Dual-radar or multi-radar wind field retrieval method based on physical information neural network

Abstract

This invention discloses a dual-radar or multi-radar wind field inversion method based on a physical information neural network, belonging to the field of meteorological detection technology. This method directly uses the physical coordinates of the original radar observation points as network input, and utilizes a residual fully connected network to establish a continuous mapping from spatial coordinates to the three-dimensional wind field. Training is performed using a loss function that incorporates physical constraints such as mass conservation, smoothness, and boundary conditions. This invention eliminates the need to interpolate radar data to a regular grid, completely avoiding errors introduced by coordinate transformation and grid interpolation, achieving gridless three-dimensional wind field inversion, and significantly improving the inversion accuracy of key wind field components such as vertical velocity.

Description

Technical Field

[0001] This invention belongs to the field of meteorological detection technology, specifically relating to a method for inverting three-dimensional wind fields using observation data from two or more Doppler weather radars, and particularly relating to a dual-radar or multi-radar wind field inversion method based on physical information neural networks. Background Technology

[0002] Three-dimensional wind fields are an irreplaceable core variable for understanding weather dynamics. Doppler weather radar is currently the only detection method capable of acquiring large-scale wind field information. However, Doppler weather radar can only measure the radial velocity component V along the radar beam direction. r This refers to the projection of the true three-dimensional wind vector onto the radar beam direction. This physical nature determines that a single radar cannot directly provide tangential wind information perpendicular to the beam, nor can it directly obtain vertical motion (unless in a special observation mode that is almost vertically oriented).

[0003] Compared to a single radar, two Doppler radars measure the radial velocity of the same precipitation volume from two different perspectives, creating a geometric constraint—when the cross beam angle (CBA) of the two radars is close to 90°, the information of the two independent components of the wind vector is most complete, achieving a geometrically meaningful three-dimensional wind field inversion. The classic dual-Doppler synthesis method directly solves for the horizontal wind component in the coplanar coordinate system of the two radars using the geometric relationship between the two radial velocities, and then obtains the vertical velocity through explicit integration from bottom to top (or top to bottom) using the mass continuity equation. The advantages of this type of method are its physical intuitiveness and computational efficiency. However, explicit vertical integration leads to error accumulation, and the arbitrariness of the lower boundary conditions, noise amplification on the integration path, and integration divergence caused by the sparsity of high-level data are inherent serious drawbacks.

[0004] In response, some scholars have proposed a dual-Doppler analysis framework based on three-dimensional variational (3DVAR): while minimizing the fitting residuals of radial velocity observations, mass continuity equations and spatial smoothness are used as weak constraints. This avoids explicit vertical integration, eliminating the problem of error accumulation; it employs inverse interpolation (from analysis grid points to observation points) to keep the original observations free from interpolation error contamination; and it uses the L-BFGS quasi-Newton method for efficient solution. Other scholars have added a viscoelastic vertical vorticity equation as a weak constraint to the 3DVAR framework. The vorticity equation couples the horizontal wind field with vertical motion through stretching / torsion terms. Even in areas less than 1.5 km from the ground where there is no dual-Doppler observation data coverage, the information from the horizontal wind field still indirectly constrains the vertical velocity through dynamic constraints, significantly improving the inversion accuracy of the vertical velocity. However, the introduction of vertical vorticity also makes the inversion method more dependent on the temporal consistency of observations at each grid point.

[0005] The 3D variational dual-Doppler analysis framework is currently the best method for obtaining 3D wind fields under existing technological conditions. However, due to the inherent limitations of the method's gridding, a conversion between regular Cartesian coordinates and radar coordinates is required, introducing errors. Although the 3D variational method itself can preserve the original observations, iterative optimization still requires interpolation from the analysis grid to the observation points; moreover, in densely observed regions, the interpolated information for different observation points comes from the same analysis grid, which is particularly significant when the analysis grid resolution differs greatly from the radar resolution. Furthermore, the need for interpolation at each step during optimization also impacts computational efficiency to some extent. Therefore, in practice, another approach is often adopted: pre-interpolating radar data to the analysis grid, such as the commonly used 3D variational dual-Doppler analysis module PyDDA. The problem is that different interpolation methods will affect the inversion results; a larger interpolation radius results in a smoother gridded radial velocity, but at the same time, smaller-scale information is lost. Summary of the Invention

[0006] The present invention aims to at least partially solve one of the technical problems existing in the related art.

[0007] The purpose of this invention is to provide a dual-radar or multi-radar wind field inversion method based on physical information neural networks, so as to solve the coordinate transformation and grid interpolation problems caused by the difference between radar observation spherical coordinates and three-dimensional Cartesian coordinates in the prior art, and realize the direct use of the original radar radial velocity observations without interpolation to perform three-dimensional wind field inversion.

[0008] To achieve the above objectives, the present invention provides a dual-radar or multi-radar wind field inversion method based on a physical information neural network, comprising the following steps:

[0009] S1. Perform quality control on the radial velocity observation data from the Doppler weather radar, and then calculate the three-dimensional wind field components based on the radar coordinates. Projection coefficients projected to each observation point ; Retain observation points with valid radial velocity data and merge radial velocity data from all radars. Information for each observation point includes its physical coordinates. radial velocity and projection coefficient ;

[0010] S2. Construct a RadarWindNet neural network based on a residual fully connected network structure, assuming the normalized spatial coordinates are... The network parameters are A continuous wind field mapping is defined as follows: ;

[0011] in, Coordinates The normalization result, It is a residual fully connected network;

[0012] The RadarWindNet neural network is used to establish a continuous mapping from spatial coordinates to three-dimensional wind fields;

[0013] S3. Define the total loss function as the observation loss. divergence constraint Smoothness constraints Lower boundary conditions and lateral boundary conditions The five-item weighted composition is represented as follows: ; in, , , , and All are weighting coefficients;

[0014] S4. Train the constructed RadarWindNet neural network using the observation data obtained in step S1, and calculate the individual losses and total loss according to the loss functions in step S3; after the network converges, a three-dimensional wind field analysis model is obtained. ;

[0015] S5. After training, the three-dimensional wind field analysis model A continuous mapping from normalized spatial coordinates to three-dimensional wind field was established. For any target grid point or any spatial location, its physical coordinates were determined. Linear transformation to Interval; calling the three-dimensional wind field analysis model Analyze the wind field .

[0016] A further preferred technical solution of the present invention is that, in step S1, the radial velocity observation data of the Doppler weather radar is subjected to quality control, mainly by velocity deblurring.

[0017] Preferably, the RadarWindNet neural network constructed in step S2 includes an input layer, a projection layer, and One residual block and output layer;

[0018] The input layer receives three-dimensional spatial coordinates, with a dimension of 3, represented as: ; The projection layer is a fully connected layer that projects the input to... Dimension, represented as: , , ;

[0019] in, These are the weighting coefficients. These are bias parameters;

[0020] The residual block is represented as: , ;

[0021] in, , ;

[0022] The output layer maps the output of the last residual block to the three-dimensional wind field components, as follows: , ;

[0023] In this RadarWindNet neural network, the activation function Network parameters It includes all weights and biases. The weights are initialized using the Kaiming normal distribution, and the initial bias is 0.

[0024] Preferably, in each loss function of the total loss function defined in step S3, the observation loss... Specifically:

[0025] For each radar radial observation point Its spatial physical coordinates are Normalized coordinates are Radial velocity observation value The corresponding radar location is Projection coefficient The radial velocity predicted by the network is: ;

[0026] The observation loss is all The mean square error of each observation point is expressed as: ;

[0027] The divergence constraint is specifically as follows:

[0028] Under the incompressible approximation, the three-dimensional wind field satisfies Since the network input is normalized coordinates, the physical divergence is calculated using the chain rule and is expressed as: ;

[0029] The partial derivatives are obtained by automatic differentiation;

[0030] Random sampling within the computational domain sampling points Calculate the divergence loss: ;

[0031] The smoothness constraint is specifically as follows:

[0032] A second derivative penalty is applied to each component of the wind field, uniformly using the Laplace operator, expressed as: ;

[0033] in, The total number of sampling points; Laplace operator Defined as: ;

[0034] The lower boundary condition is specifically as follows:

[0035] The lower boundary adopts a non-penetrating boundary condition, i.e., vertical velocity. Sampling at the bottom surface Points The lower boundary condition is expressed as: ;

[0036] The specific side boundary conditions are as follows:

[0037] The lateral boundaries employ Neumann boundary conditions, meaning the normal derivative is zero, and sampling is performed on all four sides. For each point, calculate the sum of squares of the normal derivatives, and use it as the lateral boundary condition: ;

[0038] The normal derivative is obtained by multiplying the directional derivative in normalized coordinates by the corresponding scale factor.

[0039] Preferably, in step S4, when training the constructed RadarWindNet neural network, a fixed number of internal points are randomly generated in each epoch for calculating divergence constraints and smoothness constraints. Both divergence constraints and smoothness constraints are obtained using automatic differentiation. Random sampling is performed on the bottom surface and the four sides for lower boundary conditions and side boundary conditions.

[0040] Preferably, when training the constructed RadarWindNet neural network in step S4, the Adam optimizer is used for learning, with a learning rate of [missing information]. During training, each epoch uses either all observation points or random subsampled data.

[0041] Preferably, in step S1, the three-dimensional wind field components are calculated based on the radar coordinates. Projection coefficients projected to each observation point Specifically:

[0042] For radar location and observation points The slope distance is calculated as follows: ;

[0043] The projection coefficient is defined as: ;

[0044] The method for spatial coordinate normalization in step S2 is as follows:

[0045] First, set the physical coordinates Normalized to a unit cube ,make: ;

[0046] in , , The domain size is defined in each direction.

[0047] In another aspect, the present invention provides a non-transitory computer-readable storage medium having computer instructions stored thereon, which cause a computer to execute the above-described dual-radar or multi-radar wind field inversion method based on a physical information neural network.

[0048] In another aspect, the present invention provides an electronic device, comprising: a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus, and the processor calls logical instructions in the memory to execute the above-mentioned dual-radar or multi-radar wind field inversion method based on physical information neural network.

[0049] In another aspect, the present invention provides a computer program product, the computer program product comprising a computer program stored on a non-transitory computer-readable storage medium, wherein when the computer program is executed by a processor, the computer executes the above-described dual-radar or multi-radar wind field inversion method based on a physical information neural network.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] (1) Existing 3DVar methods must be solved on a regular Cartesian grid, requiring multiple transformations and interpolations between radar spherical coordinates and Cartesian coordinates. This invention utilizes the continuous function approximation capability of physical information neural networks, directly using the physical coordinates of the original radar observation point as network input, and outputting the three-dimensional wind field components of that point. It completely eliminates the need to interpolate the data to any regular grid, fundamentally eliminating the errors introduced by coordinate transformation and grid interpolation.

[0052] (2) Existing 3DVar methods require back-interpolation from the analysis grid to the observation points to calculate the residuals during the optimization process. When multiple observation points in a densely observed region are mapped to the same analysis grid, the independent information of each observation point is confused. This invention directly calculates the radial velocity prediction value of each observation point on the network output, and each observation point contributes to the loss independently, thus maintaining the independence of the observation information.

[0053] (3) The analysis resolution of the existing 3DVar method is fixed before the solution is obtained, and the solution needs to be re-solved if the resolution is changed. After the network training of the present invention is completed, inference can be performed on any coordinate point, and the output mesh of arbitrary shape and resolution can be generated to flexibly adapt to different application requirements (such as high-resolution convection region analysis and low-resolution background field construction) without increasing the amount of computation.

[0054] (4) Existing methods need to consider the cross beam angle optimization of different radars. This invention merges the radial velocity data of multiple radars and each observation point carries its corresponding projection coefficient. It is input into the network as a unified training dataset. The network automatically learns the optimal fusion of multi-view geometric constraints without manual intervention.

[0055] (5) By embedding physical priors such as mass continuity equation (divergence constraint) and boundary conditions into the loss function, the network naturally satisfies these physical constraints after training, without the need for additional post-processing or constraint solving steps. Attached Figure Description

[0056] Figure 1 This is a flowchart of the dual-radar or multi-radar wind field inversion method based on physical information neural network of the present invention;

[0057] Figure 2 This is a comparison chart of the true vertical velocity value, the RadarWindNet inversion value, and the inversion value obtained by the three-dimensional variational method in Example 1;

[0058] Figure 3 This is the error vertical profile diagram of the three wind field components u, v, and w in Example 1. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, embodiments of this invention, and should not be construed as limiting the invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention. In the description of this invention, it should be understood that the terminology used is for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0060] The following is combined Figures 1-3 This invention describes a dual-radar or multi-radar wind field inversion method based on a physical information neural network.

[0061] Example 1: This example provides a dual-radar or multi-radar wind field inversion method based on physical information neural network. Based on the radial velocity observed by two or more Doppler radars, a three-dimensional wind field inversion is performed through physical information neural network (PINN). Taking advantage of its characteristics of not requiring grid discretization and being able to flexibly integrate physical priors and observations, it is possible to directly use the original radar radial velocity observations without interpolation. At the same time, the wind field does not need to be interpolated to the radar observation points during the training process, thus completely avoiding the error problem introduced by coordinate transformation.

[0062] like Figure 1 As shown, the method includes the following steps:

[0063] S1. Data preprocessing.

[0064] First, quality control was performed on the radial velocity observation data from the Doppler weather radar, primarily through velocity deblurring. Then, the three-dimensional wind field components were calculated based on the radar coordinates. Projection coefficients projected to each observation point The specific method is:

[0065] Specifically, regarding radar location and observation points The slant distance is: ;

[0066] The projection coefficient is defined as: ;

[0067] Normalized coordinates and projection coefficients for each observation point are pre-calculated and stored to avoid redundant calculations of geometric quantities during training. Finally, only observation points with valid radial velocity data are retained, and the radial velocity data from all radars are merged. Information for each observation point includes coordinates. radial velocity and projection coefficient .

[0068] S2. Construct a physical information neural network.

[0069] A RadarWindNet neural network based on a residual fully connected network structure is constructed, and this RadarWindNet neural network is used to establish a continuous mapping from spatial coordinates to three-dimensional wind fields.

[0070] First, set the physical coordinates Normalized to a unit cube ,make: ;

[0071] in , , The domain size is defined in each direction.

[0072] Let the normalized spatial coordinates be The network parameters are A continuous wind field mapping is defined as follows: ;

[0073] in, It is a residual fully connected network, including an input layer, a projection layer, and One residual block and output layer;

[0074] The input layer receives three-dimensional spatial coordinates, with a dimension of 3, represented as: ;

[0075] The projection layer is a fully connected layer that projects the input to... Dimension, represented as: , , ;

[0076] in, These are the weighting coefficients. These are bias parameters;

[0077] The residual block is represented as: , ;

[0078] in, , ;

[0079] The output layer maps the output of the last residual block to the three-dimensional wind field components, as follows: , ;

[0080] In this RadarWindNet neural network, the activation function Network parameters It includes all weights and biases. The weights are initialized using the Kaiming normal distribution, and the initial bias is 0.

[0081] S3. Construct the loss function.

[0082] The total loss function is defined by the observation loss. divergence constraint Smoothness constraints Lower boundary conditions and lateral boundary conditions The five-item weighted composition is represented as follows: ;

[0083] in, , , , and These are all weighting coefficients. For reference, a typical value could be set to... , , , , Specifically, adjustments can be made by monitoring the magnitude of various losses.

[0084] (1) Observation loss :

[0085] For each radar radial observation point Its spatial physical coordinates are Normalized coordinates are Radial velocity observation value The corresponding radar location is Projection coefficient The radial velocity predicted by the network, calculated according to the formula in step S1, is: ;

[0086] The observation loss is all The mean square error of each observation point is expressed as: ;

[0087] Normalized coordinates and projection coefficients are pre-calculated and stored, and can be directly read during training to avoid repeated calculation of geometric quantities.

[0088] (2) Conservation of mass (divergence constraint):

[0089] Under the incompressible (Boussinesq) approximation, the three-dimensional wind field satisfies Since the network input is normalized coordinates, the physical divergence is calculated using the chain rule and is expressed as: ;

[0090] The partial derivatives are obtained by automatic differentiation;

[0091] Random sampling within the computational domain sampling points Calculate the divergence loss: ;

[0092] (3) Smoothness constraint:

[0093] A second derivative penalty is applied to each component of the wind field, uniformly using the Laplace operator, expressed as: ;

[0094] in, The total number of sampling points; Laplace operator Defined as: ;

[0095] If normalized coordinates are used, the second derivative needs to be multiplied by the square of the corresponding scale factor. However, this formula can be calculated directly in normalized coordinates with the same physical meaning. Alternatively, the horizontal and vertical directions can be weighted independently to adjust for the vertical shear characteristics of convective storms.

[0096] (4) Lower boundary conditions:

[0097] lower boundary ( (Or terrain surface) adopts non-penetrating boundary conditions, i.e., vertical velocity Sampling at the bottom surface Points The lower boundary condition is expressed as: ;

[0098] For complex terrain, the condition can be changed to zero normal velocity.

[0099] (5) Lateral boundary conditions:

[0100] Side boundary ( The Neumann boundary condition is used, i.e., the normal derivative is zero. (No side boundary constraints are applied to the vertical component w), sampling is performed on all four sides. For each point, calculate the sum of squares of the normal derivatives, and use it as the lateral boundary condition: ;

[0101] The normal derivative is obtained by multiplying the directional derivative in normalized coordinates by the corresponding scale factor.

[0102] S4, Network Training.

[0103] The Adam optimizer is used for learning, with a learning rate of [missing information]. The processing method for each epoch during training is as follows:

[0104] (1) Use of observation data: All observation points can be used, or random subsampling (e.g., taking 20% ​​each time) can be used to improve training speed.

[0105] (2) Internal point generation: A fixed number of internal points (e.g., 50,000) are randomly generated in each epoch for the calculation of divergence constraints and smoothness constraints;

[0106] (3) Boundary point generation: Random sampling is performed on the bottom surface and four sides for boundary condition constraints;

[0107] (4) Forward propagation: Input the above sampling points into the RadarWindNet neural network to obtain the predicted wind field;

[0108] (5) Loss calculation: Calculate the various losses and the total loss according to the formula in step S3;

[0109] (6) Backpropagation: Calculate the total loss for network parameters using automatic differentiation. The gradient;

[0110] (7) Parameter update: The Adam optimizer updates the network parameters based on the gradient.

[0111] Repeat the above process until the network converges to obtain the three-dimensional wind field analysis model. .

[0112] S5, 3D wind field prediction and output.

[0113] After training, the three-dimensional wind field analysis model A continuous mapping from normalized spatial coordinates to a three-dimensional wind field was established. For any target grid point or any spatial location, its physical coordinates were determined. Linear transformation according to the formula in step S2 to Interval; calling the three-dimensional wind field analysis model Analyze the wind field .

[0114] Because the model is continuous and has a meshless property, it can output analysis meshes of arbitrary shapes (such as regular meshes, unstructured meshes, etc.) and arbitrary spatial resolutions without increasing the amount of computation or requiring retraining.

[0115] To verify the accuracy of this method, an ideal flow field with true values ​​was used in the experiment. The radial velocities of the two radars were obtained from three-dimensional Beltrami flow analytical data sampled by two virtual Doppler radars. Beltrami flow is an exact solution of the incompressible Navier-Stokes equations, where the vorticity field is aligned with the velocity field. This flow field is characterized by a set of spatially periodic, time-decaying alternating rotating updrafts and downdrafts.

[0116] Figure 2 The comparison shows the true value of vertical velocity, the inverted value from RadarWindNet, and the inverted value from the 3D variational method. It is clear that RadarWindNet accurately inverts the magnitude and distribution of the vertical velocity, including its wavenumber 2 wave structure (represented as positive and negative velocity pairs in the X and Y directions). In contrast, the 3D variational method fails to describe the intensity and wave characteristics of the airflow.

[0117] Figure 3 The vertical error profiles for the three wind field components (u, v, and w) are shown. It is evident that the inversion error increases significantly above 6 km, primarily due to the sparser radar elevation at higher altitudes, leading to reduced effective observations at those levels. For the u and v components, the accuracy of RadarWindNet and 3DVar inversions is similar, with root mean square errors of 2.0 m / s and 2.1 m / s, respectively. The vertical velocity error of RadarWindNet inversion is significantly lower than that of 3DVar inversion, with root mean square errors of 1.4 m / s and 5.3 m / s, respectively.

[0118] Overall, RadarWindNet can effectively invert 3D wind fields, reproducing wind speed, flow field structure (convergence / divergence, vortices, etc.), and wave characteristics. Compared with 3D variational methods, RadarWindNet performs better in inverting vertical velocity and its wave characteristics.

[0119] Example 2: This example provides a non-transitory computer-readable storage medium storing computer instructions that cause a computer to execute a dual-radar or multi-radar wind field inversion method based on a physical information neural network. The method includes the following steps:

[0120] S1. Perform quality control on the radial velocity observation data from the Doppler weather radar, and then calculate the three-dimensional wind field components based on the radar coordinates. Projection coefficients projected to each observation point ; Retain observation points with valid radial velocity data and merge radial velocity data from all radars. Information for each observation point includes coordinates. radial velocity and projection coefficient ;

[0121] S2. Construct a RadarWindNet neural network based on a residual fully connected network structure, assuming the normalized spatial coordinates are... The network parameters are A continuous wind field mapping is defined as follows:

[0122] ;

[0123] in, It is a residual fully connected network;

[0124] The RadarWindNet neural network is used to establish a continuous mapping from spatial coordinates to three-dimensional wind fields;

[0125] S3. Define the total loss function as the observation loss. divergence constraint Smoothness constraints Lower boundary conditions and lateral boundary conditions The five-item weighted composition is represented as follows: ;

[0126] in, , , , and All are weighting coefficients;

[0127] S4. Train the constructed RadarWindNet neural network using the observation data obtained in step S1, and calculate the individual losses and total loss according to the loss functions in step S3; after the network converges, a three-dimensional wind field analysis model is obtained. ;

[0128] S5. After training, the three-dimensional wind field analysis model A continuous mapping from spatial coordinates to a three-dimensional wind field was established. For any target mesh, the physical coordinates of the target mesh were mapped. Linear transformation to Interval; calling the three-dimensional wind field analysis model Analyze the wind field .

[0129] Example 3: This example provides an electronic device that may include a processor, a communication interface, a memory, and a communication bus. The processor, communication interface, and memory communicate with each other via the communication bus. The processor can call logical instructions from the memory to execute a dual-radar or multi-radar wind field inversion method based on a physical information neural network. This method includes the following steps:

[0130] S1. Perform quality control on the radial velocity observation data from the Doppler weather radar, and then calculate the three-dimensional wind field components based on the radar coordinates. Projection coefficients projected to each observation point ; Retain observation points with valid radial velocity data and merge radial velocity data from all radars. Information for each observation point includes coordinates. radial velocity and projection coefficient ;

[0131] S2. Construct a RadarWindNet neural network based on a residual fully connected network structure, assuming the normalized spatial coordinates are... The network parameters are A continuous wind field mapping is defined as follows:

[0132] ;

[0133] in, It is a residual fully connected network;

[0134] The RadarWindNet neural network is used to establish a continuous mapping from spatial coordinates to three-dimensional wind fields;

[0135] S3. Define the total loss function as the observation loss. divergence constraint Smoothness constraints Lower boundary conditions and lateral boundary conditions The five-item weighted composition is represented as follows: ;

[0136] in, , , , and All are weighting coefficients;

[0137] S4. Train the constructed RadarWindNet neural network using the observation data obtained in step S1, and calculate the individual losses and total loss according to the loss functions in step S3; after the network converges, a three-dimensional wind field analysis model is obtained. ;

[0138] S5. After training, the three-dimensional wind field analysis model A continuous mapping from spatial coordinates to a three-dimensional wind field was established. For any target mesh, the physical coordinates of the target mesh were mapped. Linear transformation to Interval; calling the three-dimensional wind field analysis model Analyze the wind field .

[0139] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0140] Example 4: This example provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute a dual-radar or multi-radar wind field inversion method based on a physical information neural network. The method includes the following steps:

[0141] S1. Perform quality control on the radial velocity observation data from the Doppler weather radar, and then calculate the three-dimensional wind field components based on the radar coordinates. Projection coefficients projected to each observation point ; Retain observation points with valid radial velocity data and merge radial velocity data from all radars. Information for each observation point includes coordinates. radial velocity and projection coefficient ;

[0142] S2. Construct a RadarWindNet neural network based on a residual fully connected network structure, assuming the normalized spatial coordinates are... The network parameters are A continuous wind field mapping is defined as follows:

[0143] ;

[0144] in, It is a residual fully connected network;

[0145] The RadarWindNet neural network is used to establish a continuous mapping from spatial coordinates to three-dimensional wind fields;

[0146] S3. Define the total loss function as the observation loss. divergence constraint Smoothness constraints Lower boundary conditions and lateral boundary conditions The five-item weighted composition is represented as follows: ;

[0147] in, , , , and These are all weighting coefficients; for reference, typical values ​​can be set to... , , , , Specifically, adjustments can be made by monitoring the magnitude of various losses.

[0148] S4. Train the constructed RadarWindNet neural network using the observation data obtained in step S1, and calculate the individual losses and total loss according to the loss functions in step S3; after the network converges, a three-dimensional wind field analysis model is obtained. ;

[0149] S5. After training, the three-dimensional wind field analysis model A continuous mapping from spatial coordinates to a three-dimensional wind field was established. For any target mesh, the physical coordinates of the target mesh were mapped. Linear transformation to Interval; calling the three-dimensional wind field analysis model Analyze the wind field .

[0150] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0151] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0152] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for wind field inversion based on a physical information neural network using dual-radar or multi-radar sensors, characterized in that, Includes the following steps: S1. Perform quality control on the radial velocity observation data from the Doppler weather radar, and then calculate the three-dimensional wind field components based on the radar coordinates. Projection coefficients projected to each observation point ; Retain observation points with valid radial velocity data and merge radial velocity data from all radars. Information for each observation point includes its physical coordinates. radial velocity and projection coefficient ; S2. Construct a RadarWindNet neural network based on a residual fully connected network structure, assuming the normalized spatial coordinates are... The network parameters are A continuous wind field mapping is defined as follows: ； in, These are the coordinate values. The normalization result, It is a residual fully connected network; The RadarWindNet neural network is used to establish a continuous mapping from spatial coordinates to three-dimensional wind fields; S3. Define the total loss function as the observation loss. divergence constraint Smoothness constraints Lower boundary conditions and lateral boundary conditions The five-item weighted composition is represented as follows: ； in, , , , and All are weighting coefficients; S4. Train the constructed RadarWindNet neural network using the observation data obtained in step S1, and calculate the individual losses and total loss according to the loss functions in step S3; after the network converges, a three-dimensional wind field analysis model is obtained. ; S5. After training, the three-dimensional wind field analysis model A continuous mapping from normalized spatial coordinates to three-dimensional wind field was established. For any target grid point or any spatial location, its physical coordinates were determined. Linear transformation to Interval; calling the three-dimensional wind field analysis model Analyze the wind field .

2. The dual-radar or multi-radar wind field inversion method based on physical information neural network according to claim 1, characterized in that, In step S1, the radial velocity observation data from the Doppler weather radar is subjected to quality control, mainly by deblurring the velocity.

3. The dual-radar or multi-radar wind field inversion method based on physical information neural networks according to claim 1, characterized in that, The RadarWindNet neural network constructed in step S2 includes an input layer, a projection layer, and One residual block and output layer; The input layer receives three-dimensional spatial coordinates, with a dimension of 3, represented as: ； The projection layer is a fully connected layer that projects the input to... Dimension, represented as: ， ， ； in, These are the weighting coefficients. These are bias parameters; The residual block is represented as: ， ； in, , ; The output layer maps the output of the last residual block to the three-dimensional wind field components, as follows: ， ； In this RadarWindNet neural network, the activation function Network parameters It includes all weights and biases. The weights are initialized using the Kaiming normal distribution, and the initial bias is 0.

4. The physical information neural network based dual-radar or multi-radar wind field retrieval method according to claim 1, characterized in that, In the total loss function defined in step S3, the observation loss is... Specifically: For each radar radial observation point Its spatial physical coordinates are Normalized coordinates are Radial velocity observation value The corresponding radar location is Projection coefficient The radial velocity predicted by the network is: ； The observation loss is all The mean square error of each observation point is expressed as: ； The divergence constraint is specifically as follows: Under the incompressible approximation, the three-dimensional wind field satisfies Since the network input is normalized coordinates, the physical divergence is calculated by the chain rule and expressed as: ； The partial derivatives are obtained by automatic differentiation; Randomly sampling within the computational domain points , computing divergence loss: ； The smoothness constraint is specifically as follows: A second derivative penalty is applied to each component of the wind field, uniformly using the Laplace operator, expressed as: ； wherein is the total number of sampling points; Laplacian operator is defined as: ； The lower boundary condition is specifically as follows: The lower boundary uses a non-penetrating boundary condition, i.e. the vertical velocity At the bottom surface one point The lower boundary condition is expressed as: ； The specific side boundary conditions are as follows: The lateral boundaries employ Neumann boundary conditions, meaning the normal derivative is zero, and sampling is performed on all four sides. For each point, calculate the sum of squares of the normal derivatives, and use it as the lateral boundary condition: ； The normal derivative is obtained by multiplying the directional derivative in normalized coordinates by the corresponding scale factor.

5. The dual-radar or multi-radar wind field inversion method based on physical information neural network according to claim 4, characterized in that, In step S4, when training the constructed RadarWindNet neural network, a fixed number of internal points are randomly generated in each epoch for calculating divergence constraints and smoothness constraints. Both divergence constraints and smoothness constraints are obtained using automatic differentiation. Random sampling is performed on the bottom surface and the four sides for lower boundary conditions and side boundary conditions.

6. The physical information neural network based dual-radar or multi-radar wind field retrieval method according to claim 5, characterized in that, In step S4, the constructed RadarWindNet neural network is trained, using an Adam optimizer for learning with a learning rate of ; and all observation points or randomly subsampled points are used for each epoch during the training process.

7. The physical information neural network based dual-radar or multi-radar wind field retrieval method according to claim 1, characterized in that, Step S1 calculating three-dimensional wind field components from radar coordinates Projection coefficients to project to each observation point Specifically: For radar position and observation point , the slant range is calculated as: ； The projection coefficient is defined as: ； The method for spatial coordinate normalization in step S2 is as follows: First, the physical coordinates are normalized to the unit cube , letting: ； wherein , , is the domain size in each direction.

8. A non-transitory computer-readable storage medium, comprising: It stores computer instructions that cause the computer to execute the dual-radar or multi-radar wind field inversion method based on physical information neural network as described in any one of claims 1-7.

9. An electronic device, comprising: include: The system includes a processor, a communication interface, a memory, and a communication bus. The processor, communication interface, and memory communicate with each other via the communication bus. The processor calls logical instructions from the memory to execute the dual-radar or multi-radar wind field inversion method based on physical information neural networks as described in any one of claims 1-7.

10. A computer program product, characterized in that, The computer program product includes a computer program stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer performs the dual-radar or multi-radar wind field inversion method based on physical information neural networks as described in any one of claims 1-7.

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