SMAP high-resolution sea surface salinity inversion method based on multi-scale feature fusion network

Abstract

The invention belongs to the technical field of remote sensing, and relates to an SMAP high-resolution sea surface salinity inversion method based on a multi-scale feature fusion network, and the method comprises the steps: obtaining low-resolution and high-resolution brightness temperature data, and carrying out the segmentation to form one-to-one matched low-resolution and high-resolution data pairs which are used for a brightness temperature super-resolution reconstruction model; the method comprises the following steps: designing an improved U-shaped network model by integrating a pyramid pooling module, performing resolution reconstruction on low-resolution brightness temperature data to obtain reconstructed high-resolution brightness temperature data, and performing space-time matching, resampling, high rainfall value elimination and missing value elimination on all the data; and on the basis of the reconstructed high-resolution brightness temperature data, constructing a DNN inversion model to obtain a salinity inversion result. The method does not depend on prior knowledge, can quickly and directly convert a low-resolution image into high-resolution salinity data, shows extremely high stability under various marine environments and extreme weather conditions, and is of great significance to marine scientific research, resource development and the like.

Description

Technical Field

[0001] The present invention belongs to the technical field of remote sensing, and particularly relates to a method for retrieving high-resolution sea surface salinity of SMAP based on a multi-scale feature fusion network. Background Art

[0002] In terms of salinity retrieval, existing technologies usually measure the sea surface brightness temperature through L-band microwave radiometers (such as SMAP, SMOS) and estimate the sea surface salinity by combining physical inversion algorithms. These methods perform well in open waters. However, the low spatial resolution of microwave radiometers limits their effectiveness in ocean applications. Especially in the coastal area, limited by the low spatial resolution (usually 25 - 50 km) and land pollution interference, it is difficult to accurately capture the fine spatial distribution of salinity. Improving the resolution of the brightness temperature data observed by microwave radiometers is crucial for overcoming this problem. By improving the resolution, more detailed information on ocean variables can be obtained, thereby more accurately understanding the spatio-temporal characteristics of the ocean environment.

[0003] Resolution enhancement methods are mainly divided into physical methods and deep learning methods. Physical methods include Backus-Gilbert (BG), Sequential Image Reconstruction, and Wiener Deconvolution. Although these methods are effective, they all have limitations such as the need for prior knowledge, high computational complexity, noise amplification, and over-smoothing of images. Although existing physical methods can achieve a certain degree of improvement in the resolution of brightness temperature, their high computational complexity, long processing time, and easy amplification of noise during the enhancement process lead to over-smoothing or artifacts in the image. In addition, these methods often rely on prior knowledge such as antenna patterns and image characteristics, which limits their wide application in actual ocean scenarios. Especially in the coastal area, the low spatial resolution of microwave remote sensing data can no longer meet the high-precision requirements of salinity monitoring. At the same time, radio frequency interference (RFI) and land pollution often cause the brightness temperature deviation within 50 kilometers from the shoreline to reach 3 to 5 K, seriously affecting the accuracy of salinity inversion.

[0004] In recent years, deep learning technology has provided new ideas for the resolution enhancement of brightness temperature images, which can quickly and directly map low-resolution images to high-resolution images and become an effective alternative. However, existing deep learning methods usually only focus on simply improving the resolution of brightness temperature data, and fail to deeply fuse the reconstructed high-resolution brightness temperature data with geographical and environmental factors such as the distance from the shore and sea surface temperature. Therefore, it is difficult to comprehensively capture the dynamic changes of sea surface salinity over time and space in the coastal area and fully invert the complex salinity distribution in the coastal area. Summary of the Invention

[0005] In order to solve the problem of limited nearshore salinity inversion accuracy caused by the insufficient spatial resolution of microwave radiometers (25-50 km) and land pollution interference in existing methods, this paper proposes a SMAP high-resolution sea surface salinity inversion method based on a multi-scale feature fusion network. This method is an innovative method based on the super-resolution reconstruction of brightness temperature of a multi-scale feature fusion network and the collaborative inversion of multi-factor DNN. First, the spatial resolution of the L-band brightness temperature data is reconstructed through an improved U-type network with an integrated pyramid pooling module, which is four times the original resolution, i.e., 9 km. Subsequently, the enhanced high-resolution brightness temperature image is used as input, and the marine environmental parameters and geographic information are integrated to realize the inversion of sea surface salinity through a deep neural network (DNN), thereby accurately capturing the characteristics of the spatiotemporal variation of salinity in a complex nearshore environment, significantly improving the inversion accuracy, stability and generalization ability, and effectively solving the shortcomings of the existing technology in the application of nearshore salinity monitoring.

[0006] The technical solution of the present invention is: A SMAP high-resolution sea surface salinity inversion method based on a multi-scale feature fusion network, characterized in that it comprises the following steps: (1) Obtain low-resolution and high-resolution brightness temperature data, select appropriate pixels to segment the low-resolution and high-resolution data, and form a one-to-one matching low-resolution and high-resolution data pair. On this basis, a high-resolution dataset and a low-resolution dataset are formed for the brightness temperature super-resolution reconstruction model; (2) By integrating the pyramid pooling module to design an improved U-shaped network model, the input low-resolution brightness temperature data is reconstructed and the output is high-resolution brightness temperature data; (3) Obtain reconstructed high-resolution brightness temperature data, match all data in space and time, resample all data, remove high rainfall values ​​based on rainfall data, and remove all data containing null values ​​to ensure data integrity and consistency; (4) Based on the reconstructed high-resolution brightness temperature data, a DNN inversion model with physical constraints is constructed, and salinity inversion is performed by combining geographical factors and environmental factors. The reconstructed high-resolution brightness temperature data and polarization difference characteristics are input into the DNN inversion model together with the time factor to obtain the salinity inversion result.

[0007] Furthermore, in step (1), the acquired high-resolution and low-resolution brightness temperature data are subjected to sea and land masking and outlier removal, wherein the outliers include sea ice and sea fog data.

[0008] Further, in step (2), the preprocessed low-resolution brightness temperature data in step (1) is input into an improved U-shaped network model, and multi-scale feature extraction is performed layer by layer during the encoding stage to obtain multi-scale feature information; during the decoding stage, multi-scale pooling is performed on the feature map through a pyramid pooling module. After the processed feature maps are integrated, the finally generated high-resolution brightness temperature data is output.

[0009] Further, in step (3), all data including brightness temperature feature data, geographical factors, environmental factors, and time factors is preprocessed. The preprocessing includes spatio-temporal matching, resampling, removing high rainfall values, and removing missing values.

[0010] Further, the brightness temperature features include the reconstructed high-resolution brightness temperature data, polarization ratio, and polarization difference. The geographical factors include longitude, latitude, and offshore distance. The environmental factors include sea surface temperature, sea surface wind speed, sea surface wind direction, and rainfall. The time factor includes the time period term.

[0011] Further, the preprocessing spatially and temporally matches all data through bilinear interpolation, resamples all data to grids of the same size. Subsequently, using the longitude and latitude coordinates of the grid points, the offshore distance from the shoreline is calculated. Finally, samples with instantaneous rainfall greater than 0.15 mm / h are removed according to the rainfall data, and at the same time, all data containing null values are removed to ensure the integrity and consistency of the data.

[0012] Further, in step (4), feature importance analysis is performed on all input factors in the DNN inversion model. The SHAP method is used to quantify the importance of each input feature. Through SHAP value analysis, the priority order of the input factors is determined. Based on this sorting principle, the input feature set of the model is optimized and designed to ensure the full utilization of key factors in the inversion model; then, for the key hyperparameters in the DNN including the number of hidden layer neurons, learning rate, and dropout rate, the parameter combinations are systematically traversed through the grid search method, and the performance of each group of parameters is evaluated using K-fold cross-validation. Finally, the configuration with the lowest validation set error is selected as the optimal model.

[0013] Advantages of the present invention: (1)The sea surface salinity inversion method of the present invention innovatively uses the reconstructed high-resolution brightness temperature data as the core input feature, deeply fuses it with polarization features and multi-source environmental factors, and constructs a DNN inversion model with physical constraints. Compared with the traditional single data source inversion scheme, this method significantly improves the generalization ability in complex environments through multi-scale information fusion and feature selection optimized by SHAP values; the model can learn complex non-linear interaction relationships from multi-dimensional parameters, fully capture the influence of ocean and geographical factors on salinity changes, and ensure that the salinity inversion results have higher resolution and better linear correlation. Especially in the complex nearshore environment, the reconstructed high-resolution brightness temperature data provides high-resolution input for the model and optimizes the reliability of salinity.

[0014] The reconstructed high-resolution brightness temperature data not only significantly improves in terms of detail expressiveness and global semantic information acquisition, but also provides a more accurate input basis for salinity inversion, ensuring the reliability of the inversion model.

[0015] (2)The deep learning method based on the pyramid pooling module and U-shaped network provided by the present invention effectively solves the deficiency of traditional physical methods in detail restoration through the joint optimization of multi-scale feature fusion and the gradient change of brightness temperature images. The method of the present invention does not rely on prior knowledge, can quickly and directly convert low-resolution images into high-resolution salinity data, shows extremely strong stability in various ocean environments and extreme weather conditions, can accurately capture the gradient change of brightness temperature, improve the stability and generalization ability of resolution enhancement, and achieve efficient data acquisition. The method of the present invention is of great significance for marine scientific research, marine resource development and protection, and marine environmental protection. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is a flowchart of the salinity inversion method provided by the present invention; Figure 2 is a framework diagram of the U-shaped model integrating pyramid pooling. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0017] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0018] To further understand the present invention, the present invention will be further described in conjunction with the accompanying drawings and embodiments.

[0019] Such as Figure 1As shown in the figure, the present invention provides a method for inverting SMAP high-resolution sea surface salinity based on a multi-scale feature fusion network, comprising the following steps: Step 1: Input and preprocessing of brightness temperature data First, obtain 36 km low-resolution brightness temperature data and 9 km high-resolution brightness temperature data (Tbv and Tbh) in the L band from microwave radiometers such as SMAP, and perform land masking to remove data with outliers such as sea ice and sea fog.

[0020] Select an appropriate pixel size to crop the low- and high-resolution data to form a one-to-one matching low-high resolution data pair. On this basis, a high-resolution dataset and a low-resolution dataset for super-resolution reconstruction of brightness temperature are formed to adapt to the input requirements of the network model.

[0021] Step 2: Integration of the pyramid pooling module and the U-shaped network The preprocessed low-resolution brightness temperature data is subjected to high-resolution reconstruction through a U-shaped network integrated with a pyramid pooling module. The network realizes the improvement of the spatial resolution of the brightness temperature data through the following improvements. The improved U-shaped network integrates a pyramid pooling module on the basis of the standard structure, which improves the ability of the model to capture multi-scale features.

[0022] Input stage: The preprocessed low-resolution brightness temperature data is input into the improved U-shaped network as the initial input of the model.

[0023] Encoding stage: In the encoder, the network extracts features layer by layer from the input low-resolution image, gradually compresses the spatial information and refines the multi-scale feature information.

[0024] Decoding stage and pyramid pooling module (PPM): During the decoding process, the image is reconstructed by gradually restoring the features of the encoding stage. A pyramid pooling module (PPM) is integrated at the end of the decoder. This module performs multi-scale pooling on the feature map by using four different sizes of convolutional kernels (1×1, 2×2, 3×3, 6×6), enhancing the model's ability to capture global semantic information and local detail information. After the processed feature maps are integrated, they are used to generate a more accurate high-resolution brightness temperature image.

[0025] Skip connection: Between the encoder and the decoder, features from the encoding stage are passed through skip connections, enabling the decoder to make full use of multi-scale features, reducing the loss of detail information, and restoring more original information during the decoding process.

[0026] Output stage: The finally generated high-resolution brightness temperature image not only has the ability to express global context but also retains rich details and precise structures, thus realizing the improvement of the spatial resolution of the brightness temperature data.

[0027] This multi-scale feature enhances the acquisition of global context information, while optimizing the effectiveness of feature transmission through skip connections in the decoding stage and reducing detail loss.

[0028] Step 3: Preprocessing of data for salinity inversion In the subsequent salinity inversion section, the high-resolution brightness temperature data reconstructed in Step 2 is used. In addition, other parameters affecting sea surface salinity are considered, such as sea surface temperature, wind field information, geographical factor information. Also, in order to better quantify seasonal variations, the time encoding, i.e., the day of the year, is used as an input value.

[0029] The core input features include: Brightness temperature features: Reconstructed 9-km brightness temperature (Tbv / Tbh), polarization ratio (v / h), polarization difference (v - h) Geographical factors: Latitude (lat), longitude (lon), distance from shore (dis) Environmental factors: Sea surface temperature (SST), wind speed at sea surface (WS), wind direction at sea surface (Wdir), rainfall (Rain) Time factor: Time period term (θ) All data, such as brightness temperature feature data and environmental factor data, are preprocessed. Spatial and temporal matching is performed through bilinear interpolation, and all data is resampled to a grid of the same size. Subsequently, the distance from the shoreline of each grid point is calculated using its longitude and latitude coordinates. Finally, samples with an instantaneous rainfall greater than 0.15 mm / h are removed according to the rainfall data, and all data containing null values is removed to ensure the integrity and consistency of the data.

[0030] Step 4: DNN salinity inversion modeling Based on the reconstructed high-resolution brightness temperature data, a multi-factor deep neural network (DNN) based on physical mechanisms is constructed to perform salinity inversion by combining geographical factors and environmental factors, achieving joint optimization of resolution enhancement and salinity inversion.

[0031] To optimize the model architecture and improve the inversion performance, first, the input features are sorted by importance based on SHAP value analysis, and redundant features are removed by calculating the contribution degree of each feature. Then, a method combining grid search and K-fold cross-validation (K = 5) is used to systematically tune key hyperparameters such as the number of neurons in the hidden layer, learning rate, and dropout rate. Finally, the optimal parameter combination that can minimize the loss of the validation set is determined. This optimization strategy can improve the inversion accuracy of the DNN model. Example

[0032] This embodiment takes the SMAP (Soil Moisture Active and Passive) brightness temperature data and the East China Sea and part of the South China Sea (covering the area of ​​25°N to 37°N, 119°E to 130°E) as an example to illustrate the salinity inversion method based on deep learning of the present invention.

[0033] Install Python programming software on the user terminal and configure Python-3.6, TensorFlow-2.6.0, and Keras-2.6.0 environment packages to support deep learning tasks. TensorFlow, as a flexible open source deep learning platform, can be used to build, train, and deploy complex neural network models; Keras, as an advanced API, provides a simple interface to quickly build common neural network models.

[0034] Step 1: Brightness temperature data acquisition and preprocessing SMAP satellite brightness temperature data from 2016 to 2020 were used as the basis for training and testing, with the spatial resolution of low-resolution brightness temperature data being 36 kilometers and the resolution of high-resolution brightness temperature data being 9 kilometers. First, land masking was performed to remove outlier data such as sea ice and sea fog. Image segmentation was then performed to segment low-resolution images into 24×24 pixel sub-images and high-resolution images into 96×96 pixel sub-images, forming a one-to-one matching data pair. The high- and low-resolution data sets that make up the brightness temperature super-resolution reconstruction are used for modeling of brightness temperature super-resolution reconstruction. The processed data were divided into two parts according to time: data from 2016 to 2019 were used as model training set validation, and data from 2020 were used for independent testing.

[0035] Step 2: UNet model training and optimization based on integrated pyramid pooling module This embodiment designs an improved U model by integrating the pyramid pooling module to efficiently improve the spatial resolution of low-resolution brightness temperature data. The main implementation steps are as follows: (1) Input and output settings Input layer: The input is a segmented low-resolution brightness and temperature sub-image with a size of 24×24 pixels. Output layer: The output is a high-resolution brightness-temperature sub-map with a size of 96×96 pixels. (2) Coding stage The sub-image is pre-upsampled to 96 × 96 pixels. The upsampled 96 × 96 pixel feature map is subjected to multi-layer pooling for feature extraction.

[0036] (3) Integration of the decoding stage and the pyramid pooling module (PPM) The decoder gradually recovers the feature maps extracted in the encoding stage and expands them back to 96×96 pixels.

[0037] In the Pyramid Pooling Module (PPM), the following operations are performed: Multiscale pooling is carried out on the feature map through convolutional kernels (1×1, 2×2, 3×3, and 6×6) to extract context information in different spatial ranges.

[0038] (4)Skip connection A skip connection is added between the encoder and the decoder: The feature map output by each layer in the encoding stage is directly passed to the corresponding layer of the decoder to ensure that rich detailed features are retained during the decoding process.

[0039] Training parameter configuration: To ensure the optimization effect of the model, the L1+PSNR composite loss function is used during training. The L1 loss function can accurately measure the deviation of image brightness values, while the PSNR metric further optimizes the model's evaluation of image quality, thereby generating clearer and more consistent high-resolution images. The Adam optimizer is used for model training, the initial learning rate is set to 0.001, and the batch size is 128. To prevent overfitting, a learning rate decay strategy and an early stopping mechanism are introduced.

[0040] Step 3: Preprocessing of data for salinity inversion First, use the model in Step 2 to reconstruct the resolution of the low-resolution brightness temperature data to obtain the high-resolution brightness temperature data after reconstruction. The resolution of the high-resolution brightness temperature data is 0.09°. Align the data in time, and then resample the high-resolution brightness temperature data, other environmental factor data, and time factors, and resample all data to a 0.09-degree grid. Subsequently, use the longitude and latitude coordinates of the grid points to calculate the offshore distance of each point from the coastline through GMT tools. Finally, according to the rainfall data, samples with instantaneous rainfall greater than 0.15 mm / h are removed, and all data containing null values are removed to ensure the integrity and consistency of the data. The processed data is divided by time as follows: The data from 2016 to 2019 is used as the model training set for verification, and the data in 2020 is used for independent testing.

[0041] Step 4: DNN salinity inversion modeling Based on the high-resolution brightness temperature data, combined with geographical and environmental factors, the salinity inversion result is output.

[0042] After that, to ensure the effectiveness of the model, the following steps are implemented: First, perform feature importance analysis on all input factors, and use the SHAP (Shapley Additive Explanations) method to quantify the importance of each input feature. Through SHAP value analysis, the priority ranking of the input factors is determined, and the result is: Tbv > lat > SST > lon > θ > v-h > dis. According to this ranking principle, optimize the input feature set of the design model to ensure the full utilization of key factors in the inversion model.

[0043] Then, optimize the hyperparameters of the model through the grid search method, and determine the network structure of the DNN according to the optimization results. The finally designed DNN model includes the following layers: Input layer: High-resolution brightness temperature features (such as Tbv, polarization ratio v / h, polarization difference v-h), geographical factors (latitude lat, longitude lon, offshore distance dis), environmental factors (sea surface temperature SST), and time influence factor (time period term θ).

[0044] Hidden layer: Adopt a three-layer hidden layer structure, with the number of neurons in each layer being 1024, 32, and 32 respectively. Use the ReLU activation function to ensure the full extraction and expression of non-linear features.

[0045] Output layer: Generate the salinity inversion result.

[0046] In the optimization and training stage, select the Adam optimizer to improve the training efficiency, and set the initial learning rate to 0.008. Introduce K-fold cross-validation (K = 5) during the training process to enhance the generalization ability of the model, ensure its strong adaptability and not easy to overfit. In addition, monitor the performance of the validation set through the early stopping mechanism and terminate the training in time to prevent the model from overfitting.

[0047] Experimental Example 1 Model Performance Evaluation and Experimental Verification Verify the accuracy of salinity inversion through the RMSE and corr metrics.

[0048] Specifically, the steps for evaluating the model stability are as follows: To verify the stability of the model of the present invention, the present invention compares the performance of different machine learning models (including RF, XGBoost) in the salinity inversion task. Compare the model inversion results with the in-situ observation data, and use the same dataset to evaluate the accuracy of the SMAP salinity product.

[0049] Among them, the resolution of the SMAP product is 40 km, and the resolution of the DNN inversion result is 9 km. The results are shown in Table 1.

[0050] Table 1 Model Stability Evaluation Results

[0051] The experimental results show that the model constructed by the present invention is superior to the comparative methods in all evaluation metrics. Specifically, it shows a 15.2% reduction in the RMSE metric compared to the SMAP official product and a 27.0% reduction compared to the optimal comparative model (RF). In terms of bias control, although there is still a positive bias of 0.56 PSU, it shows better systematicness compared to the negative bias (-0.46 PSU) of the SMAP product. The correlation coefficient reaches 0.80, significantly higher than other comparative methods, proving that this method can better capture the spatio-temporal variation characteristics of salinity.

[0052] The above description is only the preferred embodiment of the present invention and is not a limitation to the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, modifications, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A SMAP high-resolution sea surface salinity inversion method based on a multi-scale feature fusion network, characterized in that: The following steps are involved: (1) Obtain low-resolution and high-resolution brightness temperature data, select appropriate pixels to segment the low-resolution and high-resolution data, and form a one-to-one matching low-resolution and high-resolution data pair. On this basis, a high-resolution dataset and a low-resolution dataset are formed for the brightness temperature super-resolution reconstruction model; (2) By integrating the pyramid pooling module to design an improved U-shaped network model, the input low-resolution brightness temperature data is reconstructed and the output is high-resolution brightness temperature data; (3) Obtain reconstructed high-resolution brightness temperature data, match all data in space and time, resample all data, remove high rainfall values ​​based on rainfall data, and remove all data containing null values ​​to ensure data integrity and consistency; (4) Based on the reconstructed high-resolution brightness temperature data, a DNN inversion model with physical constraints is constructed, and salinity inversion is performed by combining geographical factors and environmental factors. The reconstructed high-resolution brightness temperature data and polarization difference characteristics are input into the DNN inversion model together with the time factor to obtain the salinity inversion result.

2. The SMAP high-resolution sea surface salinity inversion method based on a multi-scale feature fusion network according to claim 1, characterized in that: In the step (1), the acquired high-resolution and low-resolution brightness temperature data are subjected to sea and land masking and outlier removal, wherein the outliers include sea ice and sea fog data.

3. The SMAP high-resolution sea surface salinity inversion method based on a multi-scale feature fusion network according to claim 1, characterized in that: In the step (2), the low-resolution brightness temperature data preprocessed in the step (1) is input into the improved U-shaped network model, and features are extracted layer by layer in the encoding stage to obtain multi-scale feature information; In the decoding stage, the feature map is multi-scale pooled through the pyramid pooling module. After the processed feature map is integrated, the high-resolution brightness temperature data is finally output.

4. The SMAP high-resolution sea surface salinity inversion method based on a multi-scale feature fusion network according to claim 1, characterized in that: In the step (3), all data including brightness temperature characteristic data, geographical factors, environmental factors and time factors are preprocessed, and the preprocessing includes time-space matching, resampling, removal of high rainfall values ​​and removal of missing values.

5. The SMAP high-resolution sea surface salinity inversion method based on a multi-scale feature fusion network according to claim 4 is characterized in that: The brightness temperature characteristics include reconstructed high-resolution brightness temperature data, polarization ratio and polarization difference; the geographical factors include longitude, latitude and offshore distance; the environmental factors include sea surface temperature, sea surface wind speed, sea surface wind direction and rainfall; and the time factors include time period items.

6. The SMAP high-resolution sea surface salinity inversion method based on a multi-scale feature fusion network according to claim 4 is characterized in that: The preprocessing is to match all data in space and time through the bilinear interpolation method, resample all data to grids of uniform size, and then calculate the offshore distance from the coastline using the latitude and longitude coordinates of the grid points. Finally, samples with instantaneous rainfall greater than 0.15 mm / h are eliminated based on the rainfall data, and all data containing null values ​​are removed to ensure the integrity and consistency of the data.

7. The SMAP high-resolution sea surface salinity inversion method based on a multi-scale feature fusion network according to claim 1, characterized in that: In the step (4), feature importance analysis is performed on all input factors in the DNN inversion model, and the importance of each input feature is quantified using the SHAP method. The priority ranking of the input factors is determined through SHAP value analysis. Based on this ranking principle, the input feature set of the design model is optimized to ensure that the key factors are fully utilized in the inversion model. Then, for key hyperparameters in the DNN, including the number of hidden layer neurons, learning rate, and dropout rate, the parameter combinations are systematically traversed through the grid search method, and the performance of each group of parameters is evaluated using K-fold cross validation. Finally, the configuration with the lowest error in the validation set is selected as the optimal model.

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