Electromagnetic scattering calculation method based on deep learning

Abstract

The invention discloses an electromagnetic scattering calculation method based on deep learning under the condition that the shape and electrical parameters of a scatterer are not completely known. The electromagnetic scattering calculation method comprises the following steps: step 1, inputting electrical parameters of a known part of the scatterer, such as relative dielectric constant and magnetic conductivity, an incident field, a small amount of scattered field (observation / measurement) data and position coordinates of a to-be-solved scattered field; 2, solving an internal total field under the condition that only the known part of the scatterer exists and the unknown part does not exist by adopting a moment method; 3, inputting a small amount of scattered field (observation / measurement) data, an internal total field under the condition that only the known part of the scatterer exists and the unknown part does not exist, and the electrical parameters of the known part of the scatterer into a deep learning neural network, and obtaining the electrical parameters of the unknown part of the scatterer through the network, such as a relative dielectric constant and magnetic conductivity; 4, inputting the internal total field under the condition that only the known part of the scatterer exists and the unknown part does not exist, the electrical parameters of the unknown part of the scatterer and the electrical parameters of the known part of the scatterer into another neural network, and obtaining the internal total field of the complete scatterer through the network; and 5, calculating a total field or a scattering field at any position according to a moment method. According to the method, prediction of the scattering characteristics of the scatterer of which the shape and the electrical parameters are not completely known can be completed under the condition that only a very small amount of scattering field (observation / measurement) data is needed.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic scattering technology, and in particular to a deep learning-based electromagnetic scattering calculation method when the shape and electrical parameters of a scatterer are not completely known. Background Art

[0002] In the study of electromagnetic scattering, it is often assumed that the geometry and electrical parameters of the scatterer, such as relative permittivity and permeability, are completely known. For such situations, many researchers have developed methods to obtain the scattered field emitted by the scatterer under incident wave illumination. Currently, there are two main approaches to solving electromagnetic scattering problems: traditional numerical methods and artificial intelligence (AI) methods. The former can be further divided into two categories: high-frequency approximation methods and full-wave numerical methods. High-frequency approximation methods are typically used for scattering problems caused by electrically large targets. Full-wave numerical methods, on the other hand, are often used when the electrical size of the scatterer is comparable to the wavelength. Common full-wave numerical methods include the finite-difference time-domain method, the finite element method, and the method of moments. In addition to these traditional numerical methods, AI methods, particularly deep learning, have recently become an emerging technology for solving electromagnetic scattering problems. Within the framework of traditional algorithms, deep learning can leverage the ability of neural networks to fit nonlinearities, serving as accelerators or components of traditional solvers. Within the deep learning framework, specially designed neural networks can be trained using data-driven, physics-inspired, or a combination of these approaches to fit a direct mapping from input to output. But without exception, these methods require an accurate description of the scatterer, that is, the scatterer's geometric shape and electrical parameters such as relative permittivity and magnetic permeability are completely known.

[0003] However, when the geometric shape and electrical parameters of the scatterer are not completely known, these traditional or artificial intelligence methods will not be able to calculate the scattered field excited by the scatterer under the irradiation of the incident wave. The present invention proposes a solution based on deep learning for such situations, which is detailed as follows. First, the electrical parameters of the known part of the scatterer, such as relative dielectric constant and magnetic permeability, the incident field, and a small amount of scattered field (observation / measurement) data are obtained. Secondly, the method of moments is used to solve the internal total field when only the known part of the scatterer exists and the unknown part does not exist. Then, a small amount of scattered field (observation / measurement) data, the internal total field when only the known part of the scatterer exists and the unknown part does not exist, and the electrical parameters of the scattering known part are used to train a deep learning neural network, and the electrical parameters of the unknown part of the scatterer, such as relative dielectric constant and magnetic permeability, are obtained through the neural network. When the neural network training is completed, it only needs one forward calculation to complete the deduction of the electrical parameters of the unknown part of the scatterer. Then, the internal total field when only the known part of the scatterer exists and the unknown part does not exist, the electrical parameters of the unknown part of the scatterer, and the electrical parameters of the known part of the scatterer are input into another deep learning neural network for training, and the internal total field of the complete scatterer is obtained through the network. Similarly, after the neural network training is completed, only one forward calculation is needed to obtain the internal total field of the complete scatterer. Finally, according to the moment method, the scattering field generated by the scatterer after being irradiated by the incident wave can be calculated through the total field inside the scatterer. The present invention can complete the prediction of the scattering characteristics of a scatterer whose shape and electrical parameters are not completely known, under the condition that only a very small amount of scattering field (observation / measurement) data is required. Summary of the Invention

[0004] The present invention aims to provide a deep learning-based method for calculating electromagnetic scattering when the scatterer's shape and electrical parameters are incompletely known. This method first uses a neural network to extract the electrical parameters and total field of the unknown portion of the scatterer from a very small amount of scattered field (observation / measurement) data. Then, using the method of moments, it obtains the complete scattered field information generated by the scatterer when it is illuminated by an incident wave.

[0005] To achieve the above objectives, combined Figure 1 The present invention proposes a method for calculating electromagnetic scattering based on deep learning when the shape and electrical parameters of the scatterer are not completely known. The method comprises:

[0006] Step S1: Input the electrical parameters of the known part of the scatterer, such as relative permittivity and permeability, the incident field, a small amount of scattered field (observation / measurement) data, and the position coordinates of the scattered field to be determined;

[0007] Step S2: using the moment method to solve the internal total field when only the known part of the scatterer exists and the unknown part does not exist;

[0008] Step S3: A small amount of scattered field (observation / measurement) data, the total internal field when only the known part of the scatterer is present and the unknown part is absent, and the electrical parameters of the scatterer are input into a deep learning neural network. The network is used to obtain the electrical parameters of the unknown part of the scatterer, such as relative permittivity and permeability.

[0009] Step S4: inputting the total internal field when only the known part of the scatterer exists and the unknown part does not exist, the electrical parameters of the unknown part of the scatterer, and the electrical parameters of the known part of the scatterer into another neural network, and obtaining the total internal field of the complete scatterer through the network;

[0010] Step S5: Calculate the total field or scattered field at any position according to the method of moments.

[0011] In a further embodiment, in step S1, the electrical parameters of the known part of the scatterer are expressed in the form of a matrix χ p1 The incident field in the scatterer region is expressed as a matrix E inc , a small amount of scattered field (observation / measurement) data is expressed in vector form E sca , the position coordinate of the scattered field to be determined is marked as r.

[0012] In a further embodiment, the total internal field obtained by the moment method in step S2 when only the known part of the scatterer exists and the unknown part does not exist is recorded as E p1 The calculation method is as follows:

[0013] E p1 =mat[(IG D ·diag(χ p1 )) -1 vec(E inc )],

[0014] Where mat(·) means transforming the vector in the brackets into a matrix, diag(·) means constructing a diagonal matrix with the diagonal elements being the elements of the matrix or vector in the brackets, vec(·) means transforming the matrix in the brackets into a vector, I is the identity matrix, G D is the Green function matrix.

[0015] In a further embodiment, the input of the deep learning neural network in step S3 is E sca 、E p1 , and χ p1 , the output is the electrical parameter of the unknown part of the scatterer, denoted as χ p2 During the training phase, the neural network adopts the supervised batch training method, and its loss function is expressed as follows:

[0016]

[0017] Where B is the number of training set batches, M is χ p2 Number of elements, is the neural network prediction value of the b-th sample, is the label of the bth sample. After training, the neural network only needs one forward calculation to output the χ value of a specific scatterer. p2 .

[0018] In a further embodiment, the input of the deep learning neural network in step S4 is E p1 , χ p2 and χ p1 , the output is the total internal field of the complete scatterer, denoted as E tot During the training phase, the neural network adopts the supervised batch training method, and its loss function is expressed as follows:

[0019]

[0020] Where B is the number of training batches, is the neural network prediction value of the b-th sample, is the label of the bth sample. After the training is completed, the neural network only needs one forward calculation to output the total field E under the incident wave. tot .

[0021] In a further embodiment, in step S5, the scattered field at the position r to be determined is calculated from the internal total field of the complete scatterer, denoted as e(r), and the specific calculation method is as follows:

[0022]

[0023] where g S is the Green's function vector at the specific position r of the scattering area.

[0024] Compared with the existing ones, the technical solution of the present invention has the significant beneficial effect that the traditional electromagnetic scattering algorithm cannot solve the electromagnetic scattering problem when the shape and electrical parameters of the scatterer are not completely known, while the present invention can solve such problems.

[0025] It should be understood that all combinations of the foregoing concepts and the additional concepts described in more detail below, as long as such concepts are not mutually inconsistent, can be considered part of the inventive subject matter of this disclosure. In addition, all combinations of the claimed subject matter are considered part of the inventive subject matter of this disclosure.

[0026] The foregoing and other aspects, embodiments, and features of the present invention will be more fully understood from the following description in conjunction with the accompanying drawings. Other additional aspects of the present invention, such as features and / or beneficial effects of the exemplary embodiments, will become apparent from the following description or through practice of specific embodiments according to the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The accompanying drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component shown in various figures may be represented by the same reference numeral. For the sake of clarity, not every component is labeled in every figure. Embodiments of various aspects of the present invention will now be described by way of example and with reference to the accompanying drawings, in which:

[0028] Figure 1 This is a flowchart of the electromagnetic scattering calculation method based on deep learning of the present invention when the scatterer shape and electrical parameters are not completely known.

[0029] Figure 2 This is also a flowchart of the electromagnetic scattering calculation method based on deep learning of the present invention when the scatterer shape and electrical parameters are not completely known.

[0030] Figure 3 This is the solution of the invention for a two-dimensional scatterer with incompletely known shape and electrical parameters. The first column shows the actual scatterer target, the second column shows the known portion of the target, the third column gives the contrast predicted by the neural network, the fourth and seventh columns show the error between the actual and predicted values, the fifth column shows the actual total field, the sixth column shows the predicted total field, and the final column shows the predicted and actual scattered fields. DETAILED DESCRIPTION

[0031] To better understand the technical content of this invention, specific embodiments are described below with accompanying drawings. The present invention aims to provide a deep learning-based method for calculating electromagnetic scattering when the scatterer's shape and electrical parameters are incompletely known. This method first uses a neural network to obtain the electrical parameters and total field of the unknown portion of the scatterer from a very small amount of scattered field (observation / measurement) data. The method of moments then uses the method of moments to obtain the complete scattered field information generated by the scatterer being illuminated by an incident wave.

[0032] To achieve the above objectives, combined Figure 2 、 Figure 3 The present invention proposes a method for calculating electromagnetic scattering based on deep learning when the shape and electrical parameters of the scatterer are not completely known. The method comprises:

[0033] Step 1: Input the electrical parameters of the known part of the scatterer, such as relative permittivity and permeability, the incident field, a small amount of scattered field (observation / measurement) data, and the position coordinates of the scattered field to be determined;

[0034] Step 2: Use the moment method to solve the internal total field when only the known part of the scatterer exists and the unknown part does not exist;

[0035] Step 3: The scattered field (observation / measurement) data, the total internal field when only the known part of the scatterer is present and the unknown part is absent, and the electrical parameters of the scatterer with known parts are input into a deep learning neural network. The network is used to obtain the electrical parameters of the unknown part of the scatterer, such as relative permittivity and permeability.

[0036] Step 4: Input the total internal field when only the known part of the scatterer exists and the unknown part does not exist, the electrical parameters of the unknown part of the scatterer, and the electrical parameters of the known part of the scatterer into another neural network, and obtain the total internal field of the complete scatterer through the network;

[0037] Step 5: Calculate the total field or scattered field at any position using the moment method.

[0038] In a specific application embodiment, the detailed steps of S1 are:

[0039] S101: Assume that the size of the two-dimensional scatterer area is 0.64×0.64m 2 , centered at (0, 0) m. The mesh size of the moment method is 64×64. The scattered field is uniformly distributed on a circle with a radius of 5 m, with a total of 32 points. The incident wave frequency is 1 GHz and the direction is horizontal. The electrical parameter of the known part of the scatterer, in this case the contrast, is expressed in the matrix form χ p1 The incident field in the scatterer region is expressed as a matrix E inc , a small amount of scattered field (observation / measurement) data is expressed in vector form E sca Assume that both the real and imaginary parts of the contrast vary between 0 and 1.

[0040] S102: Repeat S101 until the collection of 15,000 scatterer data is completed to form a training set for neural network training.

[0041] S103: The position r of the scattered field to be determined is taken as 360 points uniformly distributed on a circle with a radius of 10 m.

[0042] In a specific application embodiment, the detailed steps of S2 are:

[0043] S201: Use the moment method to calculate the total field when only the known part of the scatterer exists and the unknown part does not exist, denoted as E p1 The specific calculation method is as follows:

[0044] E p1 =mat[(IG D ·diag(χp1 )) -1 vec(E inc )],

[0045] Where mat(·) means transforming the vector in the brackets into a matrix, diag(·) means constructing a diagonal matrix with the diagonal elements being the elements of the matrix or vector in the brackets, vec(·) means transforming the matrix in the brackets into a vector, I is the identity matrix, G D is the Green function matrix.

[0046] S202: Repeat S201 until the calculation of the internal total field of 15,000 scatterers in the training set is completed when only the known parts of the scatterers exist and the unknown parts do not exist, and add them to the training set.

[0047] In a specific application embodiment, the detailed steps of S3 are:

[0048] S301: Use the training set to train the deep learning neural network. The input of the neural network is E sca 、E p1 , and χ p1 , the output is the electrical parameter χ of the unknown part of the scatterer p2 The training method uses supervised batch training, and the loss function has the following expression:

[0049]

[0050] Where B = 30 is the number of training set batches, M = 4096 is the number of χ p2 Number of elements, is the neural network prediction value of the b-th sample, is the label of the b-th sample.

[0051] S302: After the training is completed, the neural network input E sca 、E p1 , and χ p1 , a single forward calculation can output the χ of a specific scatterer p2 . Figure 3 The third column gives the contrast results predicted by the neural network when the scatterer shape and contrast are known in the second column.

[0052] In a specific application embodiment, the detailed steps of S4 are:

[0053] S401: Use the training set to train another deep learning neural network. The input of the neural network is E p1 , χ p2 , and χ p1 , the output is the total internal field E of the complete scatterer totDuring the training phase, the neural network adopts the supervised batch training method, and its loss function is expressed as follows:

[0054]

[0055] in is the neural network prediction value of the b-th sample, is the label of the b-th sample.

[0056] S402: After the training is completed, the neural network input E p1 , χ p2 , and χ p1 , only one forward calculation is needed to get the total field E tot . Figure 3 Column 6 gives the total field results predicted by the neural network.

[0057] In a specific application embodiment, the detailed steps of S5 are:

[0058] S501: By E tot The specific calculation method for calculating the scattered field at the position r to be determined is as follows:

[0059]

[0060] where g S is the Green's function vector at the specific position r of the scattering area. Figure 3 Column 8 gives the predicted scattered field results.

[0061] Various aspects of the present invention are described in this disclosure with reference to the accompanying drawings, in which a number of illustrative embodiments are shown. The embodiments of the present disclosure are not necessarily defined to include all aspects of the present invention. It should be understood that the various concepts and embodiments introduced above, as well as those described in more detail below, can be implemented in any of many ways, because the concepts and embodiments disclosed in the present invention are not limited to any embodiment. In addition, some aspects of the present disclosure can be used alone or in any appropriate combination with other aspects of the present disclosure.

[0062] While the present invention has been disclosed above with reference to preferred embodiments, this is not intended to limit the present invention. Persons skilled in the art will readily appreciate that various modifications and variations can be made without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be determined by the claims.

Claims

1. A deep learning-based electromagnetic scattering calculation method, characterized by: The method for solving the scattered field generated by the scatterer under the irradiation of an incident wave when the shape and electrical parameters of the scatterer are not completely known includes: S1: Input the electrical parameters of the known part of the scatterer, such as relative permittivity and permeability, the incident field, a small amount of scattered field (observation / measurement) data, and the position coordinates of the scattered field to be determined; S2: Use the method of moments to solve the total internal field when only the known part of the scatterer exists and the unknown part does not exist; S3: A small amount of scattered field (observation / measurement) data, the total internal field when only the known part of the scatterer is present and the unknown part is absent, and the electrical parameters of the scatterer with known parts are input into a deep learning neural network. The network is used to obtain the electrical parameters of the unknown part of the scatterer, such as relative dielectric constant and magnetic permeability. S4: Inputting the total internal field when only the known part of the scatterer exists and the unknown part does not exist, the electrical parameters of the unknown part of the scatterer, and the electrical parameters of the known part of the scatterer into another neural network, and obtaining the total internal field of the complete scatterer through the network; S5: Calculate the total field or scattered field at any position according to the method of moments.

2. The method for calculating electromagnetic scattering based on deep learning when the shape and electrical parameters of a scatterer are not completely known according to claim 1, characterized in that: In step S1, the scattered field is introduced into the electromagnetic forward scattering problem, and the solutions of the scattering and inverse scattering problems are linked.

3. The method for calculating electromagnetic scattering based on deep learning when the scatterer shape and electrical parameters are not completely known according to claim 1, characterized in that: In step S2, the moment method uses pulse basis functions and point matching to decouple the physical parameters of the scatterer from the impedance matrix, thereby calculating the total internal field when only the known part exists.

4. The method for calculating electromagnetic scattering based on deep learning when the scatterer shape and electrical parameters are not completely known according to claim 1, characterized in that: The networks in step S3 and step S4 are connected in series to effectively transfer the error of the loss function.

5. The method for calculating electromagnetic scattering based on deep learning when the shape and electrical parameters of a scatterer are not completely known according to claim 4, characterized in that: The network described in S3 takes as input a small amount of scattered field (observation / measurement) data, the total internal field when only the known part of the scatterer is present and the unknown part is absent, and the electrical parameters of the scattering body with known parts, thereby ensuring that the neural network inputs as much prior information as possible.

6. The method for calculating electromagnetic scattering based on deep learning when the shape and electrical parameters of a scatterer are not completely known according to claim 4, characterized in that: The network output described by S3 is the electrical parameters of the unknown part of the scatterer, and the operator fitted is the operator that maps the scattered field to the electrical parameters of the scatterer.

7. The method for calculating electromagnetic scattering based on deep learning when the shape and electrical parameters of a scatterer are not completely known according to claim 4, characterized in that: The network described by S4 takes as input the total internal field when only the known part of the scatterer exists and the unknown part does not exist, the electrical parameters of the unknown part of the scatterer output by the network described by S3, and the electrical parameters of the known part of the scatterer, thereby ensuring that the neural network inputs as much prior information as possible.

8. The method for calculating electromagnetic scattering based on deep learning when the scatterer shape and electrical parameters are not completely known according to claim 4, characterized in that: The output of the network described in S4 is the total internal field of the complete scatterer, which is fitted by the operator that maps the scatterer's electrical parameters to the scattered field.

9. The method for calculating electromagnetic scattering based on deep learning when the scatterer shape and electrical parameters are not completely known according to claim 1, characterized in that: In step S5, the total field or scattered field at any position is calculated according to the method of moments, which requires using the outputs of the neural networks in steps S3 and S4 at the same time.

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