Electromagnetic inverse scattering solving method and system

Abstract

The invention relates to an electromagnetic inverse scattering solving method and system, and the method comprises the steps: S1, constructing a scatterer electromagnetic scattering equation in an integral form, and converting the scatterer electromagnetic scattering equation into a matrix operation form; s2, calculating an initial solution of an inverse scattering problem through a contrast source inversion method according to scattered fields under plane waves of different incident angles; s3, constructing two groups of neural networks to respectively predict total electric field distribution and relative dielectric constant distribution of a scatterer, and pre-training the two groups of neural networks according to an initial solution of an inverse scattering problem; and S4, introducing a state equation and a data equation into the loss function as physical constraints, and carrying out training solution by adopting the two groups of pre-trained neural networks to obtain predicted total electric field distribution and relative dielectric constant distribution of the scatterer so as to realize electromagnetic inverse scattering solution. Compared with the prior art, the method can realize high-precision electromagnetic inverse scattering solution under the condition of no data set requirement.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of electromagnetic inverse scattering, and in particular to an electromagnetic inverse scattering solving method and system. BACKGROUND

[0002] The electromagnetic inverse scattering problem is an important research direction in computational physics, and the goal is to inversely deduce the geometric shape, medium distribution and physical parameters of the target object by measuring the scattering field information of the object under the excitation of external electromagnetic waves. Compared with the calculation of the scattering field problem, the inverse scattering problem belongs to the uncertain problem, that is, the uncertainty, instability and sensitivity to noise of the solution. In the field of electromagnetics, the inverse scattering problem is widely used in radar imaging, geophysical exploration, medical imaging, non-destructive testing of parts and case detection and other application scenarios.

[0003] For the inverse scattering problem, the number of scattering field information obtained is usually much smaller than the number of physical parameters of the target object to be solved, so the inverse scattering problem has serious nonlinearity and ill-posedness, and it is difficult to obtain a stable solution by using traditional analytical methods. Common solving methods mainly include iterative algorithms based on optimization process (such as contrast source inversion method, subspace optimization algorithm, etc.), Born approximation method based on integral equation, and some regularization techniques. The traditional numerical algorithm mainly has the following problems: 1) high nonlinearity and ill-posedness, the mapping relationship between the scattering field and the target parameters is complex, which leads to unstable inversion solution; 2) limited measurement data and noise sensitivity, in actual application, the data of the measurement points is limited, which leads to the decrease of the inversion accuracy, and the experimental noise will be amplified; 3) dependence on prior information, many algorithms depend on the prior assumptions of the shape of the target and the medium characteristics.

[0004] In recent years, methods combining machine learning and neural networks have gradually emerged, which greatly improves the reconstruction accuracy and speed of inverse scattering imaging. However, at present, most of the neural network-based methods require a large amount of data set and a large amount of neural network training time, which greatly increases the solving cost of the inverse scattering problem. SUMMARY

[0005] The purpose of the present application is to overcome the defects of the prior art and provide an electromagnetic inverse scattering solving method and system, which can realize high-precision electromagnetic inverse scattering solving without data set.

[0006] The purpose of the present application can be achieved by the following technical solutions: According to a first aspect of the present application, an electromagnetic inverse scattering solving method is provided, comprising: S1, constructing an integral form of the scattering body electromagnetic scattering equation, and converting it into a matrix operation form; S2. Based on the scattered field of plane waves at different incident angles, calculate the initial solution of the inverse scattering problem by the comparative source inversion method; S3. Construct two sets of neural networks to predict the total electric field distribution and the relative permittivity distribution of the scatterer, respectively, and pre-train the two sets of neural networks based on the initial solution of the inverse scattering problem; S4. State equations and data equations are introduced into the loss function as physical constraints. Two pre-trained neural networks are used for training and solving to obtain the predicted total electric field distribution and the relative permittivity distribution of the scatterer, thus realizing the solution of electromagnetic inverse scattering.

[0007] Preferably, in step S1, the electromagnetic scattering equation of the scatterer is constructed in integral form and transformed into matrix operation form, specifically including: S101. Based on the volume integral method, construct the integral form of the electromagnetic scattering equation of the scatterer, the expression of which is: , , in, It is the incident electric field. It is the total electric field. It is a scattered field. It is the free space wavenumber. It is angular frequency. It is the vacuum permeability. It is the vacuum permittivity. It is a two-dimensional Green's function in free space. These are the coordinates of the electric field position to be solved. These are the coordinates of the integration region. It is the solution domain. It is the measurement region of the scattered field. It is the electromagnetic property function of the material to be solved; S102. The solution domain is transformed into a grid domain using the method of moments, and the integral form of the electromagnetic scattering equation of the scatterer is transformed into a matrix operation form, as shown in the following expression: , , in, It is the discrete total electric field. It is a discrete scattering field. It is a discrete incident field. The solution domain Green's function in discrete free space, It is the discrete free-space Green's function that maps the solution domain to the scattering domain. These are discrete electromagnetic properties of materials.

[0008] Preferably, the solution region Green's function in discrete free space The calculation expression is: , in, and The center coordinate vector of a discrete regular grid. For a Bessel function of the first kind, It is a Hankel function of the first kind of order 0. It is a first-order Hankel function of the first kind. The equivalent radius of the regular grid. The side length of the regular grid. i It is the imaginary unit.

[0009] Preferably, the step of calculating the initial solution for reconstructing the scatterer based on the scattered field under plane waves at different incident angles using the source inversion method specifically includes: Construct the objective function for the comparative source inversion method: , in, For the first The contrast current corresponding to each incident wave For the first Discrete electric fields corresponding to each incident wave For the first An incident wave in the measurement area The measured scattering field, For the first The incident field corresponding to each incident wave The number of incident antennas, The measurement area for the scattered field L2 norm on To solve the region L2 norm on; The objective function is optimized using the conjugate gradient method to obtain the initial solution to the inverse scattering problem.

[0010] Preferably, in step S3, two sets of neural networks are constructed to predict the total electric field distribution and the relative permittivity distribution of the scatterer, respectively, specifically including: The first set of neural networks contains multiple first neural networks, the number of which is the same as the number of incident fields. The input of each first neural network is the coordinates of the sampling points in the solution region. The output is the total electric field distribution of the corresponding incident field. The subscript p corresponds to the p-th incident field; The second set of neural networks includes a second neural network used to predict the relative permittivity distribution of the scatterer. The input of the second neural network is the coordinates of the sampling points in the solution region. The output is a relative permittivity distribution. .

[0011] Preferably, in the pre-training process of S3, the loss function used by the first neural network is... Specifically: , in, This represents the total electric field distribution of the p-th incident field obtained using the comparative source inversion method. This represents the total electric field distribution output by the first neural network corresponding to the p-th incident field. For the number of incident fields, The attenuation coefficient is... This represents the number of pre-training iterations.

[0012] Preferably, the first neural network and the second neural network adopt a fully connected neural network structure, wherein, before training and solving S4, an additional parameter is added to the output of the second neural network. Activation function layer.

[0013] Preferably, in step S4, state equations and data equations are introduced into the loss function as physical constraints, specifically including: State loss term corresponding to the state equation The expression is: , in, For the number of incident fields, This represents the total electric field distribution output by the first neural network corresponding to the p-th incident field. It is a two-dimensional free space Green's function. For discrete electromagnetic properties of materials, Let p be the discrete incident field corresponding to the p-th incident field; and the data loss term corresponding to the data equation The expression is: , in, It is the two-dimensional free-space Green's function for calculating the scattered field. For the first Each incident wave corresponds to a discrete scattering field.

[0014] Preferably, the loss function in S4 The calculation expression is: , , in, This refers to the data loss term corresponding to the data equation. This refers to the data loss term corresponding to the data equation. The coefficients of the global variational regularization term are . For global variational regularization, The number of grid cells used to spatially discretize the solution domain. The first relative permittivity matrix obtained by neural network estimation is the first... Line number The element values ​​of the column.

[0015] According to a second aspect of the present invention, an electromagnetic inverse scattering solution system is provided, employing the above-described method, the system comprising: The module is used to construct the integral form of the electromagnetic scattering equation of the scatterer and convert it into matrix operation form; The initial solution module is used to calculate the initial solution of the inverse scattering problem based on the scattered field of plane waves at different incident angles by using the comparative source inversion method. The pre-training module is used to construct two sets of neural networks to predict the total electric field distribution and the relative permittivity distribution of the scatterer, respectively, and to pre-train the two sets of neural networks based on the initial solution of the inverse scattering problem. The training and solving module is used to introduce state equations and data equations as physical constraints into the loss function. It uses two pre-trained neural networks for training and solving to obtain the predicted total electric field distribution and the relative permittivity distribution of the scatterer, thus realizing the electromagnetic inverse scattering solution.

[0016] Compared with the prior art, the present invention has the following beneficial effects: (1) This invention uses two sets of physical-driven neural networks to solve electromagnetic inverse scattering. The training process of the neural network is guided by the physical process of the inverse scattering problem. Compared with the traditional data-driven neural network method, it does not require the construction of a large dataset, which reduces the time cost and computing resources of constructing the dataset and large-scale training. At the same time, the inverse scattering solution is more flexible and the solution results are more accurate and reliable.

[0017] (2) The initial solution of the reconstructed scatterer was calculated by using the comparative source inversion method. The two sets of neural networks were pre-trained respectively, which improved the stability of the neural networks and enabled the calculation results of the neural networks to converge faster and more accurately.

[0018] (3) In the pre-training stage, an exponential decay coefficient is introduced into the loss function of the first neural network used to estimate the total electric field distribution, making the training process more stable.

[0019] (4) Considering the consistency of the relative permittivity of the material and the characteristic that the material is a whole, a global variational regularization term is introduced into the loss function in the training and solving stage to effectively solve the noise problem and guide the neural network to estimate a more accurate solution. Attached Figure Description

[0020] Figure 1 This is a flowchart of the method of the present invention.

[0021] Figure 2 This is a schematic diagram of the residual neural network structure in the embodiment.

[0022] Figure 3 This is a schematic diagram of the architecture for optimizing the solution process in the embodiment.

[0023] Figure 4 This is a schematic diagram of the original scattering field of the scatterer in the embodiment.

[0024] Figure 5 The diagram shows the results of contrastive inversion reconstruction and the reconstruction results of the method of the present invention in the embodiment; wherein (a) to (c) correspond to the original scattering field of the scatterer, the results of contrastive inversion reconstruction and the reconstruction results of the method of the present invention, respectively.

[0025] Figure 6 Comparison of scattered fields under different global variational canonical coefficients; where (a) corresponds to the original scattered field of the scatterer, and (b) corresponds to... and (c) corresponds to and (d) corresponds to and (e) corresponds to and (f) corresponds to and .

[0026] Figure 7 This diagram illustrates the change in structural similarity during the training and solving of a neural network after adding a regularization term. Detailed Implementation

[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0028] Example 1 like Figure 1As shown, this embodiment provides a method for solving electromagnetic inverse scattering, which includes: S1. Construct the integral form of the electromagnetic scattering equation of the scatterer and transform it into matrix operation form, which includes the following sub-steps: S101. Based on the volume integral method, construct the integral form of the electromagnetic scattering equation of the scatterer, the expression of which is: , , in, It is the incident electric field. It is the total electric field. It is a scattered field. It is the free space wavenumber. It is angular frequency. It is the vacuum permeability. It is the vacuum permittivity. It is a two-dimensional Green's function in free space. These are the coordinates of the electric field position to be solved. These are the coordinates of the integration region. It is the solution domain. It is the measurement region of the scattered field. It is the electromagnetic property function of the material to be solved; S102. The solution domain is transformed into a grid domain using the method of moments, and the integral form of the electromagnetic scattering equation of the scatterer is transformed into a matrix operation form, as shown in the following expression: , , in, It is the discrete total electric field. It is a discrete scattering field. It is a discrete incident field. The solution domain Green's function in discrete free space, It is the discrete free-space Green's function that maps the solution domain to the scattering domain. These are discrete electromagnetic properties of materials.

[0029] Solution domain Green's function in discrete free space The calculation expression is: , in, and The center coordinate vector of a discrete regular grid. For a Bessel function of the first kind, It is a Hankel function of the first kind of order 0. It is a first-order Hankel function of the first kind. The equivalent radius of the regular grid. The side length of the regular grid. i It is the imaginary unit.

[0030] S2. Based on the scattered field under plane waves at different incident angles, the initial solution to the inverse scattering problem is calculated using the contrastive source inversion method. The contrastive source inversion method reconstructs the scatterer by minimizing the constructed objective function through optimization. The conjugate gradient method is used to optimize the objective function to obtain the initial solution to the inverse scattering problem. Specifically, this includes: S201. Based on the electromagnetic scattering equation of the scatterer, construct the objective function of the contrast source inversion method: , in, For the first The contrast current corresponding to each incident wave For the first Discrete electric fields corresponding to each incident wave For the first An incident wave in the measurement area The measured scattering field, For the first The incident field corresponding to each incident wave The number of incident antennas, The measurement area for the scattered field L2 norm on To solve the region The L2 norm on.

[0031] S202. Calculate the derivative of the objective function with respect to the current to be solved. : , in, Indicates the first The comparison current obtained after the second iteration. Indicates the first The relative permittivity obtained after the iteration.

[0032] S203. Calculate the update direction for each iteration based on the derivative of the objective function with respect to the comparison current: , in, Indicates the first The update direction of the contrast current obtained after the next iteration.

[0033] S204. Based on the obtained update direction, calculate the comparison current after each iteration: , in, Indicates the first The update coefficients of the comparison current in the next iteration.

[0034] S205. Calculate the initial solution obtained by the comparative current inversion method: .

[0035] S3. Construct two sets of neural networks to predict the total electric field distribution and the relative permittivity distribution of the scatterer, respectively, and pre-train the two sets of neural networks based on the initial solution of the inverse scattering problem.

[0036] The first set of neural networks contains multiple first neural networks, the number of which is the same as the number of incident fields. The input of the first neural network is the coordinates of the sampling points in the solution region. The output is the total electric field distribution of the corresponding incident field. , is represented as: The subscript p corresponds to the p-th incident field. This represents the first neural network that estimates the total electric field. For the number of incident fields, Indicates the use of estimating the first The first neural network of the total electric field of each incident field.

[0037] The second set of neural networks includes a second neural network used to predict the relative permittivity distribution of the scatterer. The input to the second neural network is the coordinates of the sampling points in the solution region. The output is a relative permittivity distribution. , is represented as: , For the second neural network, These are the parameters of the second neural network.

[0038] In this embodiment, the first neural network and the second neural network adopt a fully connected neural network structure, such as... Figure 2 As shown, the input to the neural network is the coordinates of points uniformly sampled in the solution region. The outputs of the neural network are the predicted distribution of relative permittivity and the total electric field distribution, respectively.

[0039] Since the network parameters and output of a neural network are initialized randomly, training the network with a random initial solution can lead to it getting trapped in local optima during training, resulting in inaccurate inverse scattering solutions. Therefore, pre-training the neural network with a preliminary estimate from the contrast source inversion method is necessary. This pre-training process not only accelerates the training process but also increases the accuracy of the inverse scattering solution estimation.

[0040] The pre-training process consists of two parts: pre-training the neural network for estimating the relative permittivity and pre-training the neural network for estimating the total electric field. The pre-training process uses the relative permittivity distribution and total electric field distribution obtained by the relative source inversion method as reference solutions to train a randomly initialized neural network, giving it a good initial solution for formal training.

[0041] (1) The process of pre-training the first neural network for estimating the total electric field involves setting the coordinates of the sampling points. Introducing a neural network to estimate the total electric field distribution In this process, the estimated total electric field distribution for the p-th incident field is obtained. The estimated solution is compared with the total electric field distribution obtained by the source inversion method. By subtracting the values, we obtain the corresponding pre-trained loss function: , in, This represents the total electric field distribution of the p-th incident field obtained using the comparative source inversion method. This represents the total electric field distribution output by the first neural network corresponding to the p-th incident field. The number of incident fields; The attenuation coefficient is used to make the training process more stable through the attenuation process of the loss function. The number of pre-training iterations is set to 2000 in this embodiment.

[0042] (2) The process of pre-training the second neural network for estimating the relative permittivity.

[0043] The coordinates of the points sampled in the solution domain The relative permittivity is input into the neural network used to estimate it. In this process, the estimated distribution of relative permittivity is obtained. The estimated relative permittivity distribution is compared with the relative permittivity distribution obtained by the source inversion method. By subtracting the values, we obtain the pre-trained loss function of the neural network that estimates the relative permittivity: , The pre-training process lasts approximately 2000 iterations, giving the neural network that estimates the relative permittivity a reasonable initial solution.

[0044] In this embodiment, the Adamw optimizer is used to minimize the loss function and pre-train the neural network.

[0045] S4. State equations and data equations are introduced into the loss function as physical constraints. Two pre-trained neural networks are used for training and solving to obtain the predicted total electric field distribution and the relative permittivity distribution of the scatterer, thus realizing the solution of electromagnetic inverse scattering.

[0046] Loss function during training and solving The calculation expression is: , Among them, the state loss term corresponding to the state equation The expression is: , in, For the number of incident fields, This represents the total electric field distribution output by the first neural network corresponding to the p-th incident field. It is a two-dimensional free space Green's function. For discrete electromagnetic properties of materials, Let p be the discrete incident field corresponding to the p-th incident field; Data loss term corresponding to the data equation The expression is: , in, It is the two-dimensional free-space Green's function for calculating the scattered field. The scattered field distribution is obtained by measuring the p-th incident field.

[0047] As another preferred embodiment, before training and solving S4, an additional parameter is added to the output of the second neural network. Activation function layer.

[0048] Specifically, in real-world physics, the relative permittivity is never less than 0. To make the neural network output more consistent with physical laws and further improve the accuracy of the inverse scattering problem solution, when the loss function is less than 0, i.e., when the neural network training reaches a certain level of accuracy, a factor is added to the output of the second neural network estimating the relative permittivity. Activation function layer.

[0049] The function of this activation function is to change the portion of the relative permittivity that is greater than 0, without altering the portion of the output relative permittivity that is less than 0, thus making the output of the neural network more consistent with real-world physical laws. This also allows us to reconstruct a more accurate distribution of the relative permittivity.

[0050] In this embodiment, no activation function layer is added to the second neural network in the initial pre-training process for the following reasons: Although ReLU() activation can turn negative inputs into 0, it can also cause the gradient vanishing problem in the negative input portion of the neural network. Therefore, when the neural network's estimated solution is not accurate enough, adding the ReLU() activation function will cause the estimated relative permittivity solution to suddenly deteriorate. Furthermore, due to the gradient vanishing problem, the deteriorated part is difficult to improve in subsequent training, making the reconstructed relative permittivity even worse.

[0051] To verify the accuracy and efficiency of this invention, a calculation and analysis were performed on an electromagnetic inverse scattering problem. The solution domain is a... The square region was decomposed into The solution frequency for electromagnetic scattering in the sub-region is 400 MHz. The scatterer structure follows the Austrian model, a common model for inverse scattering problems, with an equivalent relative permittivity of 2. For example... Figure 4 As shown, the scatterer consists of two circles, each centered at... and A circle with a radius of 0.2m and a center at... It consists of a ring with an inner diameter of 0.3m and an outer diameter of 0.6m.

[0052] During neural network training, the network underwent 2000 iterations of pre-training and 23000 training iterations. The resulting reconstruction was compared with that of traditional numerical methods. Figure 5 As shown, by comparing the data reconstructed by the present invention with the data reconstructed by the comparative inversion method, it can be seen that the present invention can more accurately reconstruct the shape and physical properties of the scatterer from the measured scattering field.

[0053] This embodiment also provides an electromagnetic inverse scattering solution system, which employs the above method and includes: The module is used to construct the integral form of the electromagnetic scattering equation of the scatterer and convert it into matrix operation form; The initial solution module is used to calculate the initial solution of the inverse scattering problem based on the scattered field of plane waves at different incident angles by using the comparative source inversion method. The pre-training module is used to construct two sets of neural networks to predict the total electric field distribution and the relative permittivity distribution of the scatterer, respectively, and to pre-train the two sets of neural networks based on the initial solution of the inverse scattering problem. The training and solving module is used to introduce state equations and data equations as physical constraints into the loss function. It uses two pre-trained neural networks for training and solving to obtain the predicted total electric field distribution and the relative permittivity distribution of the scatterer, thus realizing the electromagnetic inverse scattering solution.

[0054] Example 2 In this embodiment, considering that the relative permittivity of materials is usually uniform and the material is a single unit, therefore, in this embodiment, during the training and solving process, in the loss function... Adding a regularization term guides the neural network to estimate more accurate solutions. The process of adding a regularization term can effectively solve noisy problems.

[0055] Specifically, the loss function after adding a regularization term In the expression, the calculation is as follows: , , in, This refers to the data loss term corresponding to the data equation. This refers to the data loss term corresponding to the data equation. The coefficients of the global variational regularization term are . For global variational regularization, The number of grid cells used to spatially discretize the solution domain. The first relative permittivity matrix obtained by neural network estimation is the first... Line number The element values ​​of the column.

[0056] Figure 6 For different coefficients The inverse scattering results are illustrated below, as shown in the diagram. Figure 7 As shown, the structural similarity of the reconstructed relative permittivity is significantly improved after adding the regularization term.

[0057] The other settings in this embodiment are the same as in Embodiment 1.

[0058] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for solving electromagnetic inverse scattering, characterized in that, include: S1. Construct the electromagnetic scattering equation of the scatterer in integral form and transform it into matrix operation form; S2. Based on the scattered field of plane waves at different incident angles, calculate the initial solution of the inverse scattering problem by the comparative source inversion method; S3. Construct two sets of neural networks to predict the total electric field distribution and the relative permittivity distribution of the scatterer, respectively, and pre-train the two sets of neural networks based on the initial solution of the inverse scattering problem; S4. State equations and data equations are introduced into the loss function as physical constraints. Two pre-trained neural networks are used for training and solving to obtain the predicted total electric field distribution and the relative permittivity distribution of the scatterer, thus realizing the solution of electromagnetic inverse scattering.

2. The electromagnetic inverse scattering solution method according to claim 1, characterized in that, The integral form of the electromagnetic scattering equation of the scatterer in S1 is constructed and transformed into matrix operation form, specifically including: S101. Based on the volume integral method, construct the integral form of the electromagnetic scattering equation of the scatterer, the expression of which is: ， ， in, It is the incident electric field. It is the total electric field. It is a scattered field. It is the free space wavenumber. It is angular frequency. It is the vacuum permeability. It is the vacuum permittivity. It is a two-dimensional Green's function in free space. These are the coordinates of the electric field position to be solved. These are the coordinates of the integration region. It is the solution domain. It is the measurement region of the scattered field. It is the electromagnetic property function of the material to be solved; S102. The solution domain is transformed into a grid domain using the method of moments, and the integral form of the electromagnetic scattering equation of the scatterer is transformed into a matrix operation form, as shown in the following expression: ， ， in, It is the discrete total electric field. It is a discrete scattering field. It is a discrete incident field. The solution domain Green's function in discrete free space, It is the discrete free-space Green's function that maps the solution domain to the scattering domain. These are discrete electromagnetic properties of materials.

3. The electromagnetic inverse scattering solution method according to claim 2, characterized in that, The solution region Green's function in discrete free space The calculation expression is: ， in, and The center coordinate vector of a discrete regular grid. For a Bessel function of the first kind, It is a Hankel function of the first kind of order 0. It is a first-order Hankel function of the first kind. The equivalent radius of the regular grid. The side length of the regular grid. i It is the imaginary unit.

4. The electromagnetic inverse scattering solution method according to claim 2, characterized in that, The method of calculating and reconstructing the initial solution of the scattering body based on the scattering field under plane waves at different incident angles using the source inversion method specifically includes: Construct the objective function for the comparative source inversion method: ， in, For the first The contrast current corresponding to each incident wave For the first Discrete electric fields corresponding to each incident wave For the first An incident wave in the measurement area The measured scattering field, For the first The incident field corresponding to each incident wave The number of incident antennas, The measurement area for the scattered field L2 norm on To solve the region L2 norm on; The objective function is optimized using the conjugate gradient method to obtain the initial solution to the inverse scattering problem.

5. The electromagnetic inverse scattering solution method according to claim 2, characterized in that, In S3, two sets of neural networks are constructed to predict the total electric field distribution and the relative permittivity distribution of the scatterer, respectively. Specifically, this includes: The first set of neural networks contains multiple first neural networks, the number of which is the same as the number of incident fields. The input of each first neural network is the coordinates of the sampling points in the solution region. The output is the total electric field distribution of the corresponding incident field. The subscript p corresponds to the p-th incident field; The second set of neural networks includes a second neural network used to predict the relative permittivity distribution of the scatterer. The input of the second neural network is the coordinates of the sampling points in the solution region. The output is a relative permittivity distribution. .

6. The electromagnetic inverse scattering solution method according to claim 5, characterized in that, In the pre-training process of S3, the loss function used by the first neural network is... Specifically: ， in, This represents the total electric field distribution of the p-th incident field obtained using the comparative source inversion method. This represents the total electric field distribution output by the first neural network corresponding to the p-th incident field. For the number of incident fields, The attenuation coefficient is... This represents the number of pre-training iterations.

7. The electromagnetic inverse scattering solution method according to claim 5, characterized in that, The first and second neural networks adopt a fully connected neural network structure. Before training and solving S4, an additional parameter is added to the output of the second neural network. Activation function layer.

8. The electromagnetic inverse scattering solution method according to claim 2, characterized in that, In step S4, state equations and data equations are introduced into the loss function as physical constraints, specifically including: State loss term corresponding to the state equation The expression is: ， in, For the number of incident fields, This represents the total electric field distribution output by the first neural network corresponding to the p-th incident field. It is a two-dimensional free space Green's function. For discrete electromagnetic properties of materials, Let be the discrete incident field corresponding to the p-th incident field; and the data loss term corresponding to the data equation The expression is: ， in, It is the two-dimensional free-space Green's function for calculating the scattered field. For the first Each incident wave corresponds to a discrete scattering field.

9. The electromagnetic inverse scattering solution method according to claim 2, characterized in that, The loss function in S4 The calculation expression is: ， ， in, This refers to the data loss term corresponding to the data equation. This refers to the data loss term corresponding to the data equation. The coefficients of the global variational regularization term are . For global variational regularization, The number of grid cells used to spatially discretize the solution domain. The first relative permittivity matrix obtained by neural network estimation is the first... Line number The element values ​​of the column.

10. An electromagnetic inverse scattering solution system, characterized in that, The system, employing the method of claim 1, comprises: The module is used to construct the integral form of the electromagnetic scattering equation of the scatterer and convert it into matrix operation form; The initial solution module is used to calculate the initial solution of the inverse scattering problem based on the scattered field of plane waves at different incident angles by using the comparative source inversion method. The pre-training module is used to construct two sets of neural networks to predict the total electric field distribution and the relative permittivity distribution of the scatterer, respectively, and to pre-train the two sets of neural networks based on the initial solution of the inverse scattering problem. The training and solving module is used to introduce state equations and data equations as physical constraints into the loss function. It uses two pre-trained neural networks for training and solving to obtain the predicted total electric field distribution and the relative permittivity distribution of the scatterer, thus realizing the electromagnetic inverse scattering solution.

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