Optimization design method of metamaterial absorber based on spatial mapping network and absorber

Abstract

This invention discloses a metamaterial microwave absorber optimization design method and absorber based on a spatial mapping network. First, the trust region corresponding to the initial optimization point is determined. Then, sampling points for design parameters are obtained around the initial optimization point, and the electromagnetic response corresponding to the design parameters at the sampling points is obtained through CST full-wave simulation. Next, based on the structure of the metamaterial microwave absorber to be optimized, its equivalent circuit diagram and reflection coefficient expression are obtained. The reflection coefficient formula is used as a coarse model, and the result of CST full-wave simulation is used as a fine model. A mapping between the coarse and fine models is established through an artificial neural network model. A spatial mapping network is constructed to optimize and obtain the design parameters corresponding to the target electromagnetic response of the metamaterial microwave absorber and the predicted corresponding electromagnetic response curve. Electromagnetic simulation is used to verify whether the optimized design parameters meet the requirements. If they do, the optimization stops; otherwise, the trust region is updated, and the next round of optimization begins. This invention has high design efficiency and a short average time requirement.

Description

Technical Field

[0001] This invention belongs to the field of metamaterial absorber optimization design technology, and relates to a metamaterial absorber optimization design method and absorber, particularly a metamaterial absorber optimization design method and metamaterial absorber based on equivalent circuit theory and spatial mapping network. Background Technology

[0002] Metamaterial absorbers are one application of metamaterials in the microwave field. They can effectively absorb, suppress, or control the propagation of electromagnetic waves within a specific operating frequency band. Compared to traditional absorbing materials (such as absorbing coatings and absorbing foams), metamaterial absorbers can efficiently absorb electromagnetic waves over a wide frequency band, offering advantages such as thinness and multifunctionality. They are widely used in many fields, including electronic communications, radar systems, and stealth technology. In practical applications, the designed metamaterial absorber structure typically needs to exhibit good absorption characteristics in the target frequency band. Therefore, the efficient design of metamaterial absorbers is crucial.

[0003] Once the geometry of the metamaterial absorber is determined, it is necessary to find the optimal solution for the geometric and material parameters that meet the target electromagnetic response. Existing optimization methods for metamaterial absorbers include those based on Genetic Algorithm (GA) (Reference 1) and deep learning-based reverse design methods (Reference 2). However, for metamaterial absorbers with a fixed geometry, the optimization efficiency of existing methods is not high when designing hundreds of different target electromagnetic responses simply by changing the design parameters. The GA-based design method requires a large number of full-wave simulations to find the optimal solution, resulting in high computational and time costs. The deep learning-based reverse design method also requires tens of thousands of sets of design parameters for full-wave simulations to generate training and test datasets, and the neural networks used are relatively complex, resulting in high time costs for training the neural networks and generating datasets. While it is efficient when designing the same structure thousands or tens of thousands of times, the demand for the same structure in practical design is not that high. Therefore, existing optimization design methods for metamaterial absorbers still have some shortcomings in practical applications, and further improvements can be made in terms of optimization design efficiency.

[0004] References:

[0005] [Document 1] BRBehera and P.Suraj, "Performance analysis of microstrippatch antenna with metamaterials and genetic algorithm: Design, analysis and modeling of metamaterial based antenna using genetic algorithm," 2016 11th International Conference on Industrial and Information Systems (ICIIS), Roorkee, India, 2016, pp.160-165.

[0006] [Literature 2] J.Hou et al., "Customized Inverse Design of MetamaterialAbsorber Based on Target-Driven Deep Learning Method," IEEE Access, vol.8, pp.211849–211859, 2020. Summary of the Invention

[0007] The purpose of this invention is to provide a metamaterial wave absorber optimization design method based on equivalent circuit theory and a metamaterial wave absorber. This method can improve the optimization design efficiency of metamaterial wave absorbers. In particular, when designing a metamaterial wave absorber with a given geometric structure by changing the design parameters to design a small number (about 10) different target electromagnetic responses, it has high design efficiency and accuracy, and can quickly and accurately find the optimal design parameters that meet the design objectives.

[0008] The technical solution adopted by the method of the present invention is: a metamaterial absorber optimization design method based on spatial mapping network, comprising the following steps:

[0009] Step 1: Determine the trust region corresponding to the initial optimization point;

[0010] Step 2: Sample points for design parameters around the initial point of each optimization;

[0011] Step 3: Obtain the electromagnetic response corresponding to the design parameters of the sampling points through CST full-wave simulation;

[0012] Step 4: Based on the structure of the metamaterial absorber to be optimized, obtain its equivalent circuit diagram and reflection coefficient;

[0013] Step 5: Use the obtained reflection coefficient expression as the coarse model and the CST full-wave simulation result as the fine model. Establish the mapping between the coarse model and the fine model through an artificial neural network model.

[0014] Step 6: The neural network spatial mapping module is composed of artificial neural network module and coarse model to build spatial mapping network. The design parameters corresponding to the electromagnetic response of metamaterial absorber target and the corresponding electromagnetic response curve are obtained through spatial mapping network optimization.

[0015] Step 7: Verify whether the optimized design parameters meet the requirements using electromagnetic simulation. If they do, stop the optimization; otherwise, update the trust region, return to step 2, and start the next round of optimization.

[0016] Preferably, in step 1, n is assumed to be the number of design parameters, and each set of design parameters is represented as x = [x1, x2, x3, ..., x...]. n ] T Let k represent the number of iterations, and x represent the number of iterations. (k-1) This represents the optimal solution in the (k-1)th iteration and the center point in the kth iteration. The center point of the first iteration is represented by x. 0 This indicates that the sensitivity of design parameters is analyzed to determine the corresponding trust region range, which is represented as follows: and Let i and y represent the i-th design parameter and the corresponding trust region of the center point in the k-th iteration, respectively.

[0017] Preferably, in step 2, multiple sets of design parameters are obtained by sampling around the initial center point before optimization using the DOE sampling method.

[0018] Preferably, in step 3, the j-th sampling point of the k-th iteration is represented as x. k，j , j∈1,2,3,...,(2n+1), where n is the number of design parameters; the electromagnetic response y corresponding to each sampling point is obtained by simulation using Python in conjunction with CST. m (x k，j f)|j=1,2,3,...,n c , where n c The number of sample points in the training dataset is represented by f, which represents the frequency.

[0019] Preferably, in step 4, according to transmission line theory, the metamaterial absorber structure unit to be optimized is equivalent to a resistor, capacitor, and inductor, and the corresponding equivalent circuit is drawn; based on the equivalent circuit diagram, the reflection coefficient is expressed as:

[0020]

[0021] Where Y0 is the free-space waveguide admittance, Y in Calculated from matrix [A]:

[0022]

[0023] Among them, A 22 A 12 is an element in matrix [A].

[0024] Preferably, in step 5, the spatial mapping network includes a parameter input module, a neural network spatial mapping module, an electromagnetic simulation module, and an error calculation module. The parameter input module is used to input the design parameters and sampling frequency of the metamaterial absorber to be optimized. The neural network spatial mapping module includes a fully connected neural network model with one hidden layer and the reflection coefficient formula derived from the equivalent circuit diagram of the metamaterial absorber to be optimized, and outputs the predicted electromagnetic response. The electromagnetic simulation module is used to obtain the full-wave simulated electromagnetic response. The error calculation module is used to calculate the error between the predicted electromagnetic response and the actual simulated electromagnetic response.

[0025] Preferably, in step 5, the input to the spatial mapping network is the design parameters and the sampling frequency, and the output of the artificial neural network model in the spatial mapping network is the resistance, capacitance, and inductance values ​​in the equivalent circuit. The output of the neural network is used as the input to the reflection coefficient formula, and then the electromagnetic response S is output from the reflection coefficient formula. 11 (dB); n is the number of design parameters, and each set of design parameters is represented as x = [x1, x2, x3, ..., x...]. n ] T Let k represent the number of iterations, and x represent the number of iterations. (k-1) This represents the optimal solution in the (k-1)th iteration and the center point in the kth iteration. The center point of the first iteration is represented by x. 0 Indicates that the output of the spatial mapping network in the k-th iteration is F ANN This represents the artificial neural network model in the spatial mapping network, F. eq This represents the reflection coefficient formula, where w represents the optimized weight parameters of the artificial neural network model in the spatial mapping network. Assume w... k These are the optimized weight parameters of the spatial mapping network artificial neural network model in the k-th iteration. The training process of the spatial mapping network can be expressed by the formula:

[0026]

[0027] Where, N f The number of sampling frequency points represents the electromagnetic response; the j-th sampling point in the k-th iteration is denoted as x. k，j, j∈1,2,3,...,(2n+1), where n is the number of design parameters; the electromagnetic response y corresponding to each sampling point is obtained by simulation using Python in conjunction with CST. m (x k，j f)|j=1,2,3,...,n c , where n c The number of sample points in the training dataset is represented by f, where f represents the frequency; y c y represents the predicted electromagnetic response output by the spatial mapping network. m f represents the actual simulated electromagnetic response output by the electromagnetic simulation module. q Indicates the sampling frequency.

[0028] Preferably, in step 6, the trained spatial mapping network is used to optimize the design of the metamaterial absorber based on the target electromagnetic response, denoted by U. c The error function between (x, w, f) and the design objective is expressed as:

[0029] u(y c (x, w) k ,f))=[∑ f∈J |err f (x)| 2 ] 1 / 2 J = {f|f min ≤f≤f max};

[0030]

[0031] Among them, R f f represents the target electromagnetic response design parameters. min and f max Let x represent the lowest and highest frequencies of the electromagnetic response band of interest for the metamaterial absorber, respectively; and the optimal solution x for the k-th iteration. k for Furthermore, the optimal solution x is predicted using a trained spatial mapping network. k The corresponding electromagnetic response curve.

[0032] Preferably, in step 7, α is used to represent the error function in two adjacent iterations, and the ratio of the decrease in error value between the spatial mapping network prediction and the actual simulation in two adjacent iterations is calculated, expressed as:

[0033]

[0034] Among them, y c (x k y represents the electromagnetic response corresponding to the optimal solution predicted by the k-th iteration spatial mapping network. m (xk () represents the optimal solution obtained in the k-th iteration, and the electromagnetic response obtained from CST simulation.

[0035] The update of the center point trust radius in the iterative process is based on α, and the calculation formula is as follows:

[0036]

[0037] Where n is the number of design parameters, This represents the trust region corresponding to the i-th design parameter at the center point of the k-th iteration. and This refers to the coefficients by which the radius of the trust region of the i-th design parameter increases or decreases in the k-th iteration. M and N are preset values.

[0038] Preferably, the spatial mapping network mentioned in step 5 is a trained spatial mapping network; during the training process, the training dataset of the spatial mapping network is first constructed.

[0039] The input to the spatial mapping network is the design parameters and sampling frequency of the absorber to be optimized in the training dataset. The output of the artificial neural network model in the spatial mapping network is the resistance, capacitance, and inductance values ​​in the equivalent circuit. The output of the neural network serves as the input to the reflection coefficient formula, and then the coarse model outputs the electromagnetic response S. 11 (dB); n is the number of design parameters, and each set of design parameters is represented as x = [x1, x2, x3, ..., x...]. n ] T Let k represent the number of iterations, and x represent the number of iterations. (k-1) This represents the optimal solution in the (k-1)th iteration and the center point in the kth iteration. The center point of the first iteration is represented by x. 0 Indicates that the output of the spatial mapping network in the k-th iteration is F ANN This represents the artificial neural network model in the spatial mapping network, F. eq This represents the reflection coefficient formula, where w represents the optimized weight parameters of the artificial neural network model in the spatial mapping network. Assume w... k These are the optimized weight parameters of the spatial mapping network artificial neural network model in the k-th iteration. The training process of the spatial mapping network can be expressed by the formula:

[0040]

[0041] Where, N f The number of sampling frequency points represents the electromagnetic response; the j-th sampling point in the k-th iteration is denoted as x. k，j, j∈1,2,3,...,(2n+1), where n is the number of design parameters; the electromagnetic response y corresponding to each sampling point is obtained by simulation using Python in conjunction with CST. m (x k，j f)|j=1,2,3,...,n c , where n c The number of sample points in the training dataset is represented by f, where f represents the frequency; y c y represents the predicted electromagnetic response output by the spatial mapping network. m f represents the actual simulated electromagnetic response output by the electromagnetic simulation module. q Indicates the sampling frequency;

[0042] During training, by continuously decreasing y m (x k，j f) and The difference between the values ​​is used to train the spatial mapping network; when the difference is less than a threshold, the training is complete and a trained spatial mapping network is obtained.

[0043] The technical solution adopted by the metamaterial absorber of the present invention is: a metamaterial absorber, which is designed and manufactured using the aforementioned metamaterial absorber optimization design method based on spatial mapping network.

[0044] Compared with the prior art, the beneficial effect of the present invention is that it can further improve the optimization design efficiency of metamaterial absorbers. In particular, when designing a metamaterial absorber with a given geometry by changing the design parameters to design a small number (about 10) different target electromagnetic responses, it has high design efficiency and accuracy, and can quickly and accurately find the optimal design parameters that meet the design objectives. Attached Figure Description

[0045] The technical solutions described herein are further illustrated below using examples and specific implementation methods. Additionally, accompanying drawings are used in the description of the technical solutions. Those skilled in the art can, without any creative effort, obtain other drawings and the intent of the present invention based on these drawings.

[0046] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0047] Figure 2 This is a structural diagram of a cross-shaped metamaterial absorber according to an embodiment of the present invention;

[0048] Figure 3 The equivalent circuit diagram corresponding to the cross-shaped metamaterial absorber structure of this invention is shown in the embodiment of the present invention.

[0049] Figure 4This is a flowchart of the spatial mapping network training process according to an embodiment of the present invention;

[0050] Figure 5 The S-value predicted by the optimal solution of the design parameters obtained after optimization in the embodiments of the present invention. 11 (dB) curve and S obtained from CST simulation 11 (dB) curve, and S corresponding to the initial center point before optimization. 11 (dB) curve. Detailed Implementation

[0051] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0052] Please see Figure 1 The present invention provides an optimization design method for metamaterial absorbers based on spatial mapping networks, comprising the following steps:

[0053] Step 1: Determine the trust region corresponding to the initial optimization point;

[0054] In one implementation, assume n is the number of design parameters, and each set of design parameters is represented as x = [x1, x2, x3, ..., x...]. n ] T Let k represent the number of iterations, and x represent the number of iterations. (k-1) This represents the optimal solution in the (k-1)th iteration and the center point in the kth iteration. The center point of the first iteration is represented by x. 0 This indicates that the sensitivity of design parameters is analyzed to determine the corresponding trust region range, which is represented as follows: and Let i and y represent the i-th design parameter and the corresponding trust region of the center point in the k-th iteration, respectively.

[0055] Step 2: Obtain sampling points for the design parameters around the initial point of each optimization using a Design of Experiments (DOE) sampling method;

[0056] In one implementation, multiple sets of design parameters are obtained by sampling around the initial center point before optimization using DOE sampling.

[0057] Step 3: Obtain the electromagnetic response corresponding to the design parameters of the sampling points through CST full-wave simulation;

[0058] In one implementation, the j-th sampling point in the k-th iteration is denoted as x. k，j, j∈1,2,3,...,(2n+1), where n is the number of design parameters; the electromagnetic response y corresponding to each sampling point is obtained by simulation using Python in conjunction with CST. m (x k，j f)|j=1,2,3,...,n c , where n c The number of sample points in the training dataset is represented by f, which represents the frequency.

[0059] Step 4: Based on the structure of the metamaterial absorber to be optimized, obtain its equivalent circuit diagram and reflection coefficient;

[0060] In one implementation, based on transmission line theory, the metamaterial absorber structure unit to be optimized is equivalent to a resistor, capacitor, and inductor, and the corresponding equivalent circuit is drawn; based on the equivalent circuit diagram, the reflection coefficient is expressed as:

[0061]

[0062] Where Y0 is the free-space waveguide admittance, Y in Calculated from matrix [A]:

[0063]

[0064] Among them, A 22 A 12 is an element in matrix [A].

[0065] Step 5: Use the obtained reflection coefficient expression as the coarse model and the CST full-wave simulation result as the fine model. Establish the mapping between the coarse model and the fine model through an artificial neural network model.

[0066] In one embodiment, the spatial mapping network includes a parameter input module, a neural network spatial mapping module, an electromagnetic simulation module, and an error calculation module. The parameter input module is used to input the design parameters and sampling frequency of the metamaterial absorber to be optimized. The neural network spatial mapping module includes a fully connected neural network model with one hidden layer and a reflection coefficient formula derived from the equivalent circuit diagram of the metamaterial absorber to be optimized, and outputs the predicted electromagnetic response. The electromagnetic simulation module is used to obtain the full-wave simulated electromagnetic response. The error calculation module is used to calculate the error between the predicted electromagnetic response and the actual simulated electromagnetic response.

[0067] The inputs to the spatial mapping network are design parameters and sampling frequency. The output of the artificial neural network model in the spatial mapping network are the resistance, capacitance, and inductance values ​​in the equivalent circuit. The output of the neural network serves as the input to the reflection coefficient formula, and the electromagnetic response S is then output from the reflection coefficient formula. 11(dB); n is the number of design parameters, and each set of design parameters is represented as x = [x1, x2, x3, ..., x...]. n ] T Let k represent the number of iterations, and x represent the number of iterations. (k-1) This represents the optimal solution in the (k-1)th iteration and the center point in the kth iteration. The center point of the first iteration is represented by x. 0 Indicates that the output of the spatial mapping network in the k-th iteration is F ANN This represents the artificial neural network model in the spatial mapping network, F. eq This represents the reflection coefficient formula, where w represents the optimized weight parameters of the artificial neural network model in the spatial mapping network. Assume w... k These are the optimized weight parameters of the spatial mapping network artificial neural network model in the k-th iteration. The training process of the spatial mapping network can be expressed by the formula:

[0068]

[0069] Where, N f The number of sampling frequency points represents the electromagnetic response; the j-th sampling point in the k-th iteration is denoted as x. k，j , j∈1,2,3,...,(2n+1), where n is the number of design parameters; the electromagnetic response y corresponding to each sampling point is obtained by simulation using Python in conjunction with CST. m (x k，j f)|j=1,2,3,...,n c , where n c The number of sample points in the training dataset is represented by f, where f represents the frequency; y c y represents the predicted electromagnetic response output by the spatial mapping network. m f represents the actual simulated electromagnetic response output by the electromagnetic simulation module. q Indicates the sampling frequency.

[0070] Step 6: The neural network spatial mapping module is composed of artificial neural network module and coarse model to build spatial mapping network. The design parameters corresponding to the electromagnetic response of metamaterial absorber target and the corresponding electromagnetic response curve are obtained through spatial mapping network optimization.

[0071] In one implementation, a trained spatial mapping network is used to optimize the design of the metamaterial absorber based on the target electromagnetic response, denoted by U. c The error function between (x, w, f) and the design objective is expressed as:

[0072] U(y c (x, w) k ,f))=[∑ f∈J|err f (x)| 2 ] 1 / 2 J = {f|f min ≤f≤f max};

[0073]

[0074] Among them, R f f represents the target electromagnetic response design parameters. min and f max Let these represent the lowest and highest frequencies of the electromagnetic response band of interest for the metamaterial absorber, respectively; the optimal solution for the k-th iteration. Furthermore, the optimal solution x is predicted using a trained spatial mapping network. k The corresponding electromagnetic response curve.

[0075] Step 7: Verify whether the optimized design parameters meet the requirements using electromagnetic simulation. If they do, stop the optimization; otherwise, update the trust region, return to step 2, and start the next round of optimization.

[0076] In one implementation, α represents the ratio of the decrease in error values ​​between two adjacent iterations of the spatial mapping network prediction and the actual simulation, expressed as:

[0077]

[0078] Among them, y c (x k y represents the electromagnetic response corresponding to the optimal solution predicted by the k-th iteration spatial mapping network. m (x k The expression represents the electromagnetic response obtained from the CST simulation (fine model) of the optimal solution obtained in the k-th iteration.

[0079] The update of the center point trust radius in the iterative process is based on α, and the calculation formula is as follows:

[0080]

[0081] Where n is the number of design parameters, This represents the trust region corresponding to the i-th design parameter at the center point of the k-th iteration. and This refers to the coefficients by which the radius of the trust region of the i-th design parameter increases or decreases in the k-th iteration. M and N are preset values.

[0082] In one implementation, optimization stops if the optimal solution obtained through optimization meets the requirements or the error between the optimal solution obtained through optimization and the original center point is small enough; otherwise, a new round of iterative optimization begins. Let γ represent a threshold customized according to the expected requirements. The iteration stopping condition is described as follows:

[0083] U(y m (x k ))≤0, or

[0084] In one implementation, the spatial mapping network is a trained spatial mapping network; during the training process, a training dataset for the spatial mapping network is first constructed.

[0085] Taking the cross-shaped metamaterial absorber structure as an example, such as Figure 2 As shown, this structural unit consists of five layers of media, with the foam substrate in the middle, and its thickness is expressed as t. d This indicates that the two layers in close contact with the foam substrate are 0.175mm thick polyethylene terephthalate (PET) sheets (ε=3.2, tanδ=0.003), and the outermost two layers are resistive films. The sheet resistance of the grooved resistive film on the upper surface is denoted as r1, and the sheet resistance of the grooved resistive film on the lower surface is 10Ω / sq. The period p of this unit structure is fixed at 12mm. In this unit structure, this embodiment selected a total of six design parameters for optimization, namely w1, w2, l1, l2, t d r1, where w1, w2, l1, l2, t d r1 is the geometric parameter, and r2 is the material parameter. The six parameters are combined into a vector x = [w1, w2, l1, l2, t]. d [r1] T Where w1 is the width of the transverse groove, w2 is the width of the inner wall, l1 is the length of the inner wall, and l2 is the length of the transverse groove. Four different electromagnetic target responses were optimized by simply changing the values ​​of these six design parameters.

[0086] There are a total of 6 design parameters to be determined for optimization, represented as x = [w1, w2, l1, l2, t]. d [r1] T w1, w2, l1, l2, t d These are geometric parameters; see details below. Figure 2 r1 is a material parameter, representing the sheet resistance of the resistive films on the upper and lower surfaces. The initial optimization point and the corresponding trust region for each initial center point are determined based on four different target responses. The initial center points for the first three optimization objectives are [3.20, 0.50, 9.0, 4.0, 6.0, 90]. T The corresponding trust regions are [10%, 20%, 10%, 10%, 40%, 40%].T The initial center point of the fourth optimization objective is [3.54, 0.44, 7.22, 4.34, 4.8, 73]. T The corresponding trust regions are [10%, 20%, 10%, 10%, 20%, 20%]. T Around the initial point of each optimization, sampling points for design parameters were obtained using the DOE sampling method. A total of 25 points were sampled, which, together with the initial center point, constituted the training dataset.

[0087] The equivalent circuit corresponding to this metamaterial absorber is as follows: Figure 3 As shown, the reflection coefficient can be expressed as:

[0088]

[0089] Where Y0 is the free-space waveguide admittance, in this embodiment Y in Calculated from matrix [A]:

[0090]

[0091]

[0092] in,

[0093]

[0094] θ i =β i h i , ω = 2πf;

[0095] The spatial mapping network is then trained, and the training process is as follows: Figure 4 As shown.

[0096] The input to the spatial mapping network is the design parameters and sampling frequency of the absorber to be optimized in the training dataset. The output of the artificial neural network model in the spatial mapping network is the resistance, capacitance, and inductance values ​​in the equivalent circuit. The output of the neural network serves as the input to the reflection coefficient formula, and then the coarse model outputs the electromagnetic response S. 11 (dB); n is the number of design parameters, and each set of design parameters is represented as x = [x1, x2, x3, ..., x...]. n ] T Let k represent the number of iterations, and x represent the number of iterations. (k-1) This represents the optimal solution in the (k-1)th iteration and the center point in the kth iteration. The center point of the first iteration is represented by x. 0 Indicates that the output of the spatial mapping network in the k-th iteration is F ANNThis represents the artificial neural network model in the spatial mapping network, F. eq This represents the reflection coefficient formula, where w represents the optimized weight parameters of the artificial neural network model in the spatial mapping network. Assume w... k These are the optimized weight parameters of the spatial mapping network artificial neural network model in the k-th iteration. The training process of the spatial mapping network can be expressed by the formula:

[0097]

[0098] Where, N f The number of sampling frequency points represents the electromagnetic response; the j-th sampling point in the k-th iteration is denoted as x. k，j , j∈1,2,3,...,(2n+1), where n is the number of design parameters; the electromagnetic response y corresponding to each sampling point is obtained by simulation using Python in conjunction with CST. m (x k，j f)|j=1,2,3,...,n c , where n c The number of sample points in the training dataset is represented by f, where f represents the frequency; y c y represents the predicted electromagnetic response output by the spatial mapping network. m f represents the actual simulated electromagnetic response output by the electromagnetic simulation module. q Indicates the sampling frequency;

[0099] During training, by continuously decreasing y m (x k，j f) and The difference between the values ​​is used to train the spatial mapping network; when the difference is less than a threshold, the training is complete and a trained spatial mapping network is obtained.

[0100] This embodiment also provides a metamaterial absorber, which is designed and manufactured using the aforementioned metamaterial absorber optimization design method based on spatial mapping network.

[0101] In one implementation, a trained spatial mapping network is used to optimize and obtain the design parameters corresponding to the electromagnetic response of the metamaterial absorber target and the predicted corresponding electromagnetic response curve, such as... Figure 5 As shown in the table, the first three design objectives underwent two iterations to obtain the optimal solution that met the requirements. The fourth optimization objective underwent three iterations to obtain the optimal solution, which is shown in Table 1. The predicted electromagnetic response and the actual simulated electromagnetic response are shown in the table below. Figure 5 As shown.

[0102] Table 1

[0103]

[0104] The metamaterial absorber structure was optimized for these four design objectives using a deep learning-based reverse design method, a genetic algorithm-based optimization method, and the optimization design method proposed in this invention. The comparison results are shown in Table 2. Wherein, FTNN: Feature Transformer Neural Network, GNN: Generative Neural Network, PNN: Predictive Neural Network, and **: Number of hidden layers in the neural network.

[0105] Table 2

[0106]

[0107] It can be seen that, compared with the more commonly used reverse design methods based on genetic algorithms and deep learning, the method proposed in this invention has higher design efficiency and lower average time when optimizing the design of a small number of design targets (about 10) by changing the design parameters of the same metamaterial absorber.

[0108] It should be understood that the above description of the preferred embodiments is quite detailed, but it should not be considered as a limitation on the scope of protection of this invention. Those skilled in the art, under the guidance of this invention, can make substitutions or modifications without departing from the scope of protection of the claims of this invention, and all such substitutions or modifications fall within the scope of protection of this invention. The scope of protection of this invention should be determined by the appended claims.

Claims

1. A method for optimizing the design of metamaterial absorbers based on spatial mapping networks, characterized in that, Includes the following steps: Step 1: Determine the trust region corresponding to the initial optimization point; Assumption n The number of design parameters is [number], and each set of design parameters is represented as [example]. ,use k To represent the number of iterations, use Indicates the first k The optimal solution of the -1st iteration and the th iteration k The center point of the next iteration, the center point of the first iteration optimization is used This indicates that the sensitivity of design parameters is analyzed to determine the corresponding trust region range, which is represented as follows: , and They represent the first k The center point of the next iteration i Each design parameter and its corresponding trust domain; Step 2: Sample points for design parameters around the initial point of each optimization; Step 3: Obtain the electromagnetic response corresponding to the design parameters of the sampling points through CST full-wave simulation; Step 4: Based on the structure of the metamaterial absorber to be optimized, obtain its equivalent circuit diagram and the expression for the reflection coefficient; Step 5: Use the obtained reflection coefficient expression as the coarse model and the CST full-wave simulation result as the fine model. Establish the mapping between the coarse model and the fine model through an artificial neural network model. Step 6: The neural network spatial mapping module is composed of artificial neural network module and coarse model to build spatial mapping network. The design parameters corresponding to the electromagnetic response of metamaterial absorber target and the corresponding electromagnetic response curve are obtained through spatial mapping network optimization. Step 7: Verify whether the optimized design parameters meet the requirements using electromagnetic simulation. If they do, stop the optimization; otherwise, update the trust region, return to step 2, and start the next round of optimization. Among them, using The error function in two adjacent iterations is expressed as the ratio of the decrease in error between the spatial mapping network prediction and the actual simulation in two adjacent iterations: in, The electromagnetic response corresponding to the optimal solution predicted by the spatial mapping network. This represents the electromagnetic response obtained from CST simulation of the optimal solution obtained in the k-th iteration. The update of the center point trust radius in the iterative process is based on The calculation formula is as follows: ； in, n The number of design parameters. Indicates the first k The center point of the next iteration i Trust domains corresponding to each design parameter and It refers to the first i The coefficients for increasing and decreasing the trust region radius of each design parameter in the k-th iteration. M and N are preset values.

2. The metamaterial absorber optimization design method based on spatial mapping network according to claim 1, characterized in that: In step 3, the j-th sampling point in the k-th iteration is represented as... , n is the number of design parameters; the electromagnetic response corresponding to each sampling point is obtained by simulation using Python in conjunction with CST. ,in, This represents the number of sample points in the training dataset. It represents frequency.

3. The method for optimizing the design of metamaterial absorbers based on spatial mapping networks according to claim 1, characterized in that: In step 4, based on transmission line theory, the metamaterial absorber structure unit to be optimized is equivalent to a resistor, capacitor, and inductor, and the corresponding equivalent circuit is drawn; based on the equivalent circuit diagram, the reflection coefficient is expressed as: in, For free-space waveguide admittance, Calculated from matrix [A]: ； in, , is an element in matrix [A].

4. The method for optimizing the design of metamaterial absorbers based on spatial mapping networks according to claim 1, characterized in that: In step 5, the spatial mapping network includes a parameter input module, a neural network spatial mapping module, an electromagnetic simulation module, and an error calculation module. The parameter input module is used to input the design parameters and sampling frequency of the metamaterial absorber to be optimized. The neural network spatial mapping module includes a fully connected neural network model with one hidden layer and the reflection coefficient formula derived from the equivalent circuit diagram of the metamaterial absorber to be optimized, and outputs the predicted electromagnetic response. The electromagnetic simulation module is used to obtain the full-wave simulated electromagnetic response. The error calculation module is used to calculate the error between the predicted electromagnetic response and the actual simulated electromagnetic response.

5. The method for optimizing the design of metamaterial absorbers based on spatial mapping networks according to claim 1, characterized in that: In step 5, the inputs to the spatial mapping network are the design parameters and the sampling frequency. The output of the artificial neural network model in the spatial mapping network is the resistance, capacitance, and inductance values ​​in the equivalent circuit. The output of the neural network serves as the input to the reflection coefficient formula, and the electromagnetic response is then output from the reflection coefficient formula. ; n The number of design parameters is [number], and each set of design parameters is represented as [example]. ,use k To represent the number of iterations, use Indicates the first k The optimal solution of the -1st iteration and the th iteration k The center point of the next iteration, the center point of the first iteration optimization is used Indicates; the k The output of the next iteration of the spatial mapping network is , This represents an artificial neural network model in a spatial mapping network. This represents the formula for the reflection coefficient. Let the optimized weight parameters of the artificial neural network model in the spatial mapping network be represented, assuming... It is the first k The optimized weight parameters of the spatial mapping network artificial neural network model in the next iteration are expressed by the following formula: in, The number of sampling frequency points represents the electromagnetic response; the j-th sampling point in the k-th iteration is denoted as... , n is the number of design parameters; the electromagnetic response corresponding to each sampling point is obtained by simulation using Python in conjunction with CST. ,in, This represents the number of sample points in the training dataset. It represents frequency; This represents the predicted electromagnetic response output by the spatial mapping network. This represents the actual simulated electromagnetic response output by the electromagnetic simulation module. .

6. The method for optimizing the design of metamaterial absorbers based on spatial mapping networks according to claim 5, characterized in that: In step 6, the trained spatial mapping network is used to optimize the design of the metamaterial absorber based on the target electromagnetic response, denoted by U. The error function between the design target and the target is expressed as: , ； ； in, Indicates the target electromagnetic response design parameters. and Let these represent the lowest and highest frequencies of the electromagnetic response band of interest for the metamaterial absorber; the optimal solution for the k-th iteration. Furthermore, the optimal solution is predicted using a trained spatial mapping network. The corresponding electromagnetic response curve.

7. The method for optimizing the design of metamaterial absorbers based on spatial mapping networks according to any one of claims 1-6, characterized in that: The spatial mapping network mentioned in step 5 is a trained spatial mapping network; During training, the training dataset for the spatial mapping network is first constructed; The input to the spatial mapping network is the design parameters and sampling frequency of the absorber to be optimized in the training dataset. The output of the artificial neural network model in the spatial mapping network is the resistance, capacitance, and inductance values ​​in the equivalent circuit. The output of the neural network serves as the input to the reflection coefficient formula, and then the coarse model outputs the electromagnetic response. ; n The number of design parameters is [number], and each set of design parameters is represented as [example]. ,use k To represent the number of iterations, use Indicates the first k The optimal solution of the -1st iteration and the th iteration k The center point of the next iteration, the center point of the first iteration optimization is used Indicates; the k The output of the next iteration of the spatial mapping network is , This represents an artificial neural network model in a spatial mapping network. This represents the formula for the reflection coefficient. Let the optimized weight parameters of the artificial neural network model in the spatial mapping network be represented, assuming... It is the first k The optimized weight parameters of the spatial mapping network artificial neural network model in the next iteration are expressed by the following formula: in, The number of sampling frequency points represents the electromagnetic response; the j-th sampling point in the k-th iteration is denoted as... , n is the number of design parameters; the electromagnetic response corresponding to each sampling point is obtained by simulation using Python in conjunction with CST. ,in, This represents the number of sample points in the training dataset. It represents frequency; This represents the predicted electromagnetic response output by the spatial mapping network. This represents the actual simulated electromagnetic response output by the electromagnetic simulation module. ; During training, by continuously reducing and The difference between the values ​​is used to train the spatial mapping network; when the difference is less than a threshold, the training is complete and a trained spatial mapping network is obtained.

8. A metamaterial microwave absorber, characterized in that: It is designed and manufactured using the metamaterial absorber optimization design method based on spatial mapping network as described in any one of claims 1 to 7.

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