CN111444601B - An AI-learning electromagnetic scattering calculation method suitable for any incident field - Google Patents

Abstract

The invention discloses an AI learning type electromagnetic scattering calculation method suitable for any incident field, and belongs to the field of electromagnetic scattering. The invention adopts AI learning network to train the learning contrast

Incident wave

Nonlinear relationship to induced current: sample design: to introduce known information, network input employs

As input, calculating forward current data as a real sample of the AI learning network; network design: the AI learning type network is used as a model to complete the training and prediction process, thereby representing the relationship between the input information, namely the scatterer, the incident field and the induced current. Compared with the invention

And (3) with

As input, the method has wider application range, and under the condition of the same grid division, the method is applied to solve the scattered field, so that the time is faster than that of the traditional algorithm, the precision is improved slightly, and the effectiveness of the method is verified by simulation test.

Description

An AI learning-type electromagnetic scattering calculation method suitable for any incident field

technical field

The invention belongs to the field of electromagnetic scattering, and proposes an AI learning type electromagnetic scattering calculation method suitable for any incident field.

Background technique

It has been more than 100 years since Maxwell's equations were proposed. During this time. Electromagnetic technology and theory are developing rapidly and have been widely used, such as radio communication, radar and antenna, geological survey, biomedical imaging and so on. The propagation of electromagnetic waves in the actual environment is very complicated. Therefore, it is of great significance to study the characteristics of electromagnetic waves. Experiments and theoretical analysis and calculation are important means that complement each other.

In theoretical analysis and calculation, most of the electromagnetic problems can not be solved directly through the analytical form of Maxwell's equations, and can only rely on numerical methods. For example, the rapidly developing Computational Electromagnetics Method (CEM) can be divided into two categories: 1. Solving integral equations; 2. Solving partial differential equations. Methods based on partial differential equations include finite difference method (FDM), finite element method (FEM), and boundary element method (BEM). Meanwhile, the electromagnetic calculation method based on the integral equation consists of the method of moments (MoM) and calculation methods derived from it.

Although great progress has been made in the fast solution of the forward electromagnetic scattering problem mentioned above, it still requires a lot of time and memory space computational cost for most full-wave problems. Therefore, there is an urgent need for an accurate, low-cost, and robust solution to the electromagnetic scattering problem.

In recent years, artificial intelligence (AI) has been widely used in practical applications. As deep learning in the field of AI, it has been applied to computer vision, image processing (classification, segmentation, restoration), big data processing and learning, etc. Although the development of electromagnetic technology based on deep neural networks has just begun, many studies have recently applied it to inverse scattering problems, microwave imaging, radar and remote sensing, synthetic aperture reconstruction (SAR), multiple input/multiple output (MIMO) systems etc. Due to its powerful nonlinear approximation capabilities and fast prediction capabilities, deep learning has also emerged as a powerful framework, providing unprecedented low computational time consumption and high-precision performance in the field of computational electromagnetics. Especially in the electromagnetic inversion problem, some excellent results combined with deep learning techniques have been reported. DNNs employ convolutional neural networks (CNNs) to solve the inverse scattering problem, which can quickly generate good quantitative results. The results show that the inversion method based on deep learning significantly outperforms the traditional iterative inversion method in both image quality and computation time.

Inspired by the above work, an AI learning electromagnetic scattering calculation method suitable for any incident field is designed and invented to solve the electromagnetic scattering problem. This method does not directly obtain the scattered field information through the network, but takes the incident field and the information related to the scatterer as input, learns the forward current through the AI learning network, and then calculates the scattered field according to the current information .

Contents of the invention

与对比度/>

和入射场/>

乘积的通道数叠加，即/>

作为输入，用AI学习型网络来学习预测前向电流，最后计算得到散射场的方法。本发明的技术方案：The purpose of the present invention is to solve the traditional algorithm in the process of solving the scattering field, which requires a lot of time cost and calculation space cost when calculating the forward current, and proposes a method based on contrast

with contrast />

and incident field />

The number of channels of the product is superimposed, i.e. />

As input, use the AI learning network to learn to predict the forward current, and finally calculate the method to obtain the scattered field. Technical scheme of the present invention:

入射波/>

到感应电流之间的非线性关系，具体方案设计如下：The design method of the present invention utilizes the AI learning network to train and learn contrast

incident wave/>

The nonlinear relationship between the induced current and the specific scheme is designed as follows:

入射波/>

到感应电流之间的非线性关系，其特征在于：An AI learning electromagnetic scattering calculation method suitable for any incident field, using AI learning network to train and learn contrast

incident wave/>

to the nonlinear relationship between the induced current, characterized by:

作为输入，计算得到前向电流数据作为AI学习型网络的真实样本；Sample design: In order to introduce known information, the network input adopts

As input, calculate the forward current data as the real sample of the AI learning network;

Network design: AI learning network is used as a model to complete the training and prediction process, so as to represent the relationship between input information, that is, scatterers, incident fields, and induced currents.

Further, the calculation method of the forward current data is method of moments (MoM), finite element method (FEM), and finite difference in time domain (FDTD).

Further, the calculation method of the forward current data is the method of moments (MoM) and the calculation steps are as follows:

The total field integral equation is:

和/>

分别表示总场和入射场，r与r′分别表示第p次入射的场点与源点；/>

为二维自由空间格林公式，表示一个位于空间r处的点源对其周围空间某一点r′所产生的场，其中，/>

为第一类零阶汉克尔函数，i表示虚数，k₀是弹性波的波数，χ(r′)＝(∈(r′)-∈₀)/∈₀，它为∈_r的对比度函数，∈₀表示弹性波穿过的介质的某种物理特性。Ω表示计算区域。感应电流J(r′)可以定义为

in,

and />

represent the total field and the incident field respectively, r and r' represent the field point and source point of the pth incident respectively; />

is the two-dimensional free space Green's formula, expressing the field generated by a point source located in space r to a point r' in its surrounding space, where, />

is the first kind of zero-order Hankel function, i represents an imaginary number, k ₀ is the wave number of the elastic wave, χ(r′)=(∈(r′)-∈ ₀ )/∈ ₀ , it is the contrast function of ∈ _r , ∈ ₀ represents some physical property of the medium through which the elastic wave passes. Ω denotes the calculation area. The induced current J(r′) can be defined as

带有电流项J(r′)的电场积分方程可以定义为：In the observation area S, the scattered field

The electric field integral equation with the current term J(r′) can be defined as:

In order to facilitate the introduction of MoM to discretize formulas (1) and (2), the calculation area Ω is discretized into M small square units, M=M ₁ ×M ₂ , M ₁ , M ₂ represent the quantities in the x-axis and y-axis directions respectively . If the small cells being separated grow much smaller than a tenth of the wavelength, the induced current and the total field within each cell can be considered to be the same. Therefore, formula (1) can be discretized as:

与/>

分别表示在第p次入射时，相应对第m个网格的总场与入射场。A_m′表示第m′个网格的面积；/>

在第p次入射时，第m′个网格的感应电流。综合计算区域Ω中所有的网格，式子(3)可以写成以下矩阵形式：in,

with />

Respectively represent the total field and the incident field corresponding to the mth grid at the pth incident. A _m' represents the area of the m'th grid; />

The induced current of the m′th grid at the pth incident. Comprehensive calculation of all the grids in the area Ω, formula (3) can be written in the following matrix form:

表示从感应电流到计算区域Ω中散射场之间的二维自由空间格林公式，其可以表示为：in

Represents the two-dimensional free-space Green's formula between the induced current and the scattered field in the calculation region Ω, which can be expressed as:

表示在第p次入射时，所有单元格离散的电流分布，其可以表示为：Induced current in vector form

Indicates the discrete current distribution of all cells at the p-th incident, which can be expressed as:

是一个对角矩阵，对角线上的每个元素对应于每个网格的对比度。将式子(4)代入式子(6)，可以得到状态方程，表示如下：in,

is a diagonal matrix where each element on the diagonal corresponds to the contrast of each grid. Substituting formula (4) into formula (6), the state equation can be obtained, expressed as follows:

Similarly, the scattered field located in the observation area S can be discretized into a data equation, expressed as follows:

表示位于计算区域Ω的感应电流到观测区域S中散射场之间关系的二维格林公式。in,

Two-dimensional Green's formula expressing the relationship between the induced current located in the calculation region Ω and the scattered field in the observation region S.

Using traditional MoM to solve the state equation of induced current can be expressed as:

表示单位矩阵。利用公式(9)求出感应电流后，便可利用公式(8)求出散射场。in,

represents the identity matrix. After using the formula (9) to calculate the induced current, the formula (8) can be used to calculate the scattered field.

Furthermore, the method of calculating the induced current in formula (9) is replaced by using the conjugate gradient fast Fourier transform (CG-FFT) to solve the induced current. In the complex space, the conjugate gradient method can solve the following linear equations,

is equivalent to solving the following minimization problem:

作为未知量/>

可将公式(9)转为公式(10)的形式，进而利用共轭梯度法求解。induced current

as unknown />

Formula (9) can be transformed into the form of formula (10), and then solved by the conjugate gradient method.

Further, the solution steps of the conjugate gradient method are as follows:

1) Set the initial value x ₀ , r ₀ =g ₀ =Ax ₀ -b;

2) Determine the first gradient search direction: P ₀ =-A ^* r ₀ ;

x_k+1＝x_k+α_kP_k,r_k+1＝r_k+α_kAP_k；3)

x _k+1 = x _k +α _k P _k ,r _k+1 =r _k +α _k AP _k ;

P_k+1＝-A^*r_k+1+β_kP_k；4)

P _k+1 ＝-A ^* r _k+1 +β _k P _k ;

5) Set the iteration termination condition and judge whether the iteration termination condition is satisfied, if not, go to step 3), if yes, get x.

Among them, * in the upper right corner of the variable indicates the conjugate transpose symbol;

为Toeplitz矩阵，故可利用快速傅立叶变换(FFT)进行矩阵运算，求解步骤中，形如A^*r_k，AP_k都可以利用FFT进行运算，AP_k的运算可以简化为When using the conjugate gradient method to solve, a large number of matrix operations are involved. Considering the conversion of formula (9)

is a Toeplitz matrix, so the fast Fourier transform (FFT) can be used for matrix operations. In the solution step, the shape is A ^* r _k , AP _k can be operated by FFT, and the operation of AP _k can be simplified as

Among them, a is a vector composed of the data in the first row and the first column in the matrix A, FFT is the discrete Fourier transform, and .* means that the data between the matrices is multiplied in pairs.

Further, the AI learning network adopts CNN network, U-net, generated confrontation network GAN, and Pix2pixGAN network.

Further, the AI learning network adopts the Pix2pix GAN network, and the Pix2pix GAN network is composed of two parts of the network, that is, the generation network G and the confrontation network D.

Further, the G network is actually a 5-layer U-net network, including downsampling, upsampling, and skip connection layers. In the last layer of the G network, the network directly outputs the actual value of the scatterer at the end, without using similar Activation functions like tanh().

Further, the input of the D network includes the source and the predicted image of the G network and the input image as conditions, and a set of vectors output by the D network.

Further, the loss function of the G network and the D network adopts the least squares GAN, which is defined as follows:

表示真实电流与预测电流的L₁范数，定义为：Among them, x represents the input data of the network, and J _MoM represents the real current data obtained by the MoM algorithm. λ is an adjustable parameter,

Represents the _L1 norm of the real current and the predicted current, defined as:

Experiments have proved that this invention can solve the problem that the incident angle and irradiation intensity of the incident wave are not fixed. And there is no small improvement in accuracy.

Description of drawings

Figure 1 is a flow chart of the proposed solution for the electromagnetic scattering problem;

Figure 2 is a structural diagram of the proposed two-dimensional electromagnetic scattering problem device;

Fig. 3 is the network pix2pix GAN internal structure figure that the present invention adopts;

Figure 4 is the network input data for the first example to solve the change of incident light intensity;

Fig. 5 is a comparison chart of the forward current result obtained in the first example and the result obtained by traditional MoM;

Fig. 6 is the second example to solve the network input data that the incident light irradiation angle can be changed arbitrarily;

Fig. 7 is a comparison diagram of the forward current result obtained in the second example and the result obtained by traditional MoM;

Fig. 8 is a comparison chart of the scattered field result reconstructed in the second example and the scattered field calculated by the traditional MoM.

Detailed ways

The present invention takes the transverse electromagnetic wave as an example, and further explains the electromagnetic scattering problem to be solved by the present invention in conjunction with the accompanying drawings.

与对比度

和入射场/>

乘积的通道数叠加，即/>

作为输入，用AI学习型网络来学习预测前向电流，最后计算得到散射场的方法，该方法能有效得到发射天线入射角度任意与照射强度变化的散射场数据。Fig. 1 is a flow chart of the AI learning type electromagnetic scattering calculation method proposed by the present invention. i.e. by contrast

and contrast

and incident field />

The number of channels of the product is superimposed, i.e. />

As input, the AI learning network is used to learn and predict the forward current, and finally calculate the scattered field method. This method can effectively obtain the scattered field data with any incident angle of the transmitting antenna and the change of the irradiation intensity.

Figure 2 is a structural diagram of the electromagnetic scattering problem device. The figure is a two-dimensional cross-sectional view, the center is a cross-sectional calculation area Ω, which contains known scatterers distribution, and the outer S-domain surface is the trajectory of the transmitting antenna and receiving antenna. When the transmitting antenna irradiates the scatterer, an induced current will be induced inside the scatterer, and the induced current will excite an electromagnetic field, the so-called scattered field, which can be received by the receiving antenna. In order to simulate the scattered field data, the present invention proposes a forward current learning method, which uses known scatterers and incident fields and induced currents obtained by traditional algorithms as sample pairs, and completes complex learning by pix2pix GAN. Finally, training A good network can predict the scattered field distribution of complex scatterers outside some sample distributions.

入射波/>

到感应电流之间的非线性关系。The present invention adopts AI learning network to train and learn contrast

incident wave/>

to the nonlinear relationship between the induced current.

作为输入，并利用传统算法计算得到前向电流数据作为AI学习型网络的真实样本。传统算法如矩量法MoM，有限元法FEM，时域有限差分发FDTD等，都可以应用于此发明，由MoM算法计算感应电流的方法，计算过程如下：Sample design: In order to introduce known information, the network input adopts

As input, and use traditional algorithms to calculate the forward current data as the real sample of AI learning network. Traditional algorithms such as method of moments MoM, finite element method FEM, finite difference in time domain FDTD, etc., can be applied to this invention. The method of calculating the induced current by the MoM algorithm is as follows:

The total field integral equation is:

和/>

分别表示总场和入射场，r与r′分别表示第p次入射的场点与源点。/>

为二维自由空间格林公式，表示一个位于空间r处的点源对其周围空间某一点r′所产生的场，其中，/>

为第一类零阶汉克尔函数，i表示虚数，k₀是弹性波的波数，χ(r′)＝(∈(r′)-∈₀)/∈₀，它为∈_r的对比度函数，∈₀表示弹性波穿过的介质的某种物理特性。Ω表示计算区域。感应电流J(r′)可以定义为

in,

and />

represent the total field and the incident field, respectively, and r and r' represent the field point and source point of the pth incident, respectively. />

is the two-dimensional free space Green's formula, expressing the field generated by a point source located in space r to a point r' in its surrounding space, where, />

is the first kind of zero-order Hankel function, i represents an imaginary number, k ₀ is the wave number of the elastic wave, χ(r′)=(∈(r′)-∈ ₀ )/∈ ₀ , it is the contrast function of ∈ _r , ∈ ₀ represents some physical property of the medium through which the elastic wave passes. Ω denotes the calculation area. The induced current J(r′) can be defined as

带有电流项J(r′)的电场积分方程可以定义为：In the observation area S, the scattered field

The electric field integral equation with the current term J(r′) can be defined as:

In order to facilitate the introduction of MoM to discretize formulas (1) and (2), the calculation area Ω is discretized into M small square units, M=M ₁ ×M ₂ , M ₁ , M ₂ represent the quantities in the x-axis and y-axis directions respectively . If the small cells being separated grow much smaller than a tenth of the wavelength, the induced current and the total field within each cell can be considered to be the same. Therefore, formula (1) can be discretized as:

与/>

分别表示在第p次入射时，相应对第m个网格的总场与入射场。A_m′表示第m′个网格的面积；/>

在第p次入射时，第m′个网格的感应电流。综合计算区域Ω中所有的网格，式子(3)可以写成以下矩阵形式：in,

with />

Respectively represent the total field and the incident field corresponding to the mth grid at the pth incident. A _m' represents the area of the m'th grid; />

The induced current of the m′th grid at the pth incident. Comprehensive calculation of all the grids in the area Ω, formula (3) can be written in the following matrix form:

表示从感应电流到计算区域Ω中散射场之间的二维自由空间格林公式，其可以表示为：in

Represents the two-dimensional free-space Green's formula between the induced current and the scattered field in the calculation region Ω, which can be expressed as:

表示在第p次入射时，所有单元格离散的电流分布，其可以表示为：Induced current in vector form

Indicates the discrete current distribution of all cells at the p-th incident, which can be expressed as:

是一个对角矩阵，对角线上的每个元素对应于每个网格的对比度。将式子(4)代入式子(6)，可以得到状态方程，表示如下：in,

is a diagonal matrix where each element on the diagonal corresponds to the contrast of each grid. Substituting formula (4) into formula (6), the state equation can be obtained, expressed as follows:

Similarly, the scattered field located in the observation area S can be discretized into a data equation, expressed as follows:

表示位于计算区域Ω的感应电流到观测区域S中散射场之间关系的二维格林公式。in,

Two-dimensional Green's formula expressing the relationship between the induced current located in the calculation region Ω and the scattered field in the observation region S.

Using traditional MoM to solve the state equation of induced current can be expressed as:

表示单位矩阵。利用公式(9)求出感应电流后，便可利用公式(8)求出散射场。in,

represents the identity matrix. After using the formula (9) to calculate the induced current, the formula (8) can be used to calculate the scattered field.

It can be seen that when using formula (9) to find the induced current, when the calculation area Ω is large, the calculation complexity is high and the calculation amount is very large, so this example uses the conjugate gradient fast Fourier transform (CG-FFT) to solve The induction current greatly improves the calculation efficiency.

The conjugate gradient (CG) method is a mathematical method for numerically solving unconstrained optimization problems. The characteristic of this algorithm is that the iterative direction used is the conjugate direction instead of the local gradient direction, and it usually converges faster than the steepest descent method.

In the space of complex numbers, the conjugate gradient method solves the following system of linear equations,

is equivalent to solving the following minimization problem:

作为未知量/>

可将公式(9)转为公式(10)的形式，进而利用共轭梯度法求解。induced current

as unknown />

Formula (9) can be transformed into the form of formula (10), and then solved by the conjugate gradient method.

The solution steps of the conjugate gradient method are as follows:

1) Set the initial value x ₀ , r ₀ =g ₀ =Ax ₀ -b;

2) Determine the first gradient search direction: P ₀ =-A ^* r ₀ ;

x_k+1＝x_k+α_kP_k,r_k+1＝r_k+α_kAP_k；3)

x _k+1 = x _k +α _k P _k ,r _k+1 =r _k +α _k AP _k ;

P_k+1＝-A^*r_k+1+β_kP_k；4)

P _k+1 ＝-A ^* r _k+1 +β _k P _k ;

5) Set the iteration termination condition and judge whether the iteration termination condition is satisfied, if not, go to step 3), if yes, get x.

Among them, * in the upper right corner of the variable indicates the conjugate transpose symbol.

为Toeplitz矩阵，故可利用快速傅立叶变换(FFT)进行矩阵运算，该变换大大降低了计算复杂度。求解步骤中，形如A^*r_k，AP_k都可以利用FFT进行运算，以AP_k为例，该运算可以简化为When using the conjugate gradient method to solve, a large number of matrix operations are involved. Considering the conversion of formula (9)

It is a Toeplitz matrix, so the fast Fourier transform (FFT) can be used for matrix operation, which greatly reduces the computational complexity. In the solution step, both A ^* r _k and AP _k can be operated by FFT. Taking AP _k as an example, the operation can be simplified as

Among them, a is a vector composed of the data in the first row and the first column in the matrix A, FFT is the discrete Fourier transform, and .* means that the data between the matrices is multiplied in pairs. It can be seen from the above that the amount of matrix calculation is greatly reduced.

Through the above method, the induced current in the sample is obtained.

Network design:

The design of the present invention uses the AI learning network as a model to complete the training and prediction process. After obtaining the sample pair, it is input into the AI learning network to complete the training, so as to represent the input information, that is, the scatterer, the incident field, and the induced current. Relationship. AI can use CNN network, U-net, generated confrontation network GAN, etc. Here, the pix2pix GAN network is taken as an example. The internal structure diagram of the pix2pix GAN network is shown in Figure 3.

Here, the Pix2pix GAN network is composed of two parts of the network, namely the generation network G and the confrontation network D. In the present invention, the G network is actually a 5-layer U-net network, which can be divided into three parts, down-sampling, up-sampling, and skip connection layers. In the last layer of the G network, the present invention deletes activation functions similar to tanh(), so that the final output of the network is the actual value of the scatterer.

The purpose of the D network is to distinguish the predicted image from the real image. The Pix2pix GAN network is based on the conditional GAN (CGAN), so the input of D not only includes the source and the predicted image of the G network, but also includes the input image as the condition. In the pix2pix GAN network, the D network outputs a set of vectors instead of a scalar, which enables D to make more subtle discrimination on the sub-region blocks on the image. In fact, each element on the vector corresponds to the image on the A receptive field, the so-called patchGAN operation.

The loss function of G and D adopts the least squares GAN, which is defined as follows:

表示真实电流与预测电流的L₁范数，定义为：Among them, x represents the input data of the network, and J _MoM represents the real current data obtained by the MoM algorithm. λ is an adjustable parameter,

Represents the _L1 norm of the real current and the predicted current, defined as:

Example 1

的强度设定为/>

The structure diagram of the experimental device designed and adopted by the present invention is shown in Fig. 2, and the centers of the rectangular frame and the S domain plane are located at (0, 0). The size of the rectangular frame is 2×2m, and the distance between the transmitting antenna and the receiving antenna is 3m from the center of the circle. A total of 32 receiving antennas are arranged at equal intervals in the S domain. When setting the sample, the transmitting antenna angle is selected at 180° (the leftmost side of the S domain), and the incident light wavelength is set to 0.75m. incident field

The intensity is set to />

数值在0.01-0.50之间随机变化，两者相互独立。样本总数为10000，其中，9500个用于训练，500个用于测试。输入样本如图4所示，/>

对应输入方案/>

The scatterer section used for training is the MNIST handwritten data set. At the same time, in order to diversify the samples, a circle is randomly added to each data section, and the radius of the circle is set to 0.15m-0.5m. The contrast between the handwritten data and the circle is at

Values vary randomly between 0.01-0.50, independent of each other. The total number of samples is 10000, of which 9500 are used for training and 500 are used for testing. The input sample is shown in Figure 4, />

Corresponding input scheme />

In order to compare the accuracy of the experimental results of the present invention with the traditional MoM algorithm, the grid is discretized to 64×64 first, and after using the traditional MoM algorithm to obtain the induced current (denoted as J ₆₄ ), the equidistant sampling is 32×32, denoted for J _64to32 . At the same time, the induced current calculated by the traditional MoM algorithm is denoted as J ₃₂ when the grid is divided into 32×32. J _64to32 is the current data input into the network, and it is also the standard for evaluating the current predicted by the network and J ₃₂ . J _pix2pix represents the current predicted by the network.

The patchGAN in the Pix2pix GAN network is set to 15×15, and the number of network channels N in Figure 3 is set to 64. The initial learning rate of G network and D network is 0.0002, and it is reduced by half every 100 cycles, and the total cycle is 300. Batchsize is set to 64, and the parameter λ in formula (14) is set to 100.

第二个测试的对比度为0.4，入射光照强度为/>

两个例子具有相同的/>

同时，实验增加了/>

与/>

两个输入方案作为对比。图中(a)表示计算区域真实截面；(b)表示J₆₄；(c)表示J_64to32；(d)表示J₃₂；(e)分别J₃₂与J_64to32的绝对误差；(f)-(h)分别表示/>

三种作为网络输入所预测的电流与J_64to32的绝对误差图。表1包含了2个例子的散射体介电常数信息以及平均绝对误差数据。Figure 5 is a comparison chart of the current predicted by the two networks and the current calculated by the traditional MoM algorithm. The contrast of the first test of this experiment is 0.2, and the incident light intensity is

The second test has a contrast ratio of 0.4 and an incident light intensity of />

Both examples have the same />

At the same time, the experiment added />

with />

Two input schemes are used for comparison. In the figure (a) represents the real section of the calculation area; (b) represents J ₆₄ ; (c) represents J _64to32 ; (d) represents J ₃₂ ; (e) the absolute error of J ₃₂ and J _64to32 respectively; (f)-( h) represent respectively />

Absolute error plot of J _64to32 for the three currents predicted as input to the network. Table 1 contains the scatterer permittivity information and mean absolute error data for the two examples.

作为输入的方案比其他两种方案(即/>

作为输入)效果好很多，且比传统MoM算法精度高，且能够模拟出样本之外复杂散射体的散射场数据分布，在计算速度上也比传统算法快得多。It can be seen that when the irradiation intensity of the incident antenna is not fixed, under the same grid division, the forward current learning method adopted in the present invention,

The scheme as input is more efficient than the other two schemes (ie />

As the input), the effect is much better, and the accuracy is higher than the traditional MoM algorithm, and it can simulate the scattering field data distribution of the complex scatterer outside the sample, and the calculation speed is much faster than the traditional algorithm.

Table 1 The forward current result obtained in Example 1 and the current mean absolute error data obtained by traditional MoM

Example 2

The structure diagram of the experimental device designed and adopted by the present invention is shown in Fig. 2, and the centers of the rectangular frame and the S domain plane are located at (0, 0). The size of the rectangular frame is 2×2m, and the distance between the transmitting antenna and the receiving antenna is 3m from the center of the circle. A total of 32 receiving antennas are arranged at equal intervals in the S domain. When setting samples, the position of the transmitting antenna is not unique. An incident point is set every 10°, and the incident points are distributed between 0°-360°. The incident light wavelength was set to 0.75m.

对应输入方案/>

图中三个样本发射天线的采样点分别位于310°，10°，80°。The scatterer section used for training is the MNIST handwritten data set. At the same time, in order to diversify the samples, we randomly added a circle to each data section, and the radius of the circle was set to 0.15m-0.5m. The contrast between the handwritten data and the circle was randomly varied from 0.01 to 0.50, independent of each other. The total number of samples is 20,000, of which 19,000 are used for training and 1,000 are used for testing. The input sample is shown in Figure 6,

Corresponding input scheme />

The sampling points of the three sample transmitting antennas in the figure are respectively located at 310°, 10°, and 80°.

In order to compare the experimental results of the present invention with the traditional MoM algorithm, the grid is discretized to 64×64 for the first time. After using the traditional MoM algorithm to obtain the induced current (denoted as J ₆₄ ), the equidistant sampling is 32×32, denoted as J _64to32 . At the same time, the induced current calculated by the traditional MoM algorithm is denoted as J ₃₂ when the grid is divided into 32×32. J _64to32 is the current data input into the network, and it is also the standard for evaluating the current predicted by the network and J ₃₂ . J _pxi2pix represents the current predicted by the network.

The patchGAN in the Pix2pix GAN network is set to 15×15, and the number of network channels N in Figure 3 is set to 64. The initial learning rate of G network and D network is 0.0002, and it is reduced by half every 100 cycles, and the total cycle is 300. Batchsize is set to 64, and the parameter λ in formula (14) is set to 100.

三种作为网络输入所预测的电流与J_64to32的绝对误差图。表2包含了4个例子的散射体介电常数信息，发射天线所处位置，以及平均绝对误差数据。图8是4个例子重建的散射场结果与传统MoM计算得到的散射场对比图。可以看出，后面两个例子发射天线的入射角度在样本选取点之外，预测得到的电流数据依旧准确，故实现了天线任意发射位置散射场数据的预测。同时，在相同的网格划分下，本发明所采用的前向电流学习方法，/>

作为输入的方案比传统MoM算法精度高，且能够模拟出样本之外复杂散射体的散射场数据分布，在计算速度上也比传统算法快得多。Figure 7 is a comparison chart of the current predicted by the four networks and the current calculated by the traditional MoM algorithm. In the figure (a) represents the real section of the calculation area; (b) represents J ₆₄ ; (c) represents J _64to32 ; (d) represents J ₃₂ ; (e) the absolute error of J ₃₂ and J _64to32 respectively; (f)-( h) represent respectively

Absolute error plot of J _64to32 for the three currents predicted as input to the network. Table 2 contains information on the permittivity of the scatterers, the location of the transmitting antenna, and the mean absolute error data for the four examples. Figure 8 is a comparison of the scattered field results reconstructed in four examples and the scattered field calculated by traditional MoM. It can be seen that the incident angle of the transmitting antenna in the latter two examples is outside the sample selection point, and the predicted current data is still accurate, so the prediction of the scattered field data at any transmitting position of the antenna is realized. At the same time, under the same grid division, the forward current learning method adopted by the present invention, />

The input scheme has higher accuracy than the traditional MoM algorithm, and can simulate the distribution of scattering field data of complex scatterers outside the sample, and its calculation speed is much faster than the traditional algorithm.

The forward current result obtained in Table 2 Example 2 and the current mean absolute error data obtained by traditional MoM

Above-mentioned two examples just illustrate the method of the present invention, are not for restriction of the present invention, and the present invention is not limited to above-mentioned two examples, as long as meet the requirement of the method of the present invention, all belong to the protection domain of the method of the present invention.

Claims (10)

1. An AI learning electromagnetic scattering calculation method suitable for any incident field, using AI learning network to train and learn contrast

incident wave/>

to the nonlinear relationship between the induced current, characterized by: Sample design: In order to introduce known information, the network input adopts

As input, calculate the forward current data as the real sample of the AI learning network; Network design: AI learning network is used as a model to complete the training and prediction process, so as to represent the relationship between input information, that is, scatterers, incident fields, and induced currents. 2. A kind of AI learning type electromagnetic scattering calculation method applicable to any incident field according to claim 1, characterized in that the calculation method of the forward current data is method of moments MoM, finite element method FEM, time Finite Difference Domain Method FDTD. 3. A kind of AI learning type electromagnetic scattering calculation method applicable to any incident field according to claim 1, characterized in that the calculation method of the forward current data is the method of moments (MoM) calculation steps are as follows: The total field integral equation is:

in,

and />

represent the total field and the incident field respectively, r and r ^' represent the field point and the source point of the pth incident respectively; />

is the two-dimensional free space Green's formula, expressing the field produced by a point source located at space r to a certain point r ^' in its surrounding space, where, />

is the first kind of zero-order Hankel function, i represents an imaginary number, k ₀ is the wave number of elastic wave, χ(r ^′ )=(ε(r ^′ )-∈ ₀ )/∈ ₀ , it is the contrast function of ∈ _r , ∈ ₀ represents a certain physical property of the medium through which the elastic wave passes; Ω represents the calculation area, and the induced current J(r ^′ ) can be defined as

In the observation area S, the scattered field />

The electric field integral equation with the current term J(r ^′ ) can be defined as:

In order to facilitate the introduction of MoM to discretize formulas (1) and (2), the calculation area Ω is discretized into M small square units, M=M ₁ ×M ₂ , M ₁ , M ₂ represent the quantities in the x-axis and y-axis directions respectively , if the length of the separated small unit becomes much smaller than one-tenth of the wavelength, the induced current and the total field in each unit can be regarded as the same, therefore, formula (1) can be discretized as:

in,

with />

Respectively represent the total field and the incident field corresponding to the mth grid at the pth incident, and A _m' represents the area of the m ^' th grid; />

When the p-th incident occurs, the induced current of the m ^' th grid is comprehensively calculated for all the grids in the area Ω, and the formula (3) can be written in the following matrix form:

in

Represents the two-dimensional free-space Green's formula between the induced current and the scattered field in the calculation region Ω, which can be expressed as:

Induced current in vector form

Indicates the discrete current distribution of all cells at the p-th incident, which can be expressed as:

in,

is a diagonal matrix, and each element on the diagonal corresponds to the contrast of each grid. Substituting equation (4) into equation (6), the state equation can be obtained, expressed as follows:

Similarly, the scattered field located in the observation area S can be discretized into a data equation, expressed as follows:

in,

Two-dimensional Green's formula expressing the relationship between the induced current located in the calculation area Ω and the scattered field in the observation area S; Using traditional MoM to solve the state equation of induced current can be expressed as:

in,

Represents the unit matrix, and after using the formula (9) to calculate the induced current, the formula (8) can be used to calculate the scattering field. 4. A kind of AI learning type electromagnetic scattering calculation method applicable to any incident field according to claim 3, it is characterized in that formula (9) calculates the mode of induced current to be replaced by using conjugate gradient fast Fourier transform (CG-FFT ) to solve the induced current, in the complex space, the conjugate gradient method can solve the following linear equations,

is equivalent to solving the following minimization problem:

induced current

as unknown />

Formula (9) can be transformed into the form of formula (10), and then solved by the conjugate gradient method. 5. A kind of AI learning type electromagnetic scattering calculation method applicable to any incident field according to claim 4, characterized in that said conjugate gradient method solution steps are as follows: 1) Set the initial value x ₀ , r ₀ =g ₀ =Ax ₀ -b; 2) Determine the first gradient search direction: P ₀ =-A ^* r ₀ ; 3)

x _k+1 = x _k +α _k P _k ,r _k+1 =r _k +α _k AP _k ; 4)

P _k+1 ＝-A ^* r _k+1 +β _k P _k ; 5) Set the iteration termination condition and judge whether the iteration termination condition is satisfied, if not, turn to step 3), If so, get x; Among them, * in the upper right corner of the variable indicates the conjugate transpose symbol; When using the conjugate gradient method to solve, a large number of matrix operations are involved. Considering the conversion of formula (9)

is a Toeplitz matrix, so the fast Fourier transform (FFT) can be used for matrix operations. In the solution step, the shape is A ^* r _k , AP _k can be operated by FFT, and the operation of AP _k can be simplified as

Among them, a is a vector composed of the data in the first row and the first column in the matrix A, FFT is the discrete Fourier transform, and .* means that the data between the matrices is multiplied in pairs. 6. A kind of AI learning type electromagnetic scattering calculation method applicable to any incident field according to claim 1, characterized in that said AI learning network adopts CNN network, U-net, generating confrontation network GAN, Pix2pix GAN network . 7. A kind of AI learning type electromagnetic scattering calculation method applicable to any incident field according to claim 1, characterized in that said AI learning network adopts Pix2pix GAN network, and Pix2pix GAN network is composed of two parts of the network, namely generating Network G and confrontation network D. 8. A kind of AI learning type electromagnetic scattering calculation method applicable to any incident field according to claim 7, characterized in that the generation network G is actually a 5-layer U-net network, including downsampling, upsampling, The skip connection layer is the last layer of the generation network G, and the network directly outputs the actual value of the scatterer at the end, without using an activation function similar to tanh(). 9. An AI learning type electromagnetic scattering calculation method applicable to any incident field according to claim 7, characterized in that the input of the confrontation network D includes the source and generation network G's predicted image and input image as condition, a set of vectors output by the adversarial network D. 10. A kind of AI learning type electromagnetic scattering calculation method applicable to any incident field according to claim 7, characterized in that the loss function of the generation network G and the confrontation network D adopts the least squares GAN, which is defined as follows:

Among them, x represents the input data of the network, J _MoM represents the real current data obtained by the MoM algorithm; λ is an adjustable parameter,

Represents the _L1 norm of the real current and the predicted current, defined as:

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