CN111444601B - AI learning type electromagnetic scattering calculation method suitable for arbitrary incident field - Google Patents
AI learning type electromagnetic scattering calculation method suitable for arbitrary incident field Download PDFInfo
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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
Technical Field
The invention belongs to the field of electromagnetic scattering, and provides an AI learning type electromagnetic scattering calculation method suitable for any incident field.
Background
Up to now, maxwell's equations have been proposed for over 100 years. During this period. Electromagnetic technology and theory have evolved rapidly and have found widespread use, such as radio communications, radar and antenna, geological surveys, biomedical imaging, and the like. Electromagnetic waves propagate very complex in the actual environment, so that the research of the characteristics of the electromagnetic waves has important significance, and experiments and theoretical analysis and calculation are complementary important means.
In theoretical analysis and calculation, most of electromagnetic problems can not be directly solved by a Maxwell equation set analysis form, and only a numerical method can be relied on. As rapidly evolving Computational Electromagnetics Methods (CEMs), the population can be divided into two categories: 1. solving an integral equation; 2. and solving a partial differential equation. Methods based on partial differential equation solutions include Finite Difference Method (FDM), finite Element Method (FEM), boundary Element Method (BEM). Meanwhile, an electromagnetic calculation method based on an integral equation consists of a moment method (MoM) and a calculation method derived from the moment method.
While the above-mentioned forward electromagnetic scattering problem has made great progress in quick solution, it still requires a significant amount of time and memory space computation costs for most full wave problems. Therefore, in terms of electromagnetic scattering, there is an urgent need for a solution method that is accurate, has low computational cost, and has good robustness.
In recent years, artificial Intelligence (AI) has been widely used in practical applications, and as deep learning in the AI field, it has been applied to computer vision, image processing (classification, segmentation, restoration), big data processing, learning, and the like. Although electromagnetic technology development based on deep neural networks has just begun, there has been much research recently applied to the problems of backscatter, microwave imaging, radar and remote sensing, synthetic Aperture Reconstruction (SAR), multiple input/multiple output (MIMO) systems, and so forth. Due to the strong nonlinear approximation capability and the rapid prediction capability, deep learning is also gradually a powerful framework, and unprecedented low calculation time consumption and high precision performance are provided for the field of computational electromagnetics. Particularly in electromagnetic inversion problems, some excellent results have been reported in combination with deep learning techniques. DNNs solve the problem of back scattering by adopting Convolutional Neural Networks (CNNs), and can quickly generate good quantitative results. The result shows that the inversion method based on the deep learning is obviously superior to the traditional iterative inversion method in terms of image quality and calculation time.
Inspired by the work, the invention designs an AI learning type electromagnetic scattering calculation method suitable for any incident field to solve the electromagnetic scattering problem. According to the method, the scattered field information is not directly obtained through a network, but the incident field and information related to a scatterer are taken as input, forward current is learned through an AI learning network, and then the scattered field is calculated according to the current information.
Disclosure of Invention
The invention aims at solving the scattered field by the traditional algorithm, which requires a great amount of time cost and calculation space cost in the process of calculating forward current, and provides a method for calculating the forward current with contrast
Contrast->
And incident field->
The channel number of the product being superimposed, i.e. +.>
As input, the AI learning network is used to learn the predicted forward current, and finally the scattered field is calculated. The technical scheme of the invention is as follows:
the design method of the invention utilizes AI learning type network to train and learn contrast
Incident wave->
The nonlinear relation between the induction currents is designed as follows:
AI learning type electromagnetic scattering calculation method suitable for arbitrary incident field, and training and learning contrast ratio by using AI learning network
Incident wave->
A nonlinear relationship between the induced currents characterized by:
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.
Further, the calculation method of the forward current data is a moment method MoM, a finite element method FEM and a time domain finite difference method FDTD.
Further, the calculation method of the forward current data is a moment method MoM calculation step as follows:
the total field integral equation is:
wherein ,
and />
Respectively representing the total field and the incident field, and r' respectively represent the field point and the source point of the p-th incidence；/>
For the two-dimensional free-space green's formula, a field generated by a point source located at space r for a point r' in its surrounding space is represented, wherein +.>
For the first class of zero-order hank functions, i represents the imaginary number, k 0 Is the wave number of the elastic wave, χ (r ')= (e (r') -e) 0 )/∈ 0 It is E r E, e 0 Representing some physical property of the medium through which the elastic wave passes. Ω denotes a calculation region. The induced current J (r') can be defined as
In the observation region S, a scattered field
The electric field integral equation with the current term J (r') can be defined as:
to facilitate the introduction of MoM to discretize equations (1) and (2), the calculation region Ω is discretized into M small square units, m=m 1 ×M 2 ,M 1 ,M 2 The number of x-axis and y-axis directions are indicated, respectively. If the small cells that are separated become much smaller than one tenth wavelength, the induced current in each cell and the total field can be considered the same. Thus, equation (1) can be discretized into:
wherein ,
and->
The total field and the incident field of the corresponding pair of mth grids at the p-th incidence are shown respectively. A is that m′ Representing the area of the m' th mesh; />
At the p-th incidence, the induction current of the m' th grid. All grids in the calculation region Ω are integrated, and the equation (3) can be written in the form of the following matrix:
wherein 
A two-dimensional free space green's formula, representing the difference between the scattered fields from the induced current into the calculated region Ω, can be expressed as:
vector-form induced current
Representing the current distribution of all cell dispersion at the p-th incidence, it can be expressed as:
wherein ,
is a diagonal angleA matrix, each element on the diagonal corresponds to the contrast of each grid. Substituting equation (4) into equation (6) can yield the state equation, expressed as follows:
similarly, the fringe field at observation region S can be discretized into data equations, expressed as follows:
wherein ,
a two-dimensional green' S formula representing the relationship between the induced current in the calculated region Ω to the scattered field in the observation region S.
Solving the state equation of the induced current using a conventional MoM can be expressed as:
wherein ,
representing the identity matrix. After the induced current is obtained by using the formula (9), the scattered field can be obtained by using the formula (8).
Further, the method of calculating the induced current in the formula (9) is replaced by adopting conjugate gradient fast Fourier transform (CG-FFT) to solve the induced current, in a complex space, the conjugate gradient method can solve the following linear equation system,
equivalent to solving the following minimization problem:
by inducing current
As an unknown quantity->
Equation (9) can be converted into equation (10) and then solved by using the conjugate gradient method.
Further, the conjugate gradient method comprises the following solving steps:
1) Setting an initial value x 0 ，r 0 ＝g 0 ＝Ax 0 -b；
2) Determining a first gradient search direction: p (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) Setting an iteration termination condition, judging whether the iteration termination condition is met, if not, turning to the step 3), and if so, obtaining x.
Wherein the upper right hand corner of the variable represents the conjugate transpose symbol;
when solving by conjugate gradient method, a large number of matrix operations are involved, and after conversion is performed by considering formula (9)
Is Toeplitz matrix, so that matrix operation can be performed by Fast Fourier Transform (FFT), and the form A is obtained in the solving step * r k ，AP k Can be operated by FFT, AP k The operation of (2) can be simplified into
Where a is a vector composed of data of the first row and the first column in the matrix a, and FFT is a discrete fourier transform.
Furthermore, the AI learning network adopts a CNN network and a U-net to generate an antagonistic network GAN and a Pix2Pix GAN network.
Furthermore, the AI learning network adopts a Pix2Pix GAN network, and the Pix2Pix GAN network is composed of two parts of networks, namely a generating network G and an antagonizing network D.
Further, the G network is actually a 5-layer U-net network, including downsampling, upsampling, and jump connection layers, and at the last layer of the G network, the network outputs the actual value of the scatterer directly, without using an activation function similar to tanh ().
Further, the input of the D network comprises a predicted image and an input image of the source and G network, and a set of vectors output by the D network.
Further, the loss functions of the G network and the D network adopt least square GAN, which is defined as follows:
where x represents input data of the network, J MoM Representing the real current data obtained by the MoM algorithm. Lambda is an adjustable parameter that is used to adjust the parameter,
l representing true current and predicted current 1 Norms, defined as:
experiments prove that the method can solve the problem that the incident angle and the irradiation intensity of the incident wave are not fixed, has wider application range, and can not only be faster in time than the traditional algorithm, but also improve the precision slightly when the method is applied to solving the scattered field under the same grid division.
Drawings
FIG. 1 is a flow chart of a proposed solution to the electromagnetic scattering problem;
FIG. 2 is a block diagram of the proposed two-dimensional electromagnetic scattering problem device;
FIG. 3 is a diagram of the internal architecture of the network pix2pix GAN employed in the present invention;
FIG. 4 is network input data for a first example to account for variations in incident illumination intensity;
FIG. 5 is a graph comparing the forward current results obtained for the first example with those obtained for a conventional MoM;
FIG. 6 is a second example of network input data that addresses the arbitrary variability of the angle of incident light illumination;
FIG. 7 is a graph comparing the forward current results obtained for the second example with those obtained for the conventional MoM;
fig. 8 is a plot of the reconstructed fringe field results of the second example versus fringe fields calculated by conventional MoM calculations.
Detailed Description
The invention takes transverse electromagnetic waves as an example, and the electromagnetic scattering problem to be solved by the invention is further described with reference to the accompanying drawings.
Fig. 1 is a flowchart of an AI-learning electromagnetic scattering calculation method according to the present invention. I.e. with contrast
Contrast with contrast ratio
And incident field->
The channel number of the product being superimposed, i.e. +.>
As input, the AI learning network is used to learn and predict forward current, and finally the scattered field data of arbitrary incident angle and irradiation intensity variation of the transmitting antenna can be obtained by the method.
Fig. 2 is a block diagram of an electromagnetic scattering problem device. The figure is a two-dimensional cross-sectional view, the center is a cross-sectional calculation region omega, the inside contains known scattering body distribution, and the peripheral S domain surface is the distribution track of the transmitting antenna and the receiving antenna. When the transmitting antenna irradiates the scattering body, an induced current is excited inside the scattering body, which excites an electromagnetic field, the so-called scattering field, which is received by the receiving antenna. In order to simulate scattered field data, the invention provides a forward current learning method, which uses known scatterers, incident fields and induced currents obtained by a traditional algorithm as sample pairs, and uses pix2pix GAN to complete complex learning, and finally, a trained network can predict the scattered field distribution of complex scatterers outside the distribution of some samples.
The invention adopts AI learning network to train the learning contrast
Incident wave->
To a nonlinear relationship between the induced currents.
Sample design: to introduce known information, network input employs
As input and forward current data calculated by conventional algorithm as AITrue samples of the conventional network. The conventional algorithm such as a moment method MoM, a finite element method FEM, a time domain finite difference method FDTD and the like can be applied to the method for calculating the induced current by the MoM algorithm, and the calculation process is as follows:
the total field integral equation is:
wherein ,
and />
The total field and the incident field are respectively represented, and r' respectively represent the field point and the source point of the p-th incidence. />
For the two-dimensional free-space green's formula, a field generated by a point source located at space r for a point r' in its surrounding space is represented, wherein +.>
For the first class of zero-order hank functions, i represents the imaginary number, k 0 Is the wave number of the elastic wave, χ (r ')= (e (r') -e) 0 )/∈ 0 It is E r E, e 0 Representing some physical property of the medium through which the elastic wave passes. Ω denotes a calculation region. The induced current J (r') can be defined as
In the observation region S, a scattered field
The electric field integral equation with the current term J (r') can be defined as:
to facilitate the introduction of MoM to discretize equations (1) and (2), the calculation region Ω is discretized into M small square units, m=m 1 ×M 2 ,M 1 ,M 2 The number of x-axis and y-axis directions are indicated, respectively. If the small cells that are separated become much smaller than one tenth wavelength, the induced current in each cell and the total field can be considered the same. Thus, equation (1) can be discretized into:
wherein ,
and->
The total field and the incident field of the corresponding pair of mth grids at the p-th incidence are shown respectively. A is that m′ Representing the area of the m' th mesh; />
At the p-th incidence, the induction current of the m' th grid. All grids in the calculation region Ω are integrated, and the equation (3) can be written in the form of the following matrix:
wherein 
A two-dimensional free space green's formula, representing the difference between the scattered fields from the induced current into the calculated region Ω, can be expressed as:
vector-form induced current
Representing the current distribution of all cell dispersion at the p-th incidence, it can be expressed as:
wherein ,
is a diagonal matrix, each element on the diagonal corresponding to the contrast of each grid. Substituting equation (4) into equation (6) can yield the state equation, expressed as follows:
similarly, the fringe field at observation region S can be discretized into data equations, expressed as follows:
wherein ,
a two-dimensional green' S formula representing the relationship between the induced current in the calculated region Ω to the scattered field in the observation region S.
Solving the state equation of the induced current using a conventional MoM can be expressed as:
wherein ,
representing the identity matrix. After the induced current is obtained by using the formula (9), the scattered field can be obtained by using the formula (8).
It can be seen that when the induced current is calculated by using the formula (9), the calculation complexity is high and the calculation amount is very large when the calculation area Ω is large, so that the induced current is calculated by using the conjugate gradient fast fourier transform (CG-FFT) in this example, and the calculation efficiency is greatly improved.
The Conjugate Gradient (CG) method is a mathematical method for solving an unconstrained optimization problem by using an iterative direction that is conjugate rather than local, and generally converges faster than the steepest descent method.
In complex space, the conjugate gradient method can solve the following linear equation system,
equivalent to solving the following minimization problem:
by inducing current
As an unknown quantity->
Equation (9) can be converted into equation (10) and then solved by using the conjugate gradient method.
The conjugate gradient method comprises the following solving steps:
1) Setting an initial value x 0 ，r 0 ＝g 0 ＝Ax 0 -b；
2) Determining a 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) Setting an iteration termination condition, judging whether the iteration termination condition is met, if not, turning to the step 3), and if so, obtaining x.
Wherein the upper right hand corner of the variable represents the conjugate transpose symbol.
When solving by conjugate gradient method, a large number of matrix operations are involved, and after conversion is performed by considering formula (9)
As a Toeplitz matrix, a Fast Fourier Transform (FFT) can be used to perform matrix operations, which greatly reduces computational complexity. In the solving step, form A * r k ，AP k Can be operated by FFT to AP k For example, the operation can be reduced to
Where a is a vector composed of data of the first row and the first column in the matrix a, and FFT is a discrete fourier transform. From the above, the matrix calculation amount is greatly reduced.
By the above method, the induced current in the sample is obtained.
Network design:
the invention designs an AI learning type network as a model to complete a training prediction process, and after a sample pair is obtained, the sample pair is input into the AI learning type network to complete training, so that the relation between input information, namely a scatterer, an incident field and induced current is represented. AI may use CNN network, U-net, generate an antagonism network GAN, etc., and herein, a pix2pix GAN network is taken as an example, and the internal structure diagram of the pix2pix GAN network is shown in fig. 3.
The Pix2Pix GAN network is composed of two networks, namely a generation network G and a countermeasure network D. In the invention, the G network is actually a 5-layer U-net network and can be divided into three parts, namely downsampling, upsampling and jumping connection layers. At the last layer of the G network, the invention eliminates an activation function similar to tanh (), so that the net output is the actual diffuser value.
The purpose of the D network is to distinguish the predicted image from the real image. The Pix2Pix GAN network is based on the Condition GAN (CGAN), so the D input contains not only the predicted image of the source and G network, but also the input image as a condition. In the pix2pix GAN network, the set of vectors output by the D network instead of a scalar, allows the D to make finer discrimination on sub-region blocks on the image, in effect, each element on the vector corresponds to a receptive field on the image, a so-called patch GAN operation.
The loss functions of G and D are defined as follows using least squares GAN:
where x represents input data of the network, J MoM Representing the real current data obtained by the MoM algorithm. Lambda is an adjustable parameter that is used to adjust the parameter,
l representing true current and predicted current 1 The norm of the sample is calculated,the definition is as follows:
example 1
The experimental device structure diagram designed and adopted by the invention is shown in figure 2, and the centers of the rectangular frame and the S domain surface are both positioned at (0, 0). The size of the rectangular frame is 2 multiplied by 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 in the S domain at equal intervals, and when a sample is set, the angle of the transmitting antenna is selected to be 180 degrees (leftmost side of the S domain), and the wavelength of incident light is set to be 0.75m. Incident field
The intensity of (2) is set to +.>
The cross section of the scatterer used for training is MNIST handwriting data set, and a circle is randomly added in each data cross section for diversifying samples, and the radius range of the circle is set to be 0.15m-0.5m. The contrast of the handwriting data and the circle is that
The values vary randomly between 0.01 and 0.50, and are independent of each other. The total number of samples was 10000, of which 9500 were used for training and 500 were used for testing. The input sample is shown in FIG. 4->
Corresponding input scheme->
In order to compare the experimental result of the invention with the accuracy of the traditional MoM algorithm, the grid is firstly discretized into 64 multiplied by 64, and the induced current (marked as J) is obtained by utilizing the traditional MoM algorithm 64 ) After that, the equidistant sampling is 32×32, which is denoted as J 64to32 . Meanwhile, under the condition that the grid is divided into 32 multiplied by 32 in the traditional MoM algorithm, the calculated induced current is recorded as J 32 。J 64to32 It is the current data of the input network, and also the predicted current and J of the evaluation network 32 Is a standard of (2). J (J) pix2pix Representing the predicted current of the network.
The patchGAN in the Pix2Pix GAN network is set to 15×15, and the number N of network channels in fig. 3 is set to 64. The initial learning rate of the G and D networks was 0.0002 and was reduced by half every 100 cycles, with a total cycle of 300. The Batch size is set to 64 and the parameter λ in equation (14) is set to 100.
Fig. 5 is a graph of the current predicted by 2 networks compared to the current calculated by the conventional MoM algorithm. The contrast ratio of the first test of the experiment was 0.2, and the incident light intensity was
The contrast ratio of the second test was 0.4, the incident light intensity was +.>
Both examples have the same +.>
At the same time, the experiment is increased by->
And->
The two input schemes are used as a comparison. In the figure, (a) represents a true cross section of a calculation region; (b) Represents J 64 The method comprises the steps of carrying out a first treatment on the surface of the (c) Represents J 64to32 The method comprises the steps of carrying out a first treatment on the surface of the (d) Represents J 32 The method comprises the steps of carrying out a first treatment on the surface of the (e) Respectively J 32 And J 64to32 Absolute error of (a); (f) - (h) respectively represents->
Three predicted currents and J as network inputs 64to32 Is a graph of absolute error of (a). Table 1 contains the scatterer dielectric constant information and the average absolute error data for 2 examples.
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 by the invention,
the scheme as input is compared with the other two schemes (i.e +.>
As input), the method has a much better effect, higher precision than the traditional MoM algorithm, and can simulate the scattering field data distribution of complex scatterers outside the sample, and the calculation speed is much faster than that of the traditional algorithm.
TABLE 1 Forward Current results obtained in example 1 versus current average absolute error data obtained with conventional MoM
Example 2
The experimental device structure diagram designed and adopted by the invention is shown in figure 2, and the centers of the rectangular frame and the S domain surface are both positioned at (0, 0). The size of the rectangular frame is 2 multiplied by 2m, and the distance between the transmitting antenna and the receiving antenna is 3m from the center of the circle. The total 32 receiving antennas are arranged in the S domain at equal intervals, when a sample is arranged, the positions of the transmitting antennas are not unique, an incidence point is arranged every 10 degrees, and the incidence points are distributed between 0 degrees and 360 degrees. The wavelength of the incident light was set to 0.75m.
The cross section of the scatterer used for training is MNIST handwriting data set, and in order to diversify samples, a circle is added in each data cross section randomly, and the radius of the circle is set to be 0.15m-0.5m. The contrast between the handwritten data and the circles varies randomly between 0.01 and 0.50, and the handwritten data and the circles are independent of each other. Sample ofThe total number is 20000, of which 19000 are used for training and 1000 are used for testing. The input samples are as shown in figure 6,
corresponding input scheme->
The sampling points of the three sample transmitting antennas in the figure are respectively located at 310 degrees, 10 degrees and 80 degrees.
In order to compare the experimental results of the present invention with the conventional MoM algorithm, the grid was first discretized to 64×64, and the induced current (denoted as J 64 ) After that, the equidistant sampling is 32×32, which is denoted as J 64to32 . Meanwhile, under the condition that the grid is divided into 32 multiplied by 32 in the traditional MoM algorithm, the calculated induced current is recorded as J 32 。J 64to32 It is the current data of the input network, and also the predicted current and J of the evaluation network 32 Is a standard of (2). J (J) pxi2pix Representing the predicted current of the network.
The patchGAN in the Pix2Pix GAN network is set to 15×15, and the number N of network channels in fig. 3 is set to 64. The initial learning rate of the G and D networks was 0.0002 and was reduced by half every 100 cycles, with a total cycle of 300. The Batch size is set to 64 and the parameter λ in equation (14) is set to 100.
Fig. 7 is a graph of current predicted by 4 networks compared to current calculated by a conventional MoM algorithm. In the figure, (a) represents a true cross section of a calculation region; (b) Represents J 64 The method comprises the steps of carrying out a first treatment on the surface of the (c) Represents J 64to32 The method comprises the steps of carrying out a first treatment on the surface of the (d) Represents J 32 The method comprises the steps of carrying out a first treatment on the surface of the (e) Respectively J 32 And J 64to32 Absolute error of (a); (f) - (h) respectively represents
Three predicted currents and J as network inputs 64to32 Is a graph of absolute error of (a). Table 2 contains 4 examples of scatterer permittivity information, where the transmitting antenna is located, and average absolute error data. Fig. 8 is a plot of the reconstructed fringe field results of 4 examples versus the fringe field obtained by a conventional MoM calculation. Can be used forAs can be seen, the incident angle of the transmitting antenna of the latter two examples is outside the sample selection point, and the predicted current data is still accurate, so that the prediction of the scattered field data at any transmitting position of the antenna is realized. Meanwhile, under the same grid division, the forward current learning method adopted by the present invention, < >>
The input scheme is higher in accuracy than the traditional MoM algorithm, can simulate the scattering field data distribution of complex scatterers outside the sample, and is higher in calculation speed than the traditional algorithm.
TABLE 2 Forward Current results obtained in example 2 and current average absolute error data obtained with conventional MoM
The two examples are merely illustrative of the method of the present invention and are not intended to limit the invention, and the invention is not limited to the two examples, and the invention falls within the scope of the method of the present invention as long as the requirements of the method of the invention are met.
Claims (10)
1. AI learning type electromagnetic scattering calculation method suitable for arbitrary incident field, and training and learning contrast ratio by using AI learning network
Incident wave->
A nonlinear relationship between the induced currents characterized by:
sample design: to introduce known information, network input employs
As input, forward current data is calculated as a true 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.
2. The AI-learning electromagnetic scattering calculation method for any incident field according to claim 1, wherein the forward current data calculation method is moment method MoM, finite element method FEM, time domain finite difference method FDTD.
3. The AI-learning electromagnetic scattering calculation method for any incident field according to claim 1, wherein the forward current data calculation method is a moment method MoM calculation step as follows:
the total field integral equation is:
wherein ,
and />
Respectively represent the total field and the incident field, r and r ′ Respectively representing the field point and the source point of the p-th incidence; />
For two-dimensional free space green's formula, a point source located in space r is expressed for a point r in space around it ′ A generated field in which ∈>
For the first class of zero-order hank functions, i represents the imaginary number, k 0 Is the wave number of the elastic wave, χ (r) ′ )＝(ε(r ′ )-∈ 0 )/∈ 0 It is E r E, e 0 Representing some physical property of the medium through which the elastic wave passes; omega denotes the calculation region, induced current J (r ′ ) Can be defined as
In the observation region S, the scattering field +.>
With current term J (r ′ ) The electric field integral equation of (2) can be defined as:
to facilitate the introduction of MoM to discretize equations (1) and (2), the calculation region Ω is discretized into M small square units, m=m 1 ×M 2 ,M 1 ,M 2 Representing the number of x-axis and y-axis directions, respectively, if the small cells being separated become much smaller than one tenth wavelength, the induced current in each cell and the total field can be considered to be the same, and therefore, equation (1) can be discretized as:
wherein ,
and->
Respectively represents the total field and the incident field of the corresponding mth grid at the p-th incidence, A m′ Represents the mth ′ The area of the individual grids; />
At the p-th incidence, the m-th ′ The induced currents of the grids are calculated comprehensively, and the following matrix form can be written in the equation (3):
wherein 
A two-dimensional free space green's formula, representing the difference between the scattered fields from the induced current into the calculated region Ω, can be expressed as:
vector-form induced current
Representing the current distribution of all cell dispersion at the p-th incidence, it can be expressed as:
wherein ,
is a diagonal matrix, each element on the diagonal corresponds to the contrast of each grid, and the equation (4) is substituted into the equation (6), so that a state equation can be obtained, which is expressed as follows:
similarly, the fringe field at observation region S can be discretized into data equations, expressed as follows:
wherein ,
a two-dimensional green formula representing the relationship between the induced current in the calculation region Ω to the scattered field in the observation region S;
solving the state equation of the induced current using a conventional MoM can be expressed as:
wherein ,
the unit matrix is expressed, and the induced current is obtained by using the formula (9), and then the fringe field is obtained by using the formula (8).
4. The method for calculating the AI-learning type electromagnetic scattering suitable for any incident field as claimed in claim 3, wherein the method of calculating the induced current in the formula (9) is replaced by solving the induced current by using a conjugate gradient fast Fourier transform (CG-FFT), wherein in a complex space, the conjugate gradient method can solve the following linear equation system,
equivalent to solving the following minimization problem:
by inducing current
As an unknown quantity->
Equation (9) can be converted into equation (10) and then solved by using the conjugate gradient method.
5. The AI-learning electromagnetic scattering calculation method for any incident field of claim 4, wherein the conjugate gradient method solving steps are as follows:
1) Setting an initial value x 0 ，r 0 ＝g 0 ＝Ax 0 -b；
2) Determining a first gradient search direction: p (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) Setting iteration termination conditions and judging whether the iteration termination conditions are met, if not, turning to the step 3),
if yes, obtaining x;
wherein the upper right hand corner of the variable represents the conjugate transpose symbol;
when solving by conjugate gradient method, a large number of matrix operations are involved, and after conversion is performed by considering formula (9)
Is Toeplitz matrix, so that matrix operation can be performed by Fast Fourier Transform (FFT), and the form A is obtained in the solving step * r k ，AP k Can be operated by FFT, AP k The operation of (2) can be simplified into
Where a is a vector composed of data of the first row and the first column in the matrix a, and FFT is a discrete fourier transform.
6. The AI-learning electromagnetic scattering calculation method for any incident field according to claim 1, wherein the AI-learning network uses a CNN network, U-net, to generate an antagonism network GAN, pix2Pix GAN network.
7. The AI-learning electromagnetic scattering calculation method for any incident field according to claim 1, wherein the AI-learning network is a Pix2Pix GAN network, and the Pix2Pix GAN network is composed of two networks, namely a generation network G and an countermeasure network D.
8. The AI-learning electromagnetic scattering computation method of claim 7, wherein the generation network G is a substantially 5-layer U-net network including downsampling, upsampling, and jumping connection layers, and wherein at the last layer of the generation network G, the network outputs the actual values of the scatterers directly, without using an activation function like tanh ().
9. The AI-learning electromagnetic scattering computation method of claim 7, wherein said input to the countermeasure network D comprises a set of vectors that are derived from and conditioned by the predictive image and the input image of the generation network G, and output from the countermeasure network D.
10. The AI-learning electromagnetic scattering computation method of claim 7, wherein the loss functions of the generation network G and the countermeasure network D are least squares GAN, defined as follows:
where x represents input data of the network, J MoM Representing real current data obtained by a MoM algorithm; lambda is an adjustable parameter that is used to adjust the parameter,
l representing true current and predicted current 1 Norms, defined as:
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