A training method and device of a current density distribution identification model

Abstract

The application provides a training method and device of a current density distribution identification model, the method comprising: inputting a plurality of sampling source points into the current density distribution identification model, and obtaining a loss function in the current density distribution identification model, which is constructed based on a current density distribution function and an electric field integral equation; wherein the loss function comprises a hyperbolic tangent function, a derivative of the hyperbolic tangent function and a product of the Green function; performing series expansion on the hyperbolic tangent function in the loss function, and extracting singular terms from the electric field integral equation in the series expanded loss function to obtain a plurality of singular integrals; performing inner integral calculation and outer integral calculation on each high-order singular integral in the singular integrals to determine the current density distribution function corresponding to the minimum value of the loss function on all sampling source points. The application can quickly solve the singular integrals comprising the hyperbolic tangent function, the derivative of the hyperbolic tangent function and the product of the Green function to obtain the current density distribution function.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic field simulation technology, and in particular to a training method and apparatus for a current density distribution identification model. Background Technology

[0002] Currently, current density distribution is mainly determined through electromagnetic field numerical simulation methods, which can be broadly classified into two categories: those based on differential equations and those based on integral equations. Since the electromagnetic field integral equation uses the Green's function as the kernel and contains gradients with respect to the Green's function, it is necessary to handle integrals containing basis functions. In the numerical simulation of electromagnetic fields based on the electric field integral equation, the Duffy transform method is typically used to solve the electromagnetic field integral equation, or singular terms and discontinuous differentiable terms in the Green's function are extracted to maintain the continuity and differentiability of the remaining part. The integrals of the extracted terms are then directly calculated analytically within the triangle.

[0003] With the rapid development and application of machine learning methods in various fields, combining traditional numerical methods for computational electromagnetics with machine learning methods has become a new research direction. In machine learning methods based on electromagnetic field integral equations, singular integrals inevitably arise, involving hyperbolic tangent functions and the product of their derivatives and Green's functions. However, the singular terms introduced when using the hyperbolic tangent function as the activation function exceed the processing range of traditional singular integral methods in electromagnetic simulations. This means that traditional singular integral methods in electromagnetic simulations cannot be directly applied to singular integrals involving hyperbolic tangent functions and the product of their derivatives and Green's functions. Therefore, in machine learning methods based on electromagnetic field integral equations, how to solve for singular integrals involving hyperbolic tangent functions and the product of their derivatives and Green's functions to quickly calculate current density distribution has become a pressing problem. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a training method and apparatus for a current density distribution identification model, which can quickly solve for the current density distribution function by taking the singular integral consisting of the hyperbolic tangent function and the product of the derivative of the hyperbolic tangent function and the Green's function. It can also realize the integral calculation of higher-order singularities introduced by the activation function in the form of hyperbolic tangent, thus providing a basic support for the application of machine learning in electromagnetic field simulation calculation.

[0005] To achieve the above objectives, the technical solutions adopted in the embodiments of the present invention are as follows:

[0006] In a first aspect, embodiments of the present invention provide a training method for a current density distribution identification model, comprising:

[0007] Multiple sampling source points are input into the current density distribution identification model to obtain the loss function constructed based on the current density distribution function and the electric field integral equation in the current density distribution identification model; wherein, the loss function includes the hyperbolic tangent function and the product of the derivative of the hyperbolic tangent function and the Green's function;

[0008] The hyperbolic tangent function in the loss function is expanded into a series, and singular terms are extracted from the electric field integral equation in the expanded loss function to obtain multiple singular integrals.

[0009] Inner-layer integration and outer-layer integration are performed on each higher-order singular integral in the singular integral to determine the current density distribution function corresponding to the loss function taking the minimum value at all the sampling source points.

[0010] Furthermore, this embodiment of the invention provides a first possible implementation of the first aspect, wherein the step of performing inner-layer integration and outer-layer integration calculations on each higher-order singular integral in the singular integral to determine the current density distribution function corresponding to the loss function taking its minimum value at all the sampling source points includes:

[0011] The triangular regions corresponding to the source point and the observation point in the higher-order singular integral are projected onto the reference triangle;

[0012] The inner and outer integrals of the higher-order singular integral are analytically calculated on the reference triangle to calculate the substitution coefficients of the current density distribution function corresponding to the loss function reaching its minimum value at all the sampling source points.

[0013] Furthermore, this embodiment of the invention provides a second possible implementation of the first aspect, wherein the step of performing a series expansion of the hyperbolic tangent function in the loss function and extracting singular terms from the electric field integral equation in the series-expanded loss function includes:

[0014] The hyperbolic tangent function is rewritten in terms of the source point and the observation point, and the power series formula of the hyperbolic tangent function is expanded into a series form.

[0015] Substitute the series form of the hyperbolic tangent function and the expansion of the Green's function into the electric field integral equation, and extract the singular terms.

[0016] Furthermore, this embodiment of the invention provides a third possible implementation of the first aspect, wherein the current density distribution identification model is constructed in the following ways:

[0017] A neuron is constructed using the hyperbolic tangent function as the activation function, and the current density distribution function is constructed based on the neuron and the substitution coefficients.

[0018] Substitute the current density distribution function into the electric field integral equation, and construct the loss function based on the electric field integral equation and the current density distribution function.

[0019] Furthermore, this embodiment of the invention provides a fourth possible implementation of the first aspect, wherein the method further includes:

[0020] Uniform random sampling is performed on the target surface to obtain multiple sampling source points.

[0021] Furthermore, this embodiment of the invention provides a fifth possible implementation of the first aspect, wherein the loss function is:

[0022]

[0023] Where ω = 2πf, f is the incident wave frequency, μ is the magnetic permeability, ε is the permittivity, and J is the dielectric constant. NN (r′) is the current density distribution function, G(r,r′) is the Green's function, and E inc (r) represents the electric field intensity of the incident wave, r is the sampling source point, and r′ is the observation point.

[0024] Furthermore, this embodiment of the invention provides a sixth possible implementation of the first aspect, wherein the current density distribution function is:

[0025]

[0026] in, To find the coefficients, ω m b is the weight parameter. m This is the bias parameter.

[0027] Secondly, embodiments of the present invention also provide a training apparatus for a current density distribution identification model, comprising:

[0028] The acquisition module is used to input multiple sampling source points into the current density distribution identification model and acquire the loss function constructed based on the current density distribution function and the electric field integral equation in the current density distribution identification model; wherein, the loss function includes the hyperbolic tangent function and the product of the derivative of the hyperbolic tangent function and the Green's function;

[0029] The extraction module is used to perform a series expansion on the hyperbolic tangent function in the loss function, and extract singular terms from the electric field integral equation in the series-expanded loss function to obtain multiple singular integrals;

[0030] The calculation module is used to perform inner-layer integration and outer-layer integration calculations on each higher-order singular integral in the singular integral, so as to determine the current density distribution function corresponding to the loss function taking the minimum value at all the sampling source points.

[0031] Thirdly, embodiments of the present invention provide an electronic device, including: a processor and a storage device;

[0032] The storage device stores a computer program that, when executed by the processor, performs the method as described in any of the first aspects.

[0033] Fourthly, embodiments of the present invention provide a computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, performs the steps of the method described in any of the first aspects above.

[0034] This invention provides a training method and apparatus for a current density distribution identification model. The method includes: inputting multiple sampling source points into the current density distribution identification model to obtain a loss function constructed based on the current density distribution function and the electric field integral equation in the current density distribution identification model; wherein the loss function includes a hyperbolic tangent function and the product of the derivative of the hyperbolic tangent function and the Green's function; performing a series expansion on the hyperbolic tangent function in the loss function, and extracting singular terms from the electric field integral equation in the series-expanded loss function to obtain multiple singular integrals; performing inner-layer integration calculation and outer-layer integration calculation on each higher-order singular integral in the singular integrals to determine the current density distribution function corresponding to the loss function taking the minimum value at all sampling source points. This invention, in electromagnetic field numerical simulations based on machine learning, employs an analytical integral calculation method—including series expansion, singular term extraction, and inner and outer integral calculations—to rapidly solve for the singular integrals formed by the hyperbolic tangent function and the product of its derivative and Green's function, thus obtaining the current density distribution function. This method also enables the integral calculation of higher-order singularities introduced by activation functions in the hyperbolic tangent form, providing fundamental support for the application of machine learning in electromagnetic field simulation.

[0035] Other features and advantages of the embodiments of the present invention will be set forth in the following description, or some features and advantages may be inferred from the description or determined without doubt, or may be learned by practicing the techniques described above in the embodiments of the present invention.

[0036] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0037] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0038] Figure 1 A flowchart of a training method for a current density distribution identification model provided in an embodiment of the present invention is shown;

[0039] Figure 2 This diagram illustrates a projection transformation between an arbitrary spatial right triangle and a planar triangular unit, as provided in an embodiment of the present invention.

[0040] Figure 3 A schematic diagram of the training device structure for a current density distribution recognition model provided in an embodiment of the present invention is shown. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0042] Currently, traditional numerical simulation methods for electromagnetic fields can be broadly categorized into two types: those based on differential equations and those based on integral equations. Since the electromagnetic field integral equation uses the Green's function as the integration kernel and contains the gradient with respect to the Green's function, it is necessary to handle the... and The integral of the product with basis functions. Common basis functions are often linear functions of the position vector. Taking the method of moments based on the electric field integral equation as an example, it is necessary to calculate... as well as Let r be the source point, r' be the observation point, and q be a vertex of the discrete triangular mesh containing the observation point. The integral is singular when the observation point coincides with or is very close to the source point. In numerical simulations of electromagnetic fields based on the electric field integral equation, existing integration methods mainly target the three types of integrals mentioned above. One method uses the Duffy transform, dividing the triangle containing the observation point into three sub-triangles. The integral on the original triangle is transformed into the integral on the three sub-triangles. Then, the Duffy transform is used to convert the singular integral on the original triangle into the non-singular integral on the sub-triangles, which can be analytically solved. The sum of the integrals on the sub-triangles is the integral value on the original triangle. Another method is to extract the singular terms and discontinuous differentiable terms from the Green's function to keep the remaining part continuous and differentiable. The integral of the extracted terms is then directly calculated analytically within the triangle.

[0043] In recent years, machine learning methods have developed rapidly and been applied in various fields. The combination of traditional numerical methods in computational electromagnetics and machine learning methods has become a new research direction. In machine learning methods based on electromagnetic field integral equations, approximate solutions are represented by a combination of neurons. The construction of neurons usually uses activation functions, among which the hyperbolic tangent function is a commonly used activation function. Therefore, it is inevitable to encounter singular integrals consisting of the hyperbolic tangent function, the derivative of the hyperbolic tangent function, and the Green's function.

[0044] The use of the hyperbolic tangent function and its partial derivatives introduces nonlinear functions. When the observation point is far from the source point, numerical integration methods (such as Gaussian integration) can be directly used to calculate the integral in the electric field integral equation. When the observation point and the source point are very close, the denominator of the Green's function tends to 0, and the integral in the electric field integral equation can no longer be calculated by direct numerical integration. The two singular integration methods in traditional electromagnetic simulation cannot be directly used for singular integrals containing the hyperbolic tangent function or the product of the derivative of the hyperbolic tangent function and the Green's function. The main reason is that when using the hyperbolic tangent function as the activation function, some singular terms are introduced that exceed the processing range of the above two methods.

[0045] To improve the above problems, this invention provides a training method and apparatus for a current density distribution identification model. The following is a detailed description of the embodiments of this invention.

[0046] This embodiment provides a training method for a current density distribution identification model. This method can be applied to electronic devices such as computers. See [link to relevant documentation]. Figure 1 The flowchart shown is a training method for the current density distribution recognition model. This method mainly includes the following steps:

[0047] Step S102: Input multiple sampling source points into the current density distribution identification model to obtain the loss function constructed based on the current density distribution function and the electric field integral equation in the current density distribution identification model;

[0048] The loss function mentioned above includes the hyperbolic tangent function and the product of the derivative of the hyperbolic tangent function and the Green's function;

[0049] In one embodiment, this embodiment provides a method for constructing a current density distribution identification model, including:

[0050] Uniform random sampling is performed on the target surface to obtain multiple sampling source points. This uniform random sampling on the target surface generates a set of sampling source points r, which are used to train the current density distribution recognition model.

[0051] The hyperbolic tangent function is used as the activation function to construct the neuron tanh(ω). i·x+b i ), where ω i b is the weight parameter. i As the bias parameter, a current density distribution function is constructed based on neurons and substitution coefficients;

[0052] The current density function is expanded using neurons. in, To find the coefficients; ω m b is the weight parameter. m Here, M is the bias parameter, and M is the number of neurons.

[0053] Substitute the current density distribution function into the electric field integral equation, and construct the loss function based on the electric field integral equation and the current density distribution function.

[0054] The current density function J NN (x) Substitute into the electric field integral equation:

[0055]

[0056] Where ω is the angular frequency, ω=2πf, f is the incident wave frequency, μ is the permeability, ε is the permittivity, G(r,r′) is the Green's function, and E inc (r) represents the electric field intensity of the incident wave, r is the sampling source point, and r′ is the observation point.

[0057] The loss function can be constructed using the electric field integral equation and the approximate expansion expression of the current density:

[0058]

[0059] in, Here, i is the gradient operator, i is the imaginary unit, and Green's function is... When the distance between the sampling source point r and the observation point r′ is sufficiently close, the integral of the loss function containing the Green's function and the product of the hyperbolic tangent and the hyperbolic tangent divergence has singularity. The following steps can be used to calculate and solve the problem of minimizing the loss function, minimizing the loss function at all sampling points, thereby solving for J. NN coefficients in the expression

[0060] Step S104: Expand the hyperbolic tangent function in the loss function into a series, and extract singular terms from the electric field integral equation in the expanded loss function to obtain multiple singular integrals;

[0061] When the observation point r′ is very close to the source point r, |rr′|→0. The hyperbolic tangent function tanh(w·r′+b) is rewritten in terms of (r′-r). Then, using the sum-to-product formula for the hyperbolic tangent function, it is expanded into a power series within the region near the sampling source point. Substituting this expanded series into the electric field integral equation and extracting the singular terms, we obtain the singular integral.

[0062] In one embodiment, this embodiment provides a specific implementation method for performing a series expansion of the hyperbolic tangent function in the loss function and extracting singular terms from the electric field integral equation in the expanded loss function:

[0063] Rewrite the hyperbolic tangent function in terms of the source point and the observation point, and expand the power series formula of the hyperbolic tangent function into a series form;

[0064] Substitute the series forms of the hyperbolic tangent function and the Green's function expansions into the electric field integral equation and extract the singular terms.

[0065] Expanding the sum-to-product formula of the hyperbolic tangent function into a power series formula within the region near the sampling source point, and extracting the first N terms, we obtain:

[0066]

[0067] Where a0 = tanh((w·r+b)), a1 = [tanh((w·r+b))+1], a2 = [(tanh((w·r+b)))] 2 -tanh((w·r+b))], in the neural network model, w is the weight coefficient and b is the bias coefficient.

[0068] The Green's function can be expanded as:

[0069] Substituting the above series expansion and Green's function expansion into the integral formula ∫ S′ G(r,r′)·tanh(w·r′+b)ds′ and In the equation, R = |rr′|, and k is the wave number, we can obtain:

[0070]

[0071] Extracting the singular terms yields six types of singular integrals:

[0072]

[0073]

[0074] Step S106: Perform inner-layer integration and outer-layer integration calculations on each higher-order singular integral in the singular integral to determine the current density distribution function corresponding to the loss function taking the minimum value at all sampling source points.

[0075] Of the six singular integrals mentioned above, I0, J0, and J1 can be calculated using existing integration methods. However, the three higher-order singular integrals, I1, I2, and J2, cannot be calculated using these methods. We consider a small triangular region on the approximate surface S containing the source and observation points, representing a small area of ​​the surface that requires special handling of the singular integrals. The integrals on this small triangle are then projected onto a reference triangle. On this reference triangle, the three double integrals I1, I2, and J2 are calculated. First, the analytical formula for the inner integral is derived; then, the outer integral can be calculated using either the analytical formula or the Gaussian integral formula.

[0076] In one embodiment, this embodiment provides a specific implementation method for performing inner-layer integration and outer-layer integration calculations on each higher-order singular integral in the singular integral to determine the current density distribution function corresponding to the minimum value of the loss function at all sampling source points:

[0077] Project the triangular regions corresponding to the source and observation points in the higher-order singular integrals onto the reference triangle.

[0078] The inner and outer integrals of the higher-order singular integrals are analytically calculated on the reference triangle, and the substitution coefficients of the current density distribution function corresponding to the loss function reaching its minimum value at all sampling source points are calculated.

[0079] The triangular region corresponding to the source and observation points in the higher-order singular integral (i.e., the integral on the small triangle) is projected onto a reference triangle. For each given source point r and observation point r′ on a surface S, the electric field integral is calculated over the entire surface S. This integral exhibits singularity only when the source point r and observation point r′ are very close. Therefore, any small surface triangular region containing the source point r and observation point r′ can be selected for singular integral calculation. The selected right-angled triangular region shares the same vertices as the surface triangular region. When the surface triangle is sufficiently small, it can be approximated by a right-angled triangle with three common vertices, as shown in the example. Figure 2 The diagram shown illustrates the projection transformation between an arbitrary spatial right-angled triangle and a planar triangular element, with the unit planar right-angled triangle as the reference element. Figure 2 The right-angled triangle on the right side of the middle, any spatial triangle ( Figure 2 The projection transformation formula between the triangle on the left and the reference element is:

[0080]

[0081] Taking I1 in the above-mentioned higher-order singular integral as an example, this integral can be divided into two parts: the small triangle containing the source point and the observation point selected according to the above steps, and the part excluding the small triangle.

[0082]

[0083] Δ is a small triangle containing the source point and the observation point. If we exclude the small triangle Δ from the entire surface S, then the first term in the above integral expansion of I1... It contains no singularities and can be solved by numerical integration, while the second term... It contains oddities and requires special handling.

[0084]

[0085] The integral over any triangle is transformed onto the reference triangle using the projection transformation described above. From the projection transformation formula, the source point and the observation point in the reference triangle can be represented as:

[0086]

[0087] and These represent the points corresponding to the source point and the observation point in the two-dimensional reference triangle, respectively.

[0088] Then the second integral It can be rewritten as:

[0089]

[0090] Where, constant F = (a1a2 + b1b2 + c1c2).

[0091] Considering the first component of the above integral, it can be simplified to the following form:

[0092]

[0093] Where A, B, C, M, N, and P are all constants.

[0094] For the inner integral, the variable h can be considered a constant; therefore, the above equation can be viewed as an integral of three terms.

[0095]

[0096] because It can be seen that the inner integral of the first term on the right-hand side of equation (3) can be directly integrated using this analytical formula, that is...

[0097]

[0098] use The third term on the right-hand side of equation (3) has the following expression:

[0099]

[0100] The second term on the right-hand side of equation (5) can be integrated in a manner similar to that of equation (4).

[0101] use The second term on the right-hand side of equation (3) has the following expression:

[0102]

[0103]

[0104] The calculation of the last two terms on the right side of equation (6) is the same as that of equations (4) and (5).

[0105] Through the above derivation, equations (4)-(6) have transformed the original double integral into a single integral with respect to h only.

[0106] A single integral of equation (4) yields

[0107]

[0108] The integrand of the second term on the right-hand side of equation (7) is a constant and can be directly calculated. The first term on the right-hand side of equation (7) can be derived as follows:

[0109]

[0110]

[0111] Here, S, W, T, L, and Q are constants. The value of the double integral of the first term on the right-hand side of equation (3) can be obtained from (7) and (8).

[0112] The first term on the right-hand side of equation (5) can be expressed as the sum of two terms.

[0113]

[0114] The second term on the right-hand side of (9) can be directly integrated, and the first term on the right-hand side of (9) can be expressed as:

[0115]

[0116] O, U, W, and Z are all constants. The integral value of equation (3) can be obtained using the above formula, and the value of the extracted higher-order singular integral I1 can be obtained by substituting the corresponding coefficients.

[0117]

[0118] in, C = 2(a1a2 + b1b2 + c1c2), M = (w1a1 + w2b1 + w3c1)a1J, N = (w1a2 + w2b2 + w3c2)a2J, P = (w1a1 + w2b1 + w3c1)a2J + (w1a2 + w2b2 + w3c2)a1J. The definitions of these three vertices of the spatial triangle (a1a2 + b1b2 + c1c2) are based on the coordinates of the three vertices (a1a2 + b1b2 + c1c2). i ,b i ,c i ), i = 1, 2, 3.

[0119] According to equation (11), it can be rewritten as the three integrals on the right side of equation (3), and the integral value of I1 can be obtained by using the integration method provided in this embodiment.

[0120] The first integral on the right-hand side of equation (3) can be derived using equations (4), (7), and (8):

[0121]

[0122] in, S = B - C + A

[0123] (3) The third integral on the right-hand side can be derived using equations (5), (9), and (12):

[0124]

[0125]

[0126] The second integral on the right-hand side of (c)(3) can be derived using equations (6), (12), and (13):

[0127]

[0128]

[0129] The integral value of I1 can be analytically calculated from equations (3) and (12)-(14) above.

[0130] Correspondingly, the values ​​of higher-order singular integrals I2 and J2 can be calculated using the above-mentioned analytical integral method, which can then be used to solve the loss function constructed from the electric field integral equation in machine learning methods.

[0131] By minimizing the loss function at all sampling source points, the current density function J can be solved. NN The coefficients in (x) The expression for the current density function in the trained current density distribution recognition model is an approximate solution for the target surface current density. The electric field intensity at any point in space can be directly calculated from the target surface current density. The target can be a metallic target.

[0132] The training method for the current density distribution identification model provided in this embodiment, in electromagnetic field numerical simulation based on machine learning, employs an analytical integral calculation method involving series expansion, singular term extraction, and inner and outer integral calculations for the loss function of the current density distribution identification model containing the hyperbolic tangent function and the product of the derivative of the hyperbolic tangent function and the Green's function. This allows for the rapid solution of the singular integral formed by the hyperbolic tangent function and the product of the derivative of the hyperbolic tangent function and the Green's function to obtain the current density distribution function. It also enables the integral calculation of higher-order singularities introduced by the activation function in the form of hyperbolic tangent, providing a fundamental support for the application of machine learning in electromagnetic field simulation calculations.

[0133] Corresponding to the training method for the current density distribution recognition model provided in the above embodiments, this embodiment of the invention provides a training device for the current density distribution recognition model, see below. Figure 3 The diagram shows a training device for a current density distribution recognition model. The device includes the following modules:

[0134] The acquisition module 31 is used to input multiple sampling source points into the current density distribution identification model and acquire the loss function constructed based on the current density distribution function and the electric field integral equation in the current density distribution identification model; wherein, the loss function includes the hyperbolic tangent function and the product of the derivative of the hyperbolic tangent function and the Green's function;

[0135] Extraction module 32 is used to perform a series expansion of the hyperbolic tangent function in the loss function, and extract singular terms from the electric field integral equation in the series expanded loss function to obtain multiple singular integrals;

[0136] The calculation module 33 is used to perform inner-layer integration and outer-layer integration calculations on each higher-order singular integral in the singular integral, so as to determine the current density distribution function corresponding to the loss function taking the minimum value at all sampling source points.

[0137] The calculation module 33 is used to project and transform the triangular regions corresponding to the source points and observation points in the higher-order singular integral onto the reference triangle; to perform analytical calculations on the inner and outer integrals of the higher-order singular integral on the reference triangle; and to calculate the substitution coefficients of the current density distribution function corresponding to the loss function reaching its minimum value at all sampled source points.

[0138] Extraction module 32 is used to rewrite the hyperbolic tangent function into a function form with respect to the source point and the observation point, and expand the power series formula of the hyperbolic tangent function into a series form; substitute the series form of the hyperbolic tangent function and the expansion of the Green's function into the electric field integral equation, and extract the singular terms.

[0139] The model building module is used to construct neurons by using the hyperbolic tangent function as the activation function, and to construct the current density distribution function based on the neurons and the coefficients. The current density distribution function is then substituted into the electric field integral equation, and the loss function is constructed based on the electric field integral equation and the current density distribution function.

[0140] The sample acquisition module is used to perform uniform random sampling on the target surface to obtain multiple sampling source points.

[0141] The loss function is:

[0142]

[0143] Where ω = 2πf, f is the incident wave frequency, μ is the magnetic permeability, ε is the permittivity, and J is the dielectric constant. NN (r′) is the current density distribution function, G(r,r′) is the Green's function, and E inc (r) represents the electric field intensity of the incident wave, r is the sampling source point, and r′ is the observation point.

[0144] The current density distribution function is:

[0145]

[0146] in, To find the coefficients, ω m b is the weight parameter. m This is the bias parameter.

[0147] The training device for the current density distribution identification model provided in this embodiment, in electromagnetic field numerical simulation based on machine learning methods, for the loss function of the current density distribution identification model containing the hyperbolic tangent function and the product of the derivative of the hyperbolic tangent function and the Green's function, adopts an analytical integral calculation method of series expansion, singular term extraction, and inner and outer integral calculation. This allows for the rapid solution of the singular integral formed by the product of the hyperbolic tangent function and the Green's function to obtain the current density distribution function. It can also realize the integral calculation of higher-order singularities introduced by the activation function in the form of hyperbolic tangent, providing a basic support for the application of machine learning in electromagnetic field simulation calculation.

[0148] The device provided in this embodiment has the same implementation principle and technical effect as the aforementioned embodiments. For the sake of brevity, any parts not mentioned in the device embodiment can be referred to the corresponding content in the aforementioned method embodiment.

[0149] This invention provides an electronic device, which includes a processor and a memory. The memory stores a computer program that can run on the processor. When the processor executes the computer program, it implements the steps of the method provided in the above embodiments.

[0150] This invention provides a computer-readable medium storing computer-executable instructions. When these computer-executable instructions are invoked and executed by a processor, they cause the processor to implement the methods described in the above embodiments.

[0151] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the system described above can be referred to the corresponding process in the foregoing embodiments, and will not be repeated here.

[0152] Furthermore, in the description of the embodiments of the present invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention based on the specific circumstances.

[0153] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0154] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0155] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and 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 training a current density distribution identification model, characterized in that, The method comprises the steps of: inputting a plurality of sampling source points into the current density distribution identification model, and obtaining a loss function constructed based on a current density distribution function and an electric field integral equation in the current density distribution identification model; wherein the loss function comprises a hyperbolic tangent function, a derivative of the hyperbolic tangent function and a product of a Green function; expanding the hyperbolic tangent function in the loss function into a series, and extracting singular terms from the electric field integral equation in the loss function after the series expansion to obtain a plurality of singular integrals; performing inner integral calculation and outer integral calculation on each high-order singular integral in the singular integrals to determine the current density distribution function corresponding to the minimum value of the loss function at all the sampling source points; the construction method of the loss function comprises: constructing a neuron by taking the hyperbolic tangent function as an activation function, and constructing the current density distribution function based on the neuron and a substitution coefficient; substituting the current density distribution function into the electric field integral equation, and constructing the loss function based on the electric field integral equation and the current density distribution function; the loss function is: where ω = 2πf, f is the frequency of the incident wave, μ is the magnetic permeability, ε is the dielectric constant, J NN (r') is the current density distribution function, G(r,r') is the Green's function, E inc (r) is the electric field strength of the incident wave, r is the sampling source point, r' is the observation point; the current density distribution function is: wherein, is a weight parameter, b m is a weight parameter, b m is a bias parameter.

2. The method of claim 1, wherein, the step of performing inner integral calculation and outer integral calculation on each high-order singular integral in the singular integrals to determine the current density distribution function corresponding to the minimum value of the loss function at all the sampling source points comprises: projecting a triangular region corresponding to a source point and an observation point in the high-order singular integral onto a reference triangle; performing analytical calculation on the inner integral and the outer integral of the high-order singular integral on the reference triangle to calculate the substitution coefficient of the current density distribution function corresponding to the minimum value of the loss function at all the sampling source points.

3. The method of claim 1, wherein, the step of expanding the hyperbolic tangent function in the loss function into a series and extracting singular terms from the electric field integral equation in the loss function after the series expansion comprises: rewriting the hyperbolic tangent function into a function form with respect to a source point and an observation point, and expanding the power series formula of the hyperbolic tangent function into a series form; substituting the hyperbolic tangent function in the series form and the expansion of the Green function into the electric field integral equation, and extracting singular terms therefrom.

4. The method of claim 1, wherein, Further comprising: performing uniform random sampling on a target surface to obtain a plurality of sampling source points.

5. A device for training a current density distribution identification model, characterized by, The method comprises the steps of: an acquisition module configured to input a plurality of sampling source points into the current density distribution identification model, and acquire a loss function constructed based on a current density distribution function and an electric field integral equation in the current density distribution identification model; wherein the loss function comprises a hyperbolic tangent function, a derivative of the hyperbolic tangent function and a product of a Green function; an extraction module configured to expand the hyperbolic tangent function in the loss function into a series, and extract singular terms from the electric field integral equation in the loss function after the series expansion to obtain a plurality of singular integrals; The computing module is configured to perform inner-layer integral calculation and outer-layer integral calculation on each high-order singular integral in the singular integrals to determine the current density distribution function corresponding to the minimum value of the loss function at all the sampling source points. The obtaining module is configured to construct a neuron by taking a hyperbolic tangent function as an activation function, construct the current density distribution function based on the neuron and a derivative coefficient, and substitute the current density distribution function into the electric field integral equation to construct the loss function based on the electric field integral equation and the current density distribution function. The loss function is: where ω = 2πf, f is the frequency of the incident wave, μ is the magnetic permeability, ε is the dielectric constant, J NN (r') is the current density distribution function, G(r,r') is the Green's function, E inc (r) is the electric field strength of the incident wave, r is the sampling source point, r' is the observation point; The current density distribution function is: wherein, is a weight parameter, b m is a weight parameter, b m is a bias parameter.

6. An electronic device, comprising: The method comprises the following steps: a processor and a storage device; The storage device stores a computer program, and the computer program performs the method of any one of claims 1 to 4 when executed by the processor.

7. A computer-readable storage medium having stored thereon a computer program, characterized in that The computer program performs the steps of the method of any one of claims 1 to 4 when executed by the processor.

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