A Physically Constrained Deep Learning-Based Optimization Method for Scattering Properties of Hydrogels

Abstract

This invention discloses a method for optimizing the scattering properties of condensed objects based on physically constrained deep learning. The method includes constructing a pre-trained dataset and a fine-tuning dataset; pre-training a deep neural network model to obtain initial values ​​for the scattering properties of condensed objects; inputting the background field of the corresponding numerical model into a physical radiative transfer model for forward computation to obtain simulated brightness temperature; using the adjoint operator of the physical radiative transfer model to calculate the gradient of the brightness temperature data, establishing a complete differentiable gradient chain from observed brightness temperature to network parameters; using the consistency of the probability distribution between observed and simulated brightness temperature as the optimization objective, performing gradient descent iterative training; fine-tuning the network parameters of the deep neural network model; and embedding the trained deep neural network model into a fast radiative transfer model to generate optimized scattering properties of condensed objects in real time. This method can provide higher-quality observation operators for the assimilation of satellite data in cloud and rain areas, thereby improving the accuracy of numerical weather prediction.

Description

Technical Field

[0001] This invention relates to the field of meteorological satellite remote sensing and data assimilation technology, and in particular to a method for optimizing the scattering properties of water-condensed objects based on physically constrained deep learning. Background Technology

[0002] Effective assimilation of satellite microwave observation data in cloud and rain regions is crucial for improving the accuracy of numerical weather prediction. In recent years, several operational forecasting centers have conducted microwave data assimilation under cloud and rain conditions and achieved significant results. Successful implementation of all-sky assimilation relies on observational operators capable of accurately simulating microwave radiative transfer processes in cloud and rain regions, with the estimation of the scattering properties of condensed objects being a core factor affecting simulation accuracy. However, due to the complexity of cloud microphysics and insufficient observational constraints, the estimation of the scattering properties of condensed objects in existing fast radiative transfer models still suffers from significant uncertainties, especially for morphologically variable ice particles, where simulation biases severely limit the effectiveness of satellite data assimilation.

[0003] Current mainstream methods for optimizing volume scattering properties rely on exhaustive search of small-scale predefined parameter combinations, selecting optimal parameters from a finite pool of options by minimizing observational and simulation biases. This method has significant limitations: First, the computational cost of exhaustive search increases exponentially with the parameter dimension, allowing evaluation of only a very small number of discrete options in practical applications. Second, the globally uniform assumption of microphysical parameters ignores the regional differences and natural variability of ice particles. Furthermore, parameter search is limited to a predefined set of discrete options, making it difficult to fully explore optimal configurations within a continuous parameter space. Therefore, this invention proposes a method for optimizing the scattering properties of condensed water objects based on physically constrained deep learning. By coupling physical radiative transfer modes with deep neural networks, a fully differentiable computational path is established from satellite-observed brightness temperature to volume scattering property parameters. This enables efficient parameter optimization based on actual satellite observations, addressing the problems of insufficient precision in volume scattering property parameterization, low optimization efficiency, and difficulty in accurately characterizing the polarization scattering characteristics of ice particles in existing technologies. Summary of the Invention

[0004] The purpose of this invention is to provide a method for optimizing the scattering properties of hydrogel objects based on physical constraint deep learning.

[0005] To achieve the above objectives, the present invention is implemented according to the following technical solution:

[0006] This invention includes the following steps:

[0007] Historical numerical model background fields are acquired and the scattering properties of condensed objects are calculated to construct a pre-trained dataset. Historical observed brightness temperatures are spatiotemporally matched with historical numerical model background fields to construct a fine-tuning dataset. The numerical model background fields include atmospheric temperature, humidity, air pressure, and condensed object content. The condensed objects include rain, snow, cloud water, and cloud ice.

[0008] A deep neural network model was pre-trained using a pre-trained dataset to obtain initial values ​​of the scattering properties of the condensed object. The initial values ​​of the scattering properties of the condensed object and the corresponding numerical mode background field were then input into the physical radiative transfer mode for forward calculation to obtain the simulated brightness temperature.

[0009] Gradient calculation of brightness temperature data is performed using the adjoint operator of the physical radiative transfer mode. The loss function is calculated based on the simulated brightness temperature and the observed brightness temperature. A complete differentiable gradient chain from the loss function to the network parameters is established through backpropagation of the neural network.

[0010] With the consistency of simulated brightness temperature and observed brightness temperature probability distribution as the optimization objective, gradient descent iterative training is performed in conjunction with the complete differentiable gradient chain to fine-tune the network parameters of the deep neural network model. The second validation dataset is used to perform hyperparameter optimization on the deep neural network model to obtain the optimal network parameters.

[0011] The trained deep neural network model is embedded into the fast radiative transfer mode to generate optimized scattering properties of condensed water objects in real time, which are then used as satellite observation operators for all-sky data assimilation.

[0012] Furthermore, the method for calculating the scattering properties of hydrogels specifically involves using the RTTOV hydrogel optical lookup table generator to generate the scattering properties of hydrogels.

[0013] Furthermore, the pre-training dataset is used to pre-train the deep neural network model, including temperature, hydrophobic content, and scattering properties of hydrophobic objects, and is randomly divided into a first training dataset and a first validation dataset at a ratio of 4:1; the fine-tuning dataset is used to fine-tune the deep neural network model, including temperature, hydrophobic content, and observed brightness temperature, and is randomly divided into a second training dataset, a second validation dataset, and a second test set at a ratio of 2:1:1 according to the time series; the scattering properties of hydrophobic objects include extinction coefficient, single scattering albedo, and asymmetric factor.

[0014] Furthermore, the deep neural network model is trained independently according to the type of hydrogel, and includes an input layer, a hidden layer, and an output layer; the input data for the input layer is atmospheric temperature and hydrogel content; the output data for the output layer is the scattering properties of the hydrogel.

[0015] Furthermore, the method for calculating the loss function based on simulated brightness temperature and observed brightness temperature includes:

[0016] Calculate the probability distribution of simulated brightness temperature and observed brightness temperature; the probability distribution is approximated using Gaussian kernel density estimation, and the expression is:

[0017] ;

[0018] in For interval The probability density at that location, The number of samples in the interval. To control the bandwidth parameter for estimating smoothness, Samples within the interval Single brightness temperature measurement value For the first k The center of each interval;

[0019] The probability distributions of simulated brightness temperature and observed brightness temperature are normalized, and the loss function based on the consistency of the probability distribution is calculated. The expression is as follows:

[0020] ;

[0021] in For loss function, For the number of geographical regions, For the number of satellite channels, For the number of intervals, for Geographical region Satellite channel in k The observed brightness temperature normalized probability, for Geographical region Satellite channel in k The normalized probability of simulated brightness temperature in the interval.

[0022] Furthermore, the complete differentiable gradient chain from the loss function to the network parameters is specifically represented as follows:

[0023] ;

[0024] in loss function Network parameters of deep neural network models gradient, loss function brightness temperature data The gradient is calculated through automatic differentiation. Brightness temperature data Scattering properties of hydrogels The gradient, i.e., brightness temperature data Scattering properties of hydrogels The sensitivity was calculated using the adjoint method. Scattering properties of hydrogels Scattering properties of normalized hydrocrystalline objects The gradient originates from the inverse normalization process, including exponential and linear scaling transformations. Normalized scattering properties of condensed matter For network parameters The gradient is calculated using automatic differentiation.

[0025] Furthermore, the gradient descent iterative training optimizes the model using the Adam optimizer and an early stopping strategy.

[0026] The beneficial effects of this invention are:

[0027] This invention is a method for optimizing the scattering properties of hydrogel objects based on physical constraint deep learning. Compared with existing technologies, this invention has the following technical advantages:

[0028] This method embeds the forward and adjoint operators of the physical radiative transfer mode into the deep neural network training process, enabling efficient searching for optimal configurations in a continuous high-dimensional parameter space. Employing a loss function based on probability distribution consistency effectively avoids the double penalty problem in cloud and rain simulations, making the optimized observation-simulation bias distribution closer to a Gaussian distribution. By establishing independent output paths for vertical and horizontal polarization channels, the polarization scattering characteristics of non-spherical ice particles can be directly learned from observed brightness temperatures. This method significantly improves the accuracy and distribution consistency of brightness temperature simulations, providing higher-quality observation operators that better conform to the variational assimilation assumption for all-sky satellite data assimilation, which is of great significance for improving the accuracy of numerical weather prediction. Attached Figure Description

[0029] Figure 1 This is a flowchart illustrating the steps of the method for optimizing the scattering properties of hydrogel objects based on physical constraint deep learning, as described in this invention.

[0030] Figure 2 This is a schematic diagram of the physical deep learning coupling optimization framework provided in an embodiment of the present invention;

[0031] Figure 3 This is a comparison diagram of brightness temperature before and after optimization in a typhoon scenario provided by an embodiment of the present invention;

[0032] Figure 4 A comparison chart of the observation-simulation (OB) bias probability density function before and after optimization, provided for embodiments of the present invention. Detailed Implementation

[0033] The present invention will be further described below through specific embodiments. The illustrative embodiments and descriptions herein are used to explain the present invention, but are not intended to limit the present invention.

[0034] The present invention provides a method for optimizing the scattering properties of hydrogel objects based on physical constraint deep learning, comprising the following steps:

[0035] like Figure 1 Method flowchart and Figure 2As shown in the framework diagram, this embodiment includes the following steps:

[0036] Historical numerical model background fields are acquired and the scattering properties of condensed objects are calculated to construct a pre-trained dataset. Historical observed brightness temperatures are spatiotemporally matched with historical numerical model background fields to construct a fine-tuning dataset. The numerical model background fields include atmospheric temperature, humidity, air pressure, and condensed object content. The condensed objects include rain, snow, cloud water, and cloud ice.

[0037] A deep neural network model was pre-trained using a pre-trained dataset to obtain initial values ​​of the scattering properties of the condensed object. The initial values ​​of the scattering properties of the condensed object and the corresponding numerical mode background field were then input into the physical radiative transfer mode for forward calculation to obtain the simulated brightness temperature.

[0038] Gradient calculation of brightness temperature data is performed using the adjoint operator of the physical radiative transfer mode. The loss function is calculated based on the simulated brightness temperature and the observed brightness temperature. A complete differentiable gradient chain from the loss function to the network parameters is established through backpropagation of the neural network.

[0039] With the consistency of simulated brightness temperature and observed brightness temperature probability distribution as the optimization objective, gradient descent iterative training is performed in conjunction with the complete differentiable gradient chain to fine-tune the network parameters of the deep neural network model. The optimal network parameters are obtained by hyperparameter optimization of the deep neural network model using the second validation dataset.

[0040] In actual optimization, the specific steps are as follows:

[0041] (1) Data preparation:

[0042] First, acquire dual-polarization observation data (brightness temperature) from the GMI-166.5GHz dual-polarization satellite carried by the GPM satellite. The GPM satellite refers to the Global Precipitation Measurement (GPM) satellite. The GMI is a conical scanning microwave radiometer operating in a non-sunsynchronous orbit at an altitude of 407km, covering latitudes from 68°S to 68°N. The dual polarization includes vertical polarization (V-pol) and horizontal polarization (H-pol).

[0043] Background field data acquisition: Extract ERA5 reanalysis data. ERA5 refers to the fifth-generation atmospheric reanalysis data based on the European Centre for Medium-Range Weather Forecasts (ECMWF), providing three-dimensional atmospheric variables and two-dimensional parameters with a 0.25° grid resolution and 37 pressure layers. The three-dimensional atmospheric variables include temperature, specific humidity, air pressure, water-condensate mixture ratio (rain, snow, cloud liquid water, and cloud ice water) and cloud cover. The two-dimensional parameters include surface temperature, surface air pressure, 2-meter temperature, and 10-meter wind vector, etc.

[0044] Data quality control and spatial matching: Since the spatial resolution of GMI (6km at 166.5GHz) is much higher than the grid resolution of ERA5, all GMI observations are averaged into a grid of about 80km×80km to match the cloud and precipitation scales of the observations with the effective resolution of the numerical model. A constraint bias correction scheme is applied to reduce the systematic bias between observations and simulations. The samples for calculating the bias correction coefficients are only from clear sky areas.

[0045] Limited observation area: In the microwave band, due to the high and complex emissivity of land and sea ice, this study focuses only on the global ocean region, limiting GMI observations (cone scanning microwave radiometer) to between 50°S and 50°N latitude, and excluding scenarios that include sea ice, land or coastal zones;

[0046] Dataset Partitioning: The RTTOV hydrogel optical lookup table generator was used to generate corresponding hydrogel scattering properties for each sample of the background field data (as pre-training label data). This data, along with the background field data, formed the pre-training dataset. The hydrogel content in the lookup table ranged from 10... -7 The samples ranged from kg / m³ to 0.1 kg / m³, distributed logarithmically across 601 points, with temperature values ​​covering 100 points. Ice-phase condensates ranged from 177 K to 277 K, and liquid-phase condensates ranged from 233 K to 333 K. The spatially matched samples were used as the fine-tuning dataset, divided by time series into a training dataset (April 2021 – March 2022, approximately 12 million samples), a validation dataset (April 2022 – March 2023, approximately 6 million samples), and a test dataset (April 2023 – March 2024, approximately 6 million samples), used for model training, hyperparameter tuning, and final performance evaluation, respectively.

[0047] (2) Constructing a parameterized deep neural network model: For the four types of water condensate—rain, snow, cloud water, and cloud ice—independent deep neural networks are trained respectively. The specific operation is as follows:

[0048] (a) Design a network structure including an input layer, hidden layers, and an output layer. All hidden layers use Sigmoid weighted linear units as activation functions. The inputs of the neural network include temperature and hydrophobic content, and the outputs are extinction coefficient, single scattering albedo, and asymmetric factor. The hidden layer structure starts with a fully connected layer that projects the low-dimensional input into a high-dimensional latent space, followed by three residual blocks. Each residual block contains two fully connected layers with skip connections. The residual blocks are designed to learn residual functions, simplify the optimization process, and increase the network depth without performance degradation.

[0049] (b) Data preprocessing: To accommodate the huge changes in numerical magnitude, the hydrophobic content and extinction coefficient values ​​were logarithmically transformed during the preprocessing stage. Subsequently, all input and output variables were min-max normalized to ensure the stability of training convergence.

[0050] (c) Pre-training deep neural network models using pre-trained datasets: All models were implemented in the PyTorch framework, trained for 1000 epochs with a batch size of 128, using the Adam optimizer, an initial learning rate of 0.001, and mean squared error (MSE) as the loss function. In addition, a training strategy of decreasing learning rate was adopted, and the learning rate was reduced by 50% when the validation loss did not improve for two consecutive epochs.

[0051] (3) Constructing a coupling framework between physical radiative transfer modes and deep neural networks: The forward and adjoint operators of RTTOV are directly integrated into the deep learning training process to create a fully differentiable computational path from satellite radiance to neural network parameters. The specific operation is as follows:

[0052] (a) Design of a loss function based on probability distribution consistency: Obtain initial values ​​of the scattering properties of the condensed object. Input the initial values ​​of the scattering properties of the condensed object and the corresponding numerical model background field into the physical radiative transfer model for forward propagation to obtain the simulated brightness temperature. Use Gaussian kernel density estimation (to ensure the differentiability of the loss function) to approximate the probability density of the simulated brightness temperature and the observed brightness temperature. Obtain the corresponding probability distribution by normalizing the density estimation to make their sum equal to 1. Normalize the probability distributions of the simulated brightness temperature and the observed brightness temperature, and calculate the loss function based on probability distribution consistency. ;

[0053] Specifically, by measuring the difference between the simulated and observed brightness temperature probability distributions within a geographic region, the traditional mean square error is prevented from doubly penalizing location biases in cloud and rain simulation evaluations. This allows the optimization process to correctly enhance the scattered signal rather than systematically suppress cloud features. The JS divergence is calculated within a 10°×10° latitude and longitude region to prevent mutual compensation of biases between different regions. The JS divergence ranges from 0 to approximately 0.69, with a value of 0 indicating that the two probability distributions are completely consistent, and a larger value indicating a greater difference between the observed and simulated brightness temperature distributions.

[0054] In order to obtain a smooth probability density estimate without exceeding memory limitations, this study adopts a random sampling strategy. For each gradient descent iteration, 10 regions are selected from approximately 300 available regions worldwide, and 20,000 data points are extracted from each selected region. In the kernel density estimation formula, the bandwidth parameter is set to 5K, and the interval center ranges from 100K to 300K with an interval of 5K, ensuring comprehensive coverage of the brightness temperature spectrum while maintaining computational efficiency.

[0055] (b) Adjusting the network architecture and introducing additional input features: Before the fine-tuning stage, firstly, the weights and biases of the output layer are copied to create independent paths for the vertical and horizontal polarization channels (the motivation for this modification is that the orientation of non-spherical ice particles leads to different scattering properties between vertical and horizontal polarization); secondly, considering that the microphysical characteristics of ice phase condensates are affected by air pressure and humidity, this study introduces a Feature Linear Modulation (FiLM) layer to use these variables as additional input features of the neural network. To maintain physical stability during fine-tuning, the weights and biases of all FiLM networks are initialized to zero, and air pressure and specific humidity are min-max normalized.

[0056] (c) Perform backpropagation to establish a complete gradient chain: Perform adjoint calculations on the observed brightness temperature and simulated brightness temperature according to the physical radiative transfer model to obtain the sensitivity of brightness temperature data to volume scattering properties. The loss function is calculated through automatic differentiation. brightness temperature data gradient Normalized scattering properties of condensed matter For network parameters gradient The scattering properties of condensed objects were calculated through an inverse normalization process. Scattering properties of normalized hydrocrystalline objects gradient The above results are then connected together during the backpropagation process of the neural network to establish a complete differentiable path from the observed brightness temperature to the network parameters.

[0057] Unlike traditional methods that rely on exhaustive search of small-scale predefined parameter combinations, deep learning employs a gradient-based backpropagation method, which can efficiently find optimal solutions in continuous high-dimensional spaces. However, a key issue exists: the volume scattering properties output by the neural network and the target variable, satellite radiance, need to be connected through a physical radiative transfer mode. This mode operates outside the deep learning framework, causing gradient propagation to be interrupted and preventing direct automatic differential optimization. To achieve effective parameter optimization, this study directly integrates the forward and Jacobian operators of the physical radiative transfer mode into the deep learning training framework. This method creates a fully differentiable computational path from satellite radiance to neural network parameters, realizing gradient-based optimization.

[0058] (4) Model optimization is performed using the Adam optimizer and early stopping strategy. Performance is monitored on the validation dataset and the optimal model configuration is saved. The specific operations are as follows:

[0059] (a) Optimization using the Adam optimizer with a learning rate of 10. -5 This learning rate was chosen to balance training efficiency and physical stability; 10 -3 Or 10-4 An excessively high learning rate leads to excessively large parameter updates in each iteration, causing the network to produce outputs that violate physical boundaries, such as negative single-scattering albedo values. Conversely, a learning rate of 10... -6 Or 10 -7 A small learning rate leads to slow convergence and insufficient loss reduction.

[0060] (b) Determine the training strategy, specifically, under the control of a fixed random seed, randomly shuffle all samples to ensure that the results are reproducible, train the model for 200 cycles, and select the parameters that achieve the lowest validation error as the final model configuration;

[0061] (c) Implement an early stopping strategy to reduce overfitting, i.e., terminate training early if the validation error has not improved for several consecutive epochs;

[0062] (5) Finally, the optimized volume scattering properties are generated and applied. The specific steps include:

[0063] (a) Model inference and output: The optimal model is used to reconstruct the test samples to obtain the optimized volume scattering properties, generate a homogenized hydrogel optical lookup table or real-time prediction results, and save the optimal model weights and normalizer parameters to support the reproduction of experiments and subsequent batch processing.

[0064] (b) Integrated application: The optimized volume scattering properties are integrated into fast radiative transfer modes such as RTTOV and used as satellite observation operators for all-sky data assimilation, improving the assimilation effect of cloud and rain area observations and enhancing the accuracy of numerical weather forecasts;

[0065] (c) Performance Evaluation: Evaluate the optimization effect, calculate the Jensen-Shannon divergence of the observed background field statistical characteristics and brightness temperature distribution before and after optimization, and verify the model performance improvement, such as... Figure 3 As shown, in the case of Typhoon Doksuri on July 24, 2023, the observed brightness temperature image clearly revealed the typhoon's eye and eyewall structure. While the default microphysics scheme of RTTOV reproduced the overall structural features of the typhoon, it systematically underestimated the scattering effect of ice-phase condensates, resulting in a higher simulated brightness temperature relative to the overall observations. The neural network optimization, by enhancing the scattering effect of snow particles, accurately reproduced the extremely low brightness temperature characteristics observed in the eyewall region, significantly improving consistency with satellite observations. Figure 4 As shown, the optimized neural network model makes the OB probability density function closer to a Gaussian distribution, significantly reducing both the mean bias and skewness, and demonstrating significant improvements in both vertical and horizontal polarization channels; Figure 3 In the image, (a) shows the vertical polarization observation of GMI at 166.5 GHz, (b) shows the ERA5 snowmelt path, (c) shows the brightness temperature simulation of the original scheme, and (d) shows the brightness temperature simulation after neural network optimization.

[0066] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing the scattering properties of condensed water objects based on physically constrained deep learning, characterized in that, Includes the following steps: S1. Obtain the historical numerical model background field and calculate the scattering properties of condensed objects, construct a pre-training dataset, obtain historical observed brightness temperature and historical numerical model background field for spatiotemporal matching, and construct a fine-tuning dataset; the numerical model background field includes atmospheric temperature, humidity, air pressure and condensed object content; the condensed objects include rain, snow, cloud water and cloud ice. S2. A deep neural network model is pre-trained using a pre-trained dataset to obtain initial values ​​of the scattering properties of the condensed object. The initial values ​​of the scattering properties of the condensed object and the corresponding numerical mode background field are input into the physical radiation transfer mode for forward calculation to obtain the simulated brightness temperature. S3. Use the adjoint operator of the physical radiative transfer mode to calculate the gradient of the brightness temperature data, calculate the loss function based on the simulated brightness temperature and the observed brightness temperature, and establish a complete differentiable gradient chain from the loss function to the network parameters in the backpropagation of the neural network. S4. Taking the consistency of simulated brightness temperature and observed brightness temperature probability distribution as the optimization objective, gradient descent iterative training is performed in conjunction with the complete differentiable gradient chain to fine-tune the network parameters of the deep neural network model. The second validation dataset is used to perform hyperparameter optimization on the deep neural network model to obtain the optimal network parameters. S5. The trained deep neural network model is embedded into the fast radiative transfer mode to generate optimized scattering properties of condensed water objects in real time, which are then used as satellite observation operators for all-sky data assimilation. The pre-training dataset is used to pre-train deep neural network models, including temperature, hydrogel content, and hydrogel scattering properties, and is randomly divided into a first training dataset and a first validation dataset in a 4:1 ratio. The scattering properties of the hydrogel include extinction coefficient, single scattering albedo, and asymmetry factor. The fine-tuning dataset is used to fine-tune the deep neural network model. It includes temperature, hydrocondensate content and observed brightness temperature, and is divided into a second training dataset, a second validation dataset and a second test set according to the time series in a 2:1:1 ratio. The complete differentiable gradient chain from the loss function to the network parameters is specifically represented as follows: ； in loss function For deep neural network model network parameters gradient, loss function brightness temperature data The gradient is calculated through automatic differentiation. Brightness temperature data Scattering properties of hydrogels The gradient, i.e., brightness temperature data Scattering properties of hydrogels The sensitivity was calculated using the adjoint method. Scattering properties of hydrogels Scattering properties of normalized hydrocrystalline objects The gradient originates from the inverse normalization process, including exponential and linear scaling transformations. Normalized scattering properties of condensed matter For network parameters The gradient is calculated using automatic differentiation.

2. The method for optimizing the scattering properties of hydrogel objects based on physically constrained deep learning according to claim 1, characterized in that: The method for calculating the scattering properties of hydrogels specifically involves using the RTTOV hydrogel optical lookup table generator to generate the scattering properties of hydrogels.

3. The method for optimizing the scattering properties of condensed water objects based on physically constrained deep learning according to claim 1, characterized in that: The deep neural network model is trained independently according to the type of hydrogel, and includes an input layer, a hidden layer and an output layer; the input data of the input layer is atmospheric temperature and hydrogel content; the output data of the output layer is the scattering properties of the hydrogel.

4. The method for optimizing the scattering properties of condensed water objects based on physically constrained deep learning according to claim 1, characterized in that, The method for calculating the loss function based on simulated brightness temperature and observed brightness temperature includes: Calculate the probability distribution of simulated brightness temperature and observed brightness temperature; the probability distribution is approximated using Gaussian kernel density estimation, and the expression is: ； in For interval The probability density at that location, The number of samples in the interval. To control the bandwidth parameter for estimating smoothness, Samples within the interval The single brightness temperature measurement value, For the first k The center of each interval; The probability distributions of simulated brightness temperature and observed brightness temperature are normalized, and the loss function based on the consistency of the probability distribution is calculated. The expression is as follows: ； in For loss function, For the number of geographical regions, For the number of satellite channels, For the number of intervals, for Geographical region Satellite channel in k Normalized probability of observed brightness temperature in the interval for Geographical region Satellite channel in k Normalized probability of simulated brightness temperature in the interval.

5. The method for optimizing the scattering properties of hydrogel objects based on physically constrained deep learning according to claim 1, characterized in that: The gradient descent iterative training optimizes the model using the Adam optimizer and an early stopping strategy.

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