Atmospheric waveguide loss prediction method and system based on heterogeneous characteristics of physical equation embedding

Abstract

The invention discloses a heterogeneous atmospheric waveguide loss prediction method based on physical equation embedding. The method comprises the following steps: step 1, data preprocessing; step 2, encoding time sequence features; step 3, physical constraint prediction; step 4, decoding the space field; and 5, a multi-objective loss function is established. According to the method disclosed by the invention, rapid, accurate and physically consistent forward modeling prediction of the atmospheric waveguide propagation loss in the non-uniform region is realized. By combining a physical constraint solution operator thought with a Transform-CNN architecture capable of efficiently processing time sequence dependence, the efficiency of data driving and the preciseness of a physical model are fused, so that efficient and accurate prediction from time sequence meteorological data to a two-dimensional propagation loss field is realized.

Description

Technical Field

[0001] This invention belongs to the field of atmospheric waveguide propagation loss prediction technology, and specifically relates to an atmospheric waveguide loss prediction method and system based on the non-uniform characteristics of physical equation embedding. Background Technology

[0002] The complex and variable atmospheric environment in non-uniform regions, especially the frequent occurrence of atmospheric waveguides, can significantly impact the performance of radio communication, radar detection, and navigation systems. Traditional propagation loss prediction models based on numerical methods and data-driven models each have their limitations and are difficult to meet real-time service requirements. The main limitations are as follows:

[0003] 1) High computational cost: Numerical computation methods, especially the parabolic equation (PE) model, are widely recognized as the "gold standard." However, solving the PE model relies on dense meshing and iterative calculations over a vast space, making it computationally too expensive for real-time operations that require rapid response.

[0004] 2) Lack of physical consistency: Pure data-driven models, which are "black boxes", may make predictions that violate the basic physical laws of electromagnetic wave propagation, especially under extreme or rare conditions not covered by training data, raising questions about their generalization ability and reliability.

[0005] 3) Limitations of static modeling: Most existing work on pure data-driven models deals with static "snapshot" inputs, ignoring the dynamic evolution characteristics of the atmospheric environment (especially in non-uniform regions), making it difficult to capture the key temporal dependencies that determine the generation and dissipation of waveguides. Summary of the Invention

[0006] This invention addresses the problems of high computational cost, lack of physical consistency, and limitations of static modeling in existing propagation loss prediction models by providing an atmospheric waveguide loss prediction method and system based on the non-uniform characteristics of physical equation embedding.

[0007] The present invention adopts the following technical solution:

[0008] An improved method for predicting atmospheric waveguide loss based on the non-uniformity of physical equation embedding includes the following steps:

[0009] Step 1, Data Preprocessing:

[0010] Using ERA5, calculate the vertical profile of the atmospheric refractive index and its corrected refractive index according to ITU-R P.453;

[0011] Step 2, Temporal Feature Encoding:

[0012] First, the raw meteorological data is uniformly projected onto a high-dimensional feature space of dimension d_model through a fully connected layer;

[0013] Secondly, a fixed sine-cosine position code is introduced;

[0014] Step 3, Physical Constraint Prediction:

[0015] The physical constraint module guides the model to learn a propagation loss field that satisfies a pre-defined parameterized partial differential equation structure.

[0016] Step 4, Spatial Field Decoding:

[0017] The feature vector output by the timing encoder is converted into a two-dimensional propagation loss spatial distribution map L_pred;

[0018] Step 5, Multi-objective loss function:

[0019] Introducing mean square error, central difference, and penalty for the gradient of the predicted field, the total loss function is a weighted sum of the above terms.

[0020] Furthermore, in step 1:

[0021] Using a vertical profile with corrected refractive index as input, a wide-angle parabolic equation solver is used to simulate the propagation of electromagnetic waves.

[0022] Select a portion of ERA5 grid points within the study area and execute the above process at each time point to generate a two-dimensional propagation loss field L_struc.

[0023] Furthermore, in step 2:

[0024] The Transformer architecture is adopted as the basic model of the temporal feature encoder. This architecture includes an input embedding layer, a positional encoding layer, and a Transformer encoding layer.

[0025] The raw meteorological data is uniformly projected into a high-dimensional feature space of dimension d_model through a fully connected layer;

[0026]

[0027] In the above formula, X_embed is the high-dimensional feature space embedding of the input data, W_embed is the learnable weight matrix, X_input is the input time series, and b_embed is the bias matrix.

[0028] Introduce fixed sine-cosine position coding:

[0029]

[0030] In the above formula, PE represents the parabolic equation, pos represents the time step position, and i represents the feature dimension index;

[0031] The core consists of L identical encoder layers stacked together, each layer including a multi-head self-attention module and a feedforward neural network.

[0032]

[0033]

[0034] In the above formula, It's an attention mechanism, where Q represents the vector corresponding to the current input information to be processed, K represents the vector corresponding to all input information, V represents the actual content vector corresponding to K, and d... k Let Q be the dimension or K be the dimension, softmax be the activation function, and T be the sequence length.

[0035] MultiHead is the final output calculation formula for multi-head self-attention, and Concat refers to the concatenation operation. The first point of attention. Refers to the h-th attention head, It is a learnable output linear transformation matrix, O = Q, K, or V;

[0036] ,

[0037] Generate temporal features rich in global context information ,and R is a real matrix.

[0038] Furthermore, in step 3:

[0039] The physical constraint module is based on parametric partial differential equations:

[0040]

[0041] In the above formula, It is the generic function corresponding to the constraint. It is defined in , Physical field variables in two-dimensional spatial coordinates Indicates horizontal distance. The height is represented by c, which is the input parameter that describes different scenes, and the coefficients c0-c4 are learnable parameters.

[0042] Furthermore, in step 4:

[0043] First, feature reconstruction is performed, taking the output of the last time step of the Transformer encoder. This is achieved by passing through a fully connected layer and reshaping it into an initial low-resolution spatial tensor. , It is a dimension parameter of the channel dimension. It is a dimension parameter of the height dimension. It is a dimension parameter for the width dimension;

[0044] Spatial upsampling is then performed, using a series of transposed convolutional blocks (ConvTranspose2d) to progressively upsample the feature map and restore spatial resolution. Each block contains a transposed convolutional layer, batch normalization (BN), and a LeakyReLU activation function.

[0045]

[0046] In the above formula, It is the input feature map of the current transposed convolutional block;

[0047] Finally, cross-attention fusion is performed. A cross-attention mechanism is introduced in the intermediate layer of the decoder, which incorporates the spatial features of the current decoding layer. As a query, the complete temporal output H_seq of the Transformer encoder is used as the key and value, thereby dynamically incorporating the temporal context information most relevant to the spatial location into the decoding process:

[0048]

[0049] In the above formula, It is a learnable scaling factor. It is the target feature tensor after attention enhancement, which is the final output feature after cross-attention fusion; Represents the spatial characteristic tensor. It is a cross-attention mechanism operation used to model the relationship between spatial features and sequence features, and realizes feature interaction by calculating attention weights;

[0050] Finally, a 1*1 convolutional layer is used to reduce the number of channels in the feature map to 1, and a prediction propagation loss map L_pred is generated by passing it through a Sigmoid activation function and normalized to the [0, 1] interval.

[0051] Furthermore, in step 5:

[0052] Data fitting loss L data :

[0053] Mean square error is used to measure the predicted loss field L pred The real labels L generated by the PE model true Pixel-level differences between them:

[0054]

[0055] In the above formula, N represents the total number of samples;

[0056] Physical constraint loss L PDE :

[0057] The loss field L is predicted using the central difference calculation. pred The first and second partial derivatives are calculated, and the L2 norm of the residuals of the parameterized partial differential equation (PDE) is calculated:

[0058]

[0059] In the above formula, N, H, and W correspond to the number of nodes in the three-dimensional discrete space grid in the x, y, and z dimensions, respectively. represent The residual term is the difference between the left and right sides of the objective partial differential equation after substituting the predicted field variables into the objective partial differential equation. In the discretized grid in three-dimensional space, i is the grid node index corresponding to the x-space dimension, j is the grid node index corresponding to the y-space dimension, and k is the grid node index corresponding to the z-space dimension.

[0060] Spatial smoothing regularization term L smooth :

[0061] Penalty for the gradient of the predicted field:

[0062]

[0063] In the above formula, It is the gradient of the predicted field variable with respect to the x-space coordinates, reflecting the rate of change of the field variable in the x-direction. It is a pair of predictive field variables The gradient of spatial coordinates reflects the field variable in... The rate of change of direction in space;

[0064] Total loss function The weighted sum of the above items:

[0065]

[0066] In the above formula, and It is a hyperparameter that controls the weights of various components.

[0067] Furthermore, a phased training strategy is adopted, with only the data fitting loss L being optimized in the initial stage of training. data This allows the model to quickly learn the basic mapping relationship from meteorological characteristics to the loss field; after preheating, physical constraint loss is gradually introduced, with its weight... Within T_anneal epochs, the weights linearly increase from 0 to a preset maximum value. After the weights reach the maximum value, the model is trained under the full joint loss function until convergence. T_anneal refers to the number of annealing rounds of the physical constraint loss weights, and the unit is training rounds (epochs).

[0068] Furthermore, the training process employs the AdamW optimizer in conjunction with a cosine annealing learning rate scheduler to achieve better convergence. Gradient clipping is applied to prevent gradient explosion, and Dropout and weight decay are used in combination to prevent overfitting.

[0069] An atmospheric waveguide loss prediction system based on the non-uniformity of physical equation embedding is improved by including a data preprocessing unit, a temporal feature encoding unit, a physical constraint prediction unit, a spatial field decoding unit, and a multi-objective loss function unit.

[0070] The data preprocessing unit uses ERA5 to calculate the vertical profile of the atmospheric refractive index and its corrected refractive index according to ITU-R P.453;

[0071] The temporal feature coding unit first projects the raw meteorological data into a high-dimensional feature space of d_model dimension through a fully connected layer; then it introduces fixed sine-cosine position coding.

[0072] The physical constraint prediction unit guides the model to learn a propagation loss field that satisfies a preset parameterized partial differential equation structure, guided by the physical constraint module.

[0073] The spatial field decoding unit converts the feature vector output by the timing encoder into a two-dimensional propagation loss spatial distribution map L_pred;

[0074] The multi-objective loss function unit introduces mean square error, central difference, and penalty for the gradient of the predicted field. The total loss function is a weighted sum of the above terms.

[0075] The beneficial effects of this invention are:

[0076] The method disclosed in this invention uses a physically constrained Transformer-CNN model—ArcTCP-Net (Arctic Transformer-CNN with Physics-Constraints Network)—for predicting non-uniform waveguide loss. This model employs an innovative Transformer-CNN architecture: the Transformer encoder extracts long-range spatiotemporal dependent features from multidimensional meteorological time series (ERA5 reanalysis data); the CNN decoder decodes these features and upsamples them into a high-resolution propagation loss spatial field. Simultaneously, to ensure the physical plausibility of the prediction results, a physical constraint module based on parametric partial differential equations (PDEs) is embedded. During training, this module guides the network to learn solutions that conform to the laws of electromagnetic wave propagation in the form of a loss function, thereby achieving efficient and accurate prediction of two-dimensional propagation loss fields from time-series meteorological data.

[0077] The method disclosed in this invention enables rapid, accurate, and physically consistent forward modeling prediction of atmospheric waveguide propagation loss in non-uniform regions. By combining the concept of physically constrained solvers with the Transformer-CNN architecture, which can efficiently handle time-dependent factors, the method integrates the efficiency of data-driven approaches with the rigor of physical models, thereby achieving efficient and accurate prediction of two-dimensional propagation loss fields from time-series meteorological data.

[0078] The system disclosed in this invention utilizes the ArcTCP-Net physically constrained deep learning model for accurate prediction of atmospheric waveguide propagation loss in non-uniform regions. This model innovatively integrates a Transformer encoder and a CNN decoder, embedding PDE-based physical constraints. It achieves efficient, high-precision, and highly physically consistent end-to-end forward modeling prediction from time-series meteorological data to a two-dimensional propagation loss field, providing a new and effective tool for rapid assessment and protection of radio wave environments in non-uniform regions. Experiments show that the ArcTCP-Net model outperforms traditional deep learning baseline models in all evaluation metrics. Its prediction results are highly consistent with high-precision PE models in both numerical and structural aspects, while the computation time per cycle is reduced from tens of minutes to sub-seconds.

[0079] In summary, this invention not only provides a powerful tool for ensuring the protection of non-uniform radio wave environments, but also offers an effective solution that integrates data and physical knowledge for modeling physical processes in other Earth science fields. Attached Figure Description

[0080] Figure 1 This is a flowchart illustrating the method of the present invention. Detailed Implementation

[0081] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0082] Example 1 discloses an atmospheric waveguide loss prediction method based on the non-uniformity of physical equation embedding. It uses a physically constrained Transformer-CNN atmospheric waveguide loss prediction model, combining the idea of ​​physical constraint solvers with the Transformer-CNN architecture, which can efficiently handle time-dependent factors. This integrates the efficiency of data-driven approaches with the rigor of physical models, achieving fast, accurate, and physically consistent forward modeling prediction of atmospheric waveguide propagation loss in non-uniform regions. Figure 1 As shown, it includes the following steps:

[0083] Step 1, Data Preprocessing:

[0084] This embodiment uses the fifth-generation global climate reanalysis data (ERA5) from the European Centre for Medium-Range Weather Forecasts (ECMWF). Data from 2023 was selected, with a spatial resolution of 0.25° × 0.25° and a temporal resolution of 12 hours. For each geographic grid point, 11-dimensional meteorological characteristics were extracted from multiple pressure layers from the surface to an altitude of 5000 meters, including temperature, relative humidity, specific humidity, geopotential height, and U / V wind speed components. These variables form the basis for calculating the atmospheric refractive index profile. The time series length was set to the past 72 hours (i.e., 6 time steps) to predict the propagation loss field at a future point in time.

[0085] Due to the lack of large-scale, high spatiotemporal resolution experimental data on propagation loss, this embodiment uses a high-precision numerical model to generate the label data required for training, validation, and testing. The specific process is as follows:

[0086] Using the temperature, air pressure (converted from geopotential height), and water vapor pressure (calculated from humidity) provided by ERA5, the atmospheric refractive index N and its corrected refractive index M were calculated vertically according to the formula in ITU-R P.453. Using the corrected refractive index vertical profile as input, the propagation of electromagnetic waves was simulated using the mature Split-Step Fourier Transform (SSFT) solver. Multiple sets of data with different antenna heights and operating frequencies were simulated. It was assumed that the transmitter was located at 10 meters and 30 meters, operating at 5 GHz and 10 GHz bands, with a Gaussian antenna pattern. The simulation area was set to 75 km horizontally and 250 meters vertically. A subset of ERA5 grid points within the study area were selected, and the above process was executed at each time point to generate a two-dimensional (height vs. distance) propagation loss field L_struc.

[0087] In this embodiment, meteorological time series data is used as the model input X_input, and the corresponding PE simulated loss field is used as the label L_true, constructing a (input-output) dataset containing hundreds of thousands of sample pairs. The dataset is then randomly divided into training, validation, and test sets in an 8:1:1 ratio.

[0088] Step 2, Temporal Feature Encoding:

[0089] First, a fully connected layer is used to uniformly project the raw meteorological data into a high-dimensional feature space of dimension d_model to improve representation capabilities. Second, a fixed sine-cosine positional encoding is introduced to display the positional information of the injected time steps. Finally, the core part consists of L layers of identical encoders stacked together. Each layer includes a multi-head self-attention module and a feedforward neural network, and residual connections and layer normalization are used to ensure training stability.

[0090] The specific steps are as follows:

[0091] To fully capture the long-term dependencies and global dynamic structure in the input meteorological sequence, the Transformer architecture is adopted as the basic model of the temporal feature encoder. This architecture includes an input embedding layer, a position encoding layer, and a Transformer encoding layer.

[0092] The raw meteorological data contains 11 basic features, with significant differences in their numerical range and physical meaning. A fully connected layer is used to uniformly project the raw meteorological data into a high-dimensional feature space of dimension d_model to improve its representation capability.

[0093]

[0094] In the above formula, X_embed is the high-dimensional feature space embedding of the input data, W_embed is the learnable weight matrix, X_input is the input time series, and b_embed is the bias matrix.

[0095] Since the Transformer architecture itself does not have the capability for timing modeling, a fixed sine-cosine position encoding is introduced to display the position information of the injected time step:

[0096]

[0097] In the above formula, PE represents the parabolic equation, pos represents the time step position, and i represents the feature dimension index; the embedded features are added to the encoding position and then fed into the encoder.

[0098] The core consists of L identical encoder layers stacked together. Each layer includes a multi-head self-attention module and a feedforward neural network, and residual connections and layer normalization are used to ensure training stability. The core computation of the multi-head self-attention mechanism is as follows:

[0099]

[0100]

[0101] In the above formula, It's an attention mechanism, where Q represents the vector corresponding to the current input information to be processed, K represents the vector corresponding to all input information, V represents the actual content vector corresponding to K, and d... k For the dimension of Q or K, divide by This is to prevent the softmax gradient from vanishing due to an excessively large dot product result. Softmax is an activation function used to merge Q with... The dot product result is converted into weights (representing the degree of attention Q gives to each K), where T is the sequence length;

[0102] MultiHead is the final output calculation formula for multi-head self-attention, used to fuse features from multiple attention heads and capture dependencies in different dimensions of a sequence. Concat refers to the concatenation operation. This refers to arrive The calculation results of a total of h attention heads are concatenated; The first point of attention. Refers to the h-th attention head, It is a learnable output linear transformation matrix used to map the "concatenated multi-head features" to the target dimension of the model (such as the d_model dimension of the Transformer), so that the multi-head features can be adapted to the input of the subsequent network. O=Q, K or V.

[0103] Each attention head is an independently computed attention result, obtained by performing linear transformations on the original Q, K, and V respectively. (These are the learnable parameters of the h-th head), and then substituted into the basic attention formula Attention(Q,K,V) for calculation.

[0104] Through this mechanism, the model can capture the complex dependencies between any two time points in the sequence and generate temporal features rich in global context information. ,and R is a real matrix with shape denoted as sequence length × model dimension.

[0105] Step 3, Physical Constraint Prediction:

[0106] To improve the physical plausibility and generalization ability of the model's predictions, a physical constraint module based on parametric partial differential equations (PDEs) was designed. This module guides the model to learn a propagation loss field that satisfies a predefined parametric partial differential equation structure. During training, the spatial derivative is approximated using finite difference methods (such as central difference), and the PDE residual loss is defined.

[0107] Assuming that under certain conditions, the propagation loss field L(x,z) approximately satisfies a two-dimensional elliptic PDE, then the physical constraint module based on the parameterized partial differential equation is:

[0108]

[0109] In the above formula, It is the generic function corresponding to the constraint. It is defined in , Physical field variables in two-dimensional spatial coordinates Indicates horizontal distance. Let represent height, 'c' be the input parameter characterizing different scenes, and 'c0' to 'c4' be learnable parameters that enable the model to adaptively learn the PDE form that best reflects the underlying physical laws of the data. This equation describes the diffusion and attenuation of energy in a non-uniform medium.

[0110] Step 4, Spatial Field Decoding:

[0111] The feature vector output by the timing encoder is converted into a two-dimensional propagation loss spatial distribution map L_pred;

[0112] First, the output of the last time step of the Transformer encoder is passed through a fully connected layer to reshape it into an initial low-resolution spatial tensor. Then, spatial upsampling is performed by gradually upsampling the feature map using a series of transposed convolution (ConvTranspose2d) blocks to restore the spatial resolution. Finally, cross-attention fusion is performed. To better utilize the complete temporal information, a cross-attention mechanism is introduced in the intermediate layer of the decoder.

[0113] The specific steps are as follows:

[0114] A decoder architecture based on transposed convolution was designed and a cross-modal attention mechanism was incorporated.

[0115] First, feature reconstruction is performed, taking the output of the last time step of the Transformer encoder. This is achieved by passing through a fully connected layer and reshaping it into an initial low-resolution spatial tensor. , It is a dimension parameter of the channel dimension. It is a dimension parameter of the height dimension. It is a dimension parameter for the width dimension;

[0116] Spatial upsampling is then performed, using a series of transposed convolutional blocks (ConvTranspose2d) to progressively upsample the feature map and restore spatial resolution. Each block contains a transposed convolutional layer, batch normalization (BN), and a LeakyReLU activation function.

[0117]

[0118] In the above formula, It is the input feature map of the current transposed convolutional block (the feature data output from the previous step, containing spatial feature information of a specific dimension).

[0119] Finally, cross-attention fusion is performed. To better utilize the complete temporal information, a cross-attention mechanism is introduced in the intermediate layer of the decoder. This mechanism incorporates the spatial features of the current decoding layer. As a query, the complete temporal output H_seq of the Transformer encoder is used as the key and value, thereby dynamically incorporating the temporal context information most relevant to the spatial location into the decoding process:

[0120]

[0121] In the above formula, It is a learnable scaling factor. It is the target feature tensor after attention enhancement, which is the final output feature after cross-attention fusion; The spatial feature tensor, which typically comes from spatial dimension data (such as image feature maps, 3D point cloud spatial features, etc.), is one of the inputs to the cross-attention module. It is a cross-attention mechanism operation used to model the relationship between spatial features and sequence features, and realizes feature interaction by calculating attention weights;

[0122] Finally, a 1*1 convolutional layer is used to reduce the number of channels in the feature map to 1, and a prediction propagation loss map L_pred is generated by passing it through a Sigmoid activation function and normalized to the [0, 1] interval.

[0123] Step 5, Multi-objective loss function:

[0124] To achieve the dual goals of data fitting accuracy and physical consistency, this invention designs a multi-objective loss function consisting of three parts: First, mean squared error (MSE) is used to measure the pixel-level difference between the predicted loss field and the true labels generated by the PE model; second, the first and second partial derivatives of the predicted field L_pred are calculated using central difference, and the L2 norm of the PDE residuals is also calculated; finally, to encourage the generation of a spatially smoother and more continuous field and avoid artifacts such as the checkerboard effect, a penalty is introduced for the gradient of the predicted field. The total loss function is defined as the weighted sum of the above terms.

[0125] The specific steps are as follows:

[0126] (1) Data fitting loss L data :

[0127] Mean square error is used to measure the predicted loss field L pred The real labels L generated by the PE model true Pixel-level differences between them:

[0128]

[0129] In the above formula, N represents the total number of samples;

[0130] (2) Physical constraint loss L PDE :

[0131] This loss term penalizes the degree to which the predicted field violates the predefined PDE. The predicted loss field L is calculated using central difference. pred The first and second partial derivatives are calculated, and the L2 norm of the residuals of the parameterized partial differential equation (PDE) is calculated:

[0132]

[0133] In the above formula, N, H, and W correspond to the number of nodes in the three-dimensional discrete space grid in the x, y, and z dimensions, respectively. Therefore, NHW is the total number of nodes in the entire grid. represent The residual term is the difference between the left and right sides of the objective partial differential equation after substituting the predicted field variables into the objective equation. In the discretized grid in three-dimensional space, i is the grid node index corresponding to the x-space dimension, j is the grid node index corresponding to the y-space dimension, and k is the grid node index corresponding to the z-space dimension, used to identify the predicted field. The specific location in the discrete space (each index corresponds to a grid point).

[0134] (3) Spatial smoothing regularization term L smooth :

[0135] To encourage the generation of spatially smoother, more continuous fields and avoid artifacts such as the checkerboard effect, a penalty is introduced for the gradient of the predicted field:

[0136]

[0137] In the above formula, It is the gradient of the predicted field variable with respect to the x-space coordinates, reflecting the rate of change of the field variable in the x-direction. It is a pair of predictive field variables The gradient of spatial coordinates reflects the field variable in... The rate of change of direction in space;

[0138] Total loss function The weighted sum of the above items:

[0139]

[0140] In the above formula, and It is a hyperparameter that controls the weights of various components.

[0141] A phased training strategy is adopted to ensure stable model convergence and effective integration of physical constraints. In the initial training phase, only the data fitting loss L is optimized. data This allows the model to quickly learn the basic mapping relationship from meteorological characteristics to the loss field; after preheating, physical constraint loss is gradually introduced, with its weight... Within T_anneal epochs, the weights linearly increase from 0 to a preset maximum value. This annealing strategy prevents strong physical constraints from undermining the model's representational ability in the early stages of learning. After the weights reach their maximum value, the model is trained under the full joint loss function until convergence. T_anneal is a training hyperparameter that refers to the number of annealing epochs for the physical constraint loss weights, measured in training epochs, i.e., the number of times the model trains the entire dataset once.

[0142] The training process employs the AdamW optimizer in conjunction with a cosine annealing learning rate scheduler to achieve better convergence. Gradient clipping is used to prevent gradient explosion, and regularization techniques such as Dropout and weight decay are combined to prevent overfitting.

[0143] This embodiment also discloses an atmospheric waveguide loss prediction system based on the non-uniformity of physical equation embedding, including a data preprocessing unit, a temporal feature encoding unit, a physical constraint prediction unit, a spatial field decoding unit, and a multi-objective loss function unit;

[0144] The data preprocessing unit uses ERA5 to calculate the vertical profile of the atmospheric refractive index and its corrected refractive index according to ITU-R P.453;

[0145] The temporal feature coding unit first projects the raw meteorological data into a high-dimensional feature space of d_model dimension through a fully connected layer; then it introduces fixed sine-cosine position coding.

[0146] The physical constraint prediction unit guides the model to learn a propagation loss field that satisfies a preset parameterized partial differential equation structure, guided by the physical constraint module.

[0147] The spatial field decoding unit converts the feature vector output by the timing encoder into a two-dimensional propagation loss spatial distribution map L_pred;

[0148] The multi-objective loss function unit introduces mean square error, central difference, and penalty for the gradient of the predicted field. The total loss function is a weighted sum of the above terms.

Claims

1. A method for predicting atmospheric waveguide loss based on the non-uniformity of physical equation embedding, characterized in that, Includes the following steps: Step 1, Data Preprocessing: Using ERA5, calculate the vertical profile of the atmospheric refractive index and its corrected refractive index according to ITU-R P.453; Step 2, Temporal Feature Encoding: First, the raw meteorological data is uniformly projected onto a high-dimensional feature space of dimension d_model through a fully connected layer; Secondly, a fixed sine-cosine position code is introduced; Step 3, Physical Constraint Prediction: The physical constraint module guides the model to learn a propagation loss field that satisfies a pre-defined parameterized partial differential equation structure. Step 4, Spatial Field Decoding: The feature vector output by the timing encoder is converted into a two-dimensional propagation loss spatial distribution map L_pred; Step 5, Multi-objective loss function: Introducing mean square error, central difference, and penalty for the gradient of the predicted field, the total loss function is a weighted sum of the above terms.

2. The atmospheric waveguide loss prediction method based on the non-uniformity of physical equation embedding according to claim 1, characterized in that, In step 1: Using a vertical profile with corrected refractive index as input, a wide-angle parabolic equation solver is used to simulate the propagation of electromagnetic waves. Select a portion of ERA5 grid points within the study area and execute the above process at each time point to generate a two-dimensional propagation loss field L_struc.

3. The atmospheric waveguide loss prediction method based on the non-uniformity of physical equation embedding according to claim 1, characterized in that, In step 2: The Transformer architecture is adopted as the basic model of the temporal feature encoder. This architecture includes an input embedding layer, a positional encoding layer, and a Transformer encoding layer. The raw meteorological data is uniformly projected into a high-dimensional feature space of dimension d_model through a fully connected layer; In the above formula, X_embed is the high-dimensional feature space embedding of the input data, W_embed is the learnable weight matrix, X_input is the input time series, and b_embed is the bias matrix. Introduce fixed sine-cosine position coding: In the above formula, PE represents the parabolic equation, pos represents the time step position, and i represents the feature dimension index; The core consists of L identical encoder layers stacked together, each layer including a multi-head self-attention module and a feedforward neural network. In the above formula, It's an attention mechanism, where Q represents the vector corresponding to the current input information to be processed, K represents the vector corresponding to all input information, V represents the actual content vector corresponding to K, and d... k Let Q be the dimension or K be the dimension, softmax be the activation function, and T be the sequence length. MultiHead is the final output calculation formula for multi-head self-attention, and Concat refers to the concatenation operation. The first point of attention. Refers to the h-th attention head, It is a learnable output linear transformation matrix, O = Q, K, or V; ， Generate temporal features rich in global context information ,and R is a real matrix.

4. The atmospheric waveguide loss prediction method based on the non-uniformity of physical equation embedding according to claim 1, characterized in that, In step 3: The physical constraint module is based on parametric partial differential equations: In the above formula, It is the generic function corresponding to the constraint. It is defined in , Physical field variables in two-dimensional spatial coordinates Indicates horizontal distance. The height is represented by c, which is the input parameter that describes different scenes, and the coefficients c0-c4 are learnable parameters.

5. The atmospheric waveguide loss prediction method based on the non-uniformity of physical equation embedding according to claim 1, characterized in that, In step 4: First, feature reconstruction is performed, taking the output of the last time step of the Transformer encoder. This is achieved by passing through a fully connected layer and reshaping it into an initial low-resolution spatial tensor. , These are the dimension parameters of the channel dimension. It is a dimension parameter of the height dimension. It is a dimension parameter for the width dimension; Spatial upsampling is then performed, using a series of transposed convolutional blocks (ConvTranspose2d) to progressively upsample the feature map and restore spatial resolution. Each block contains a transposed convolutional layer, batch normalization (BN), and a LeakyReLU activation function. In the above formula, It is the input feature map of the current transposed convolutional block; Finally, cross-attention fusion is performed. A cross-attention mechanism is introduced in the intermediate layer of the decoder, which incorporates the spatial features of the current decoding layer. As a query, the complete temporal output H_seq of the Transformer encoder is used as the key and value, thereby dynamically incorporating the temporal context information most relevant to the spatial location into the decoding process: In the above formula, It is a learnable scaling factor. It is the target feature tensor after attention enhancement, which is the final output feature after cross-attention fusion; Represents the spatial characteristic tensor. It is a cross-attention mechanism operation used to model the relationship between spatial features and sequence features, and realizes feature interaction by calculating attention weights; Finally, a 1*1 convolutional layer is used to reduce the number of channels in the feature map to 1, and a prediction propagation loss map L_pred is generated by passing it through a Sigmoid activation function and normalized to the [0, 1] interval.

6. The atmospheric waveguide loss prediction method based on the non-uniformity of physical equation embedding according to claim 1, characterized in that, In step 5: Data fitting loss L data : Mean square error is used to measure the predicted loss field L pred The real labels L generated by the PE model true Pixel-level differences between them: In the above formula, N represents the total number of samples; Physical constraint loss L PDE : The loss field L is predicted using the central difference calculation. pred The first and second partial derivatives are calculated, and the L2 norm of the residuals of the parameterized partial differential equation (PDE) is calculated: In the above formula, N, H, and W correspond to the number of nodes in the three-dimensional discrete space grid in the x, y, and z dimensions, respectively. represent The residual term is the difference between the left and right sides of the objective partial differential equation after substituting the predicted field variables into the objective partial differential equation. In the discretized grid in three-dimensional space, i is the grid node index corresponding to the x-space dimension, j is the grid node index corresponding to the y-space dimension, and k is the grid node index corresponding to the z-space dimension. Spatial smoothing regularization term L smooth : Penalty for the gradient of the predicted field: In the above formula, It is the gradient of the predicted field variable with respect to the x-space coordinates, reflecting the rate of change of the field variable in the x-direction. It is a pair of predictive field variables The gradient of spatial coordinates reflects the field variable in... The rate of change of direction in space; Total loss function The weighted sum of the above items: In the above formula, and It is a hyperparameter that controls the weights of various components.

7. The atmospheric waveguide loss prediction method based on the non-uniformity of physical equation embedding according to claim 6, characterized in that: A phased training strategy is adopted, with the initial stage of training focusing only on optimizing the data fitting loss L. data This allows the model to quickly learn the basic mapping relationship from meteorological characteristics to the loss field; after preheating, physical constraint loss is gradually introduced, with its weight... Within T_anneal epochs, the weights linearly increase from 0 to a preset maximum value. After the weights reach the maximum value, the model is trained under the full joint loss function until convergence. T_anneal refers to the number of annealing rounds of the physical constraint loss weights, and the unit is training rounds (epochs).

8. The atmospheric waveguide loss prediction method based on the non-uniformity of physical equation embedding according to claim 7, characterized in that: The training process employs the AdamW optimizer in conjunction with a cosine annealing learning rate scheduler to achieve better convergence. Gradient clipping is used to prevent gradient explosion, and Dropout and weight decay are combined to prevent overfitting.

9. An atmospheric waveguide loss prediction system based on the non-uniformity of physical equation embedding, characterized in that: It includes a data preprocessing unit, a temporal feature encoding unit, a physical constraint prediction unit, a spatial field decoding unit, and a multi-objective loss function unit; The data preprocessing unit uses ERA5 to calculate the vertical profile of the atmospheric refractive index and its corrected refractive index according to ITU-R P.453; The temporal feature coding unit first projects the raw meteorological data into a high-dimensional feature space of d_model dimension through a fully connected layer; then it introduces fixed sine-cosine position coding. The physical constraint prediction unit guides the model to learn a propagation loss field that satisfies a preset parameterized partial differential equation structure, guided by the physical constraint module. The spatial field decoding unit converts the feature vector output by the timing encoder into a two-dimensional propagation loss spatial distribution map L_pred; The multi-objective loss function unit introduces mean square error, central difference, and penalty for the gradient of the predicted field. The total loss function is a weighted sum of the above terms.

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