherical harmonic representation format; Based on the target resolution, the physical quantity data is rearranged in chronological order to obtain the gridded data sequence.

3. The method as described in claim 1, characterized in that, The step of performing inverse normalization on the standardized prediction data to obtain the target TWSA recovery data includes: Obtain the mean and standard deviation parameters of the standardized prediction data for the corresponding time period; Based on the standardized prediction data, the mean parameter, and the standard deviation parameter, the standardized prediction data is denormalized to obtain unstandardized prediction data. The unstandardized prediction data is output and used as the target TWSA recovery data.

4. A TWSA data recovery device, characterized in that, The device includes: The data conversion module is used to acquire the original gravity field coefficient data and convert the original gravity field coefficient data into a gridded data sequence at the target resolution based on a preset conversion rule. The standardization module is used to normalize the gridded data sequence to obtain standardized input data; The training module is used to construct a training sample set and a target label set for an initial neural network model based on the standardized input data; train the initial neural network model based on the training sample set and the target label set; adjust the hyperparameters in the initial neural network model using a Bayesian optimization algorithm based on the training results, wherein the hyperparameters include at least one of the following: number of convolutional kernels, learning rate, and training batch size; and obtain the target neural network model based on the adjustment results. The inference module is used to extract features from the current standardized input data by inputting it into the convolutional layer of the target neural network model; obtain a spatial mask matrix based on the feature extraction results; perform weighted processing on the spatial regions of the feature extraction results based on the spatial mask matrix; output the weighted feature extraction results to obtain a weighted feature map; restore the weighted feature map to the spatial dimension of the current standardized input data by performing a deconvolution operation on the weighted feature map; and input the restored weighted feature map into the output convolutional layer to obtain standardized prediction data. The target module is used to perform inverse normalization processing on the standardized prediction data to obtain the target TWSA recovery data.

5. A computer device, characterized in that, The device includes: a memory, a processor, and a TWSA data recovery program stored in the memory and executable on the processor, the TWSA data recovery program being configured to implement the steps of the TWSA data recovery method as described in any one of claims 1 to 3.

6. A storage medium, characterized in that, The storage medium stores a TWSA data recovery program, which, when executed by a processor, implements the steps of the TWSA data recovery method as described in any one of claims 1 to 3.

7. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the steps of the TWSA data recovery method as described in any one of claims 1 to 3.

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