A Design Method for Implementing Antenna Radiation Patterns Based on Physics-Informed Neural Networks

Abstract

The present invention discloses a design method for realizing an antenna pattern based on a physics-informed neural network, belonging to the technical field of communication antennas. The method of the present invention includes the following steps: Initial customization: Set the overall two-dimensional model, and determine the corresponding far-field expected total field according to the set performance indicators; PINN architecture: Construct the PINN according to the initial defined values and the expected target; Pre-training: Obtain the initial weights of the PINN according to the initial electromagnetic information; Formal training: Add the integral equation and the Helmholtz equation of the electromagnetic inverse scattering method as physical information constraints to the PINN, and judge whether the obtained solution meets the expectation. Otherwise, execute the training process again until it meets the requirements. The method of the present invention does not rely on a large amount of training set data required by existing neural networks, and has higher efficiency; it is more flexible and has higher applicability compared with existing design methods.

Description

Technical Field

[0001] The present invention belongs to the technical field of communication antennas, and particularly relates to a design method for realizing an antenna pattern based on a physics-informed neural network. Background Art

[0002] Radiation patterns with different beam shapes, such as pencil beam, multi-beam, flat-top beam, etc., play important roles in communication fields such as radar, satellite, base station, etc., and are one of the most important objectives in antenna design. The above radiation patterns with different beam shapes can be realized by using intelligent optimization algorithms or array synthesis methods. Intelligent optimization algorithms represented by genetic algorithms and particle swarm algorithms have been fully applied in narrow beam shaping. For classical array synthesis methods, the Cheyshev method can be applied to narrow beam shaping, and the Fourier series method and Woodward-Layson method can be applied to flat-top beam shaping. However, the above methods all belong to the forward design methods for designing radiation targets by controlling the spacing, excitation, element structure, arrangement mode, etc. of the antenna array, and use the radiation target as a judgment condition to judge the quality of the design. However, there are also great disadvantages in this existing forward design method. Usually, starting from existing knowledge or experience according to a given target, engineers need to have a certain accumulation of knowledge and experience. Moreover, full-wave simulation for antenna parameter adjustment and optimization often takes a long time and sometimes fails to achieve the expected effect.

[0003] In recent years, the design method based on neural network is considered to be an efficient and fast design method. Once the training process is completed, a well-trained neural network can replace the time-consuming electromagnetic field structure simulation and significantly accelerate the design process. The prior art "Generative model for the inverse design of metasurfaces" applies the trained neural network to the inverse design problem of nano-photonic structures. The prior art "Parametric modeling of EM behavior of microwave components using combined neural networks and pole-residue-based transfer functions" discloses a method for parametric modeling of microwave components using neural networks and outputs the S parameters of the device.

[0004] However, the above design method based on the existing neural network also has obvious defects, mainly including the following two points: First, since the design method based on the existing neural network requires a large amount of accurate training data sets to be obtained in advance, the time cost is relatively high. Second, the design method based on the existing neural network does not have sufficient generalization ability, because the existing neural network does not contain any physical information, and the previously obtained training data sets only correspond to specific problems, lacking universality. Summary of the Invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned existing technologies, and provide a design method for realizing the antenna pattern based on the physics-informed neural network, introducing a neural network architecture containing physical information and applying it to the design process of the upper cladding of the antenna.

[0006] The technical problem proposed by the present invention is solved as follows:

[0007] A design method for realizing the antenna pattern based on the physics-informed neural network includes the following steps:

[0008] S1. Initial customization

[0009] Set the overall two-dimensional model, where the radiating antenna is a line current source, placed on a finite-size ground with a length of L, and the position is S; at a height h from the ground, a scatterer region with a length of l and a width of w is established, and the position is denoted as S', and the scatterer position S' is evenly divided into several grids to obtain several scatterer source points r′, and the two-dimensional coordinates of the grid points are denoted as (x′, y′); at a distance |r far |, antenna far-field sampling points are evenly established, and at the same time, the antenna far-field incident field at the far-field sampling points is determined Determine the corresponding expected total far-field of the antenna according to the expected antenna performance index

[0010] S2. Physics-informed neural network PINN architecture process

[0011] Set PINN to a two-input and three-output structure, with eight fully connected hidden layers, and 128 neurons in each layer; the two-channel input is the two-dimensional coordinates (x′, y′) of the scatterer grid, and the three-channel output is the corresponding real and imaginary part distributions and the dielectric constant ε r (x′, y′) distribution;

[0012] S3. Pretraining process

[0013] First, let the scatterer position S' be free space to obtain the free space dielectric constant distribution function Based on Obtain the updated scatterer source point r′ to the antenna far-field point rfar Background Green's function r far = |r far |e j θ ; According to the free space permittivity distribution function and the background Green's function from the updated scatterer source point r' to the far-field point calculate the total field inside the scatterer position S' Take the two-dimensional coordinates (x′, y′) as the input of the PINN, and the total field inside the free space S' and the permittivity distribution function as the output indicators of the PINN to pre-train the PINN, and save the weights τ of each neuron in the PINN after the pre-training is completed;

[0014] S4. Formal training process

[0015] Take the Helmholtz equation and the integral equation of the electromagnetic inverse scattering method as physical information constraints and add them to the PINN loaded with the weight τ; input the two-dimensional coordinates (x′, y′) into the current PINN for formal training; the current PINN outputs the total field inside the scatterer position S' and the permittivity distribution function ε r (x′, y′); Substitute the output of the current PINN into the Helmholtz equation and use the loss function to calculate the difference Loss between both sides of the equation h ; Calculate the current far-field total field using the integral equation of the electromagnetic inverse scattering method Use the loss function to calculate the difference Loss between the current far-field total field and the expected far-field total field e ;

[0016] Calculate the weighted total value Loss of the difference:

[0017] Loss = Loss e + α·Loss h

[0018] where α is the weight of Loss h ;

[0019] Judge whether the weighted total value Loss is less than the set threshold. If so, determine that the permittivity distribution function ε r (x′, y′) output by the current PINN is the desired solution, and the corresponding structure is used as the structure of the scatterer position S'; if not, use the weighted total value Loss to update the weights τ of each neuron in the current PINN and re-execute the formal training process.

[0020] Furthermore, in step S1, the grid size is λ / 20 to λ / 10.

[0021] Furthermore, in step S1, the incident field in the far zone of the antenna is determined according to the position S of the radiating antenna The specific process is as follows:

[0022] Manually determine the position S of the line current source and the distribution function of the free space permittivity The total field in the near field is obtained by the finite-difference time-domain method, and then the incident field in the far zone in the direction of the angle θ is obtained by the near-to-far field transformation method

[0023] Furthermore, in step S1, the expected total field in the far zone is determined according to the set performance index The specific process is as follows:

[0024] S1.1. Manually set the directivity coefficient D des (θ), where the angle θ ∈ [0, 2π), and the electric field strength of the expected total field in the far zone is:

[0025]

[0026] where P r is the radiation power of the antenna, and η0 is the wave impedance in free space;

[0027] S1.2. Let the phase of the sampling points in the far zone of the antenna be the same as the phase of the incident field in the far zone of the antenna at the sampling points, and the expected total field in the far zone is:

[0028]

[0029] Furthermore, in step S2, the loss function adopts the mean square error function (MSE Loss), the sin activation function is used, the optimization algorithm is Adam, and the learning rate is 1e -4 .

[0030] Furthermore, in step S3, the formula for updating the background Green's function is:

[0031]

[0032] where is the Laplace operator, k0 is the free space wave number, δ(r far -r′) is the impulse excitation function from the source point r′ of the scatterer to the far field point r far

[0033] Furthermore, in step S4, α = 0.1.

[0034] ​​Further, in step S4, the Helmholtz equation is as follows:

[0035]

[0036] Further, the integral equation of the electromagnetic inverse scattering method is used to calculate the current total far-field The specific process is as follows:

[0037] Based on the total field within the radiation antenna and the scatterer position S' The scatterer position S' and the corresponding dielectric constant distribution function ε r (x′, y′), the total far-field The specific formula is as follows:

[0038]

[0039] where G(r far - r′; ε r ) is the updated background Green's function; represents the contrast within the scatterer position S'.

[0040] The beneficial effects of the present invention are as follows:

[0041] The method of the present invention first introduces a neural network architecture containing physical information and applies it to the design of arbitrary radiation patterns of antennas, and can freely design the required radiation patterns with specific shapes according to the actual working frequency band and application scenarios. Compared with the existing traditional forward design methods, the design method of the present invention uses the design target as a known condition to participate in the design of arbitrary radiation patterns of antennas, does not need to rely on existing prior knowledge and engineering experience, and does not need time-consuming full-wave simulation, with higher efficiency. Compared with the existing neural network-based design methods, the method of the present invention deeply integrates physical information, so it does not need to spend time obtaining a large training data set and training the neural network, and has higher efficiency, greater flexibility, and higher applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is a schematic flow chart of the design method of the present invention;

[0043] Figure 2 is the overall two-dimensional model diagram in the design method of the present invention;

[0044] Figure 3 is the schematic diagram of the PINN structure in the design method of the present invention;

[0045] Figure 4 is the comparison diagram of the expected pattern and the actual pattern of the design method described in the embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0046] The present invention will be further described below in conjunction with the accompanying drawings and embodiments to facilitate the understanding of those skilled in the art of the present technology. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions made using the concept of the present invention are within the scope of protection.

[0047] This embodiment provides a design method for realizing an antenna pattern based on a physics-informed neural network, and its schematic flowchart is as Figure 1 shown, including the following steps:

[0048] S1. Initial customization

[0049] Set the overall two-dimensional model according to the desired target, as Figure 2 shown. Set the radiating antenna as a line current source, placed above a finite-size ground with a length of L, and the position is S; set up a scatterer region with a length of l and a width of w at a height h from the ground, and the position is denoted as S'. Divide the scatterer position S' evenly into several grids, and the grid size is λ / 20 to λ / 10 to obtain several scatterer source points r′, and the two-dimensional coordinates of the grid points are denoted as (x′, y′); set up antenna far-field sampling points evenly at a distance |r far | from the radiating antenna, and at the same time determine the antenna far-field incident field at the far-field sampling points Determine the corresponding antenna far-field expected total field according to the desired antenna performance index

[0050] In step S1, determine the antenna far-field incident field according to the position S of the radiating antenna The specific process is as follows:

[0051] Manually determine the position S of the line current source and the free-space permittivity distribution function Obtain the total field of the near field through the finite-difference time-domain method, and then use the near-to-far field transformation method to obtain the far-field incident field in the direction of the angle θ

[0052] In step S1, determine the corresponding far-field expected total field according to the set performance index The specific process is as follows:

[0053] S1.1. Set the directivity coefficient D des (θ), where the angle θ ∈ [0, 2π), and the electric field strength of the corresponding far-field expected total field is:

[0054]

[0055] Among them, P r is the radiation power of the antenna, and η0 is the wave impedance in free space;

[0056] S1.2. Set the phase of the sampling points in the far field area of the antenna to be the same as the phase of the incident field in the far field of the antenna at the sampling points, and the expected total field in the far field is as follows:

[0057]

[0058] S2. PINN (Physics-Informed Neural Network) architecture process

[0059] As Figure 3 shown, set the structure of PINN to have two inputs and three outputs, with eight fully connected hidden layers, each layer having 128 neurons; the two-channel input is the two-dimensional coordinates (x′, y′) of the scatterer grid, and the three-channel output is the corresponding real and imaginary parts distribution and the dielectric constant ε r (x′, y′) distribution; the loss function uses the mean square error function (MSE Loss), the sin activation function is used, the optimization algorithm is Adam, and the learning rate is 1e -4 .

[0060] S3. Pretraining process

[0061] First, assume that the scatterer position S' is free space, and thus obtain the free space dielectric constant distribution function Based on obtain the updated background Green's function from the scatterer source point r′ to the far field point r of the antenna far as r far = |r far |e jθ ; according to the free space dielectric constant distribution function and the updated background Green's function from the scatterer source point r′ to the far field point, calculate the total field within the scatterer position S' Take the two-dimensional coordinates (x′, y′) as the input of PINN, and the total field within the free space S' and the dielectric constant distribution function as the output indicators of PINN to perform pre-training on PINN, and save the weights τ of each neuron in PINN after the pre-training is completed.

[0062] In step S3, the formula for updating the background Green's function is:

[0063]

[0064] Among them,​ is the Laplace operator, k0 is the free-space wavenumber, and δ(r far - r′) is the impulse excitation function from the source point r′ of the scatterer to the far-field point r far .

[0065] S4. Formal training process

[0066] Take the Helmholtz equation and the integral equation of the electromagnetic inverse scattering method as physical information constraints and add them to the PINN with loaded weight τ; input the two-dimensional coordinates (x′, y′) into the current PINN for formal training; the current PINN outputs the total field and the dielectric constant distribution function ε r (x′, y′) within the scatterer position S'; substitute the output of the current PINN into the Helmholtz equation and use the loss function to calculate the difference Loss h on both sides of the equation; use the integral equation of the electromagnetic inverse scattering method to calculate the current far-field total field Use the loss function to calculate the difference Loss between the current far-field total field and the expected far-field total field e ;

[0067] Calculate the weighted total value Loss of the difference:

[0068] Loss = Loss e + α·Loss h

[0069] where α is the weight of Loss h , and in this embodiment, it is taken as 0.1;

[0070] Judge whether the weighted total value Loss is less than the set threshold. If so, determine that the dielectric constant distribution function ε r (x′, y′) output by the current PINN is the desired solution, and the corresponding structure is used as the structure of the scatterer position S'; if not, update the weights τ of each neuron in the current PINN using the weighted total value Loss and re-execute the formal training process.

[0071] In step S4, the Helmholtz equation is:

[0072]

[0073] Use the integral equation of the electromagnetic inverse scattering method to calculate the current far-field total field The specific process is as follows:

[0074] Based on the radiation antenna, the total field within the scatterer position S' the scatterer position S' and the corresponding dielectric constant distribution function ε r (x′, y′) to obtain the far-field total field The specific formula is as follows:

[0075]

[0076] where G(r far - r′; ε r ) is the updated background Green's function; represents the contrast within the scatterer position S'.

[0077] Figure 4 is a comparison diagram of the expected radiation pattern and the actual radiation pattern. As can be seen from Figure 4 , a good flat-top beam radiation pattern with a small roll-off angle and a low sidelobe level is obtained by the method described in this embodiment.

Claims

1. A design method for implementing an antenna pattern based on a physics-informed neural network, characterized in that, Including the following steps: S1. Initial customization Set up an overall two-dimensional model, where the radiating antenna is a line current source placed above a finite-size ground with a length of L, and the position is S; a scatterer region with a length of l and a width of w is set up at a height h from the ground, and the position is denoted as S'. The scatterer position S' is evenly divided into several grids to obtain several scatterer source points r′, and the two-dimensional coordinates of the grid points are denoted as (x′, y′); antenna far-field sampling points are evenly set up at a distance |r far | from the radiating antenna, and at the same time, the antenna far-field incident field at the far-field region sampling points is determined Determine the corresponding expected total far-field of the antenna according to the expected antenna performance indicators S2. Physical Information Neural Network (PINN) architecture process Set PINN to a two-input and three-output structure, with eight fully connected hidden layers, each layer having 128 neurons; the two-channel input is the two-dimensional coordinates (x′, y′) of the scatterer grid, and the three-channel output is the corresponding real and imaginary parts distribution and dielectric constant ε r (x′, y′) distribution; S3. Pretraining process Let the shilling scatterer position S' be free space to obtain the free space permittivity distribution function Based on Obtain the updated background Green's function from the scatterer source point r′ to the far-field point r of the antenna far ; r far = |r far |e jθ ; According to the free space permittivity distribution function And the updated background Green's function from the scatterer source point r′ to the far-field point, calculate the total field within the scatterer position S' Use the two-dimensional coordinates (x′, y′) as the input of the PINN, and the total field within the free space S' And the permittivity distribution function As the output indicators of the PINN, pre-train the PINN and save the weights τ of each neuron in the PINN after the pre-training is completed;​ S4. Formal training process Taking the Helmholtz equation and the integral equation of the electromagnetic inverse scattering method as physical information constraints, add them to the PINN with the loading weight τ; input the two-dimensional coordinates (x′, y′) into the current PINN for formal training; the current PINN outputs the total field within the scatterer position S'. and the dielectric constant distribution function ε r (x′, y′); substitute the output of the current PINN into the Helmholtz equation and calculate the difference Loss between both sides of the equation using the loss function h ; calculate the current far-field total field using the integral equation of the electromagnetic inverse scattering method Calculate the difference Loss between the current far-field total field and the expected far-field total field using the loss function e ; Calculate the weighted total value of the difference Loss: Loss=Loss e +α·Loss h where α is the weight of Loss h ; Determine whether the weighted total value Loss is less than the set threshold. If so, determine the dielectric constant distribution function ε output by the current PINN r (x′,y′) is the desired solution, and the corresponding structure is used as the structure of the scatterer position S'; if not, update the weights τ of each neuron in the current PINN using the weighted total value Loss, and re-execute the formal training process.

2. The design method for realizing an antenna pattern based on a physics-informed neural network according to claim 1, wherein In step S1, the grid size is λ / 20 to λ / 10, where λ is the antenna operating wavelength.

3. The design method for realizing an antenna pattern based on a physics-informed neural network according to claim 1, wherein In step S1, the incident field in the far zone of the antenna is determined according to the position S of the radiating antenna. The specific process is as follows: Manually determine the position S of the line current source and the free-space permittivity distribution function Obtain the total field in the near field by the finite-difference time-domain method, and then use the near-to-far field transformation method to obtain the far-field incident field in the direction of angle θ 4. The design method for realizing an antenna pattern based on a physics-informed neural network according to claim 1, wherein In step S1, the corresponding far-field expected total field is determined according to the set performance indicators. The specific process is as follows: S1.

1. Manually set the directivity coefficient D des (θ) according to the engineering design requirements, where the angle θ ∈ [0, 2π), and the electric field strength of the expected total far-field is as follows: where P r is the radiation power of the antenna, and η0 is the wave impedance in free space; S1.

2. Set the phase of the sampling points in the far field of the antenna to be the same as the phase of the incident field in the far field of the antenna at the sampling points . The expected total field in the far field is as follows:

5. The design method for realizing an antenna pattern based on a physics-informed neural network according to claim 1, characterized in that In step S2, the loss function uses the mean squared error function (MSE Loss), the sin activation function is used, the optimization algorithm is Adam, and the learning rate is 1e -4 .

6. The design method for realizing an antenna pattern based on a physics-informed neural network according to claim 1, wherein In step S3, the formula for updating the background Green's function is: Among them, is the Laplace operator, k0 is the free-space wavenumber, and δ(r far - r′) is the impulse excitation function from the source point r′ of the scatterer to the far-field point r far .

7. The design method for realizing an antenna pattern based on a physics-informed neural network according to claim 1, wherein In step S4, α = 0.

1.

8. The design method for realizing an antenna radiation pattern based on a physics-informed neural network according to claim 1, wherein In step S4, the Helmholtz equation is as follows: .

9. The design method for implementing an antenna pattern based on a physics-informed neural network according to claim 1, wherein Calculating the current far-field total field by using the integral equation of the electromagnetic inverse scattering method The specific process is as follows: Based on the total field within the radiation antenna and the scatterer position S' Scatterer position S' and the corresponding dielectric constant distribution function ε r (x′, y′) to obtain the total far-field The specific formula is as follows: Among them, G(r far - r′; ε r ) is the updated background Green's function; represents the contrast within the scatterer position S'.

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