A Design Method for Electromagnetic Metamaterials Based on Deep Learning and Structural Variables

Abstract

This invention provides a method for designing electromagnetic metamaterials based on deep learning and structural variables, belonging to the field of electromagnetic metamaterial design. The method includes the following steps: Step 1: Inputting the electromagnetic metasurface unit structure design and related parameter periodic arrangement structure into electromagnetic simulation software to obtain the corresponding electromagnetic response, and constructing a forward prediction dataset and a reverse design dataset; Step 2: Dividing the forward prediction dataset and the reverse design dataset into 80% training set and 20% test set, respectively; Step 3: Constructing a forward prediction network model; Step 4: Constructing a reverse design network model and initializing the network parameters; Step 5: Inputting the reverse design dataset into the reverse design network model to generate the R-Generator and I-Generator networks, and performing iterative training. This invention uses an indirect generation model, overcoming the errors caused by discrete mapping and improving the final accuracy of the model. The introduction of structural variables solves the problems of large discrete errors and insufficient flexibility in reverse design.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic metamaterial design, specifically a method for electromagnetic metamaterial design based on deep learning and structural variables. Background Technology

[0002] The concept of electromagnetic metamaterials was first proposed by Professor Walter in 1999. It refers to artificially manufactured, periodic, three-dimensional composite materials. Through the periodic arrangement of artificial structures, electromagnetic metamaterials can produce physical properties not found in naturally occurring materials, such as negative permittivity and negative permeability. Electromagnetic metasurfaces are artificially layered materials with a thickness less than the wavelength of the electromagnetic wave; they are considered a two-dimensional counterpart to electromagnetic metamaterials. Unlike electromagnetic metamaterials, electromagnetic metasurfaces utilize the abrupt phase and amplitude changes in electromagnetic waves across the metasurface to modulate the phase and amplitude distribution of reflected and transmitted fields in space. Electromagnetic metasurfaces allow for flexible control of electromagnetic wave amplitude and phase characteristics, exhibiting superior properties such as low loss and good ductility compared to traditional electromagnetic metamaterials.

[0003] Forward prediction of the electromagnetic response of electromagnetic metasurfaces refers to obtaining the corresponding electromagnetic response based on provided information about the arrangement of artificial structures. Currently, the mainstream method for forward prediction in electromagnetic metasurface design remains numerical iterative calculation. This involves solving Maxwell's equations numerically to obtain the corresponding electromagnetic response. Commonly used numerical methods include the method of moments (MOM), the finite element method (FEM), the finite integral method (FIT), and the finite-difference time-domain method (FDTD). This method requires extensive numerical calculations and iterations; simulations of a single example typically take minutes, making it time-consuming and labor-intensive. Therefore, forward prediction in electromagnetic metasurface design is significantly limited by numerical computation capabilities.

[0004] The reverse design of electromagnetic metasurfaces refers to designing an artificial structure arrangement whose electromagnetic response satisfies the required information based on the desired electromagnetic response. Current methods for reverse design of electromagnetic metasurfaces mainly include heuristic algorithms and deep learning algorithms. Heuristic algorithms, such as genetic algorithms, simulated annealing algorithms, and ant colony algorithms, can iteratively search within the solution space to obtain the final result. However, heuristic algorithms have poor generalization performance, and each requirement necessitates a different iterative search, leading to computational overhead. In recent years, the rise of generative models in deep learning, such as variational autoencoders and generative adversarial networks, has also led to many deep learning-based methods for electromagnetic metasurface reverse design. Based on deep learning generative models, metasurface arrangement information is typically mapped to latent space variables, while the required electromagnetic response is used as a conditional constraint input to achieve the reverse design objective. However, this common approach aims to generate a probabilistic representation of the metasurface arrangement information, ignoring the error loss caused by the discrete mapping of the probabilistic representation to the metasurface arrangement information. Due to the extreme sensitivity and nonlinearity of metasurface patterns, the final impact of this error cannot be ignored.

[0005] The proposed metasurface design method based on deep learning and structural variables employs an indirect generative model. It generates a permutation matrix, performs discretization optimization using the Gumbel-Sinkhorn operator, and then combines this with structural variables to obtain the final metasurface arrangement information. Compared to conventional deep learning generative models, this method overcomes the errors introduced during discretization, improving the final accuracy of the model. Furthermore, the introduction of structural variables significantly enhances the model's flexibility and controllability. Summary of the Invention

[0006] The purpose of this invention is to propose an electromagnetic metamaterial design method based on deep learning and structural variables, which aims to solve the problems of large discrete errors and insufficient flexibility in the reverse design of existing technologies.

[0007] Technical content: A design method for electromagnetic metamaterials based on deep learning and structural variables, comprising the following steps:

[0008] Step 1: Input the electromagnetic metasurface unit structure design and related parameter periodic arrangement structure into electromagnetic simulation software to obtain the corresponding electromagnetic response, and construct a forward prediction dataset and a reverse design dataset; the forward prediction dataset and the reverse design dataset include the generated electromagnetic response data, which includes real part simulation values ​​and imaginary part simulation values;

[0009] Step 2: Split the forward prediction dataset and reverse design dataset constructed in Step 1 into 80% training set and 20% test set, respectively;

[0010] Step 3: Construct a positive prediction network model. Train the positive prediction network model on the segmented positive prediction dataset. After training, fix the parameters of the positive prediction network model.

[0011] Step 4: Construct the reverse engineering network model, including the real part generator network R-Generator and the imaginary part generator network I-Generator, and initialize the network parameters;

[0012] Step 5: Feed the real part training subset from the reverse design dataset into the real part generator network R-Generator of the reverse design network model, and feed the imaginary part training subset from the reverse design dataset into the imaginary part generator network I-Generator of the reverse design network model, and perform iterative training.

[0013] Furthermore, in step one, the steps for constructing the forward prediction dataset and the reverse design dataset are as follows:

[0014] The electromagnetic metasurface unit comprises an upper layer, a middle layer, and a lower layer. The upper layer is divided into a coding pattern area with a width l2 = 8 mm. This coding pattern area is further divided into a 16×16 matrix. The coding pattern is made of copper metal with a conductivity of 5.8e+007 S / m, a width l3 = 0.5 mm, and a thickness t2 = 0.017 mm. The coding pattern adopts a centrally symmetrical design. The middle layer is made of F4B dielectric substrate with a dielectric constant of 2.65(1+0.003i), a width l1 = 10 mm, and a thickness t1 = 2 mm. The lower layer is entirely covered with copper, with a conductivity of 5.8e+007 S / m and a thickness t2 = 0.017 mm.

[0015] 1) Randomly generate a 16×16 encoding matrix, construct the corresponding electromagnetic metasurface unit, and send it into electromagnetic simulation software to obtain the corresponding electromagnetic response. The frequency range is set to 8-12 GHz.

[0016] 2) The 16×16 encoding matrix is ​​expanded into a 32×32 encoding matrix by horizontal and vertical replication and used as the network input;

[0017] 3) Amplitude A and phase of the electromagnetic response The following correspondence exists between the real part Re and the imaginary part Im of the electromagnetic response:

[0018]

[0019]

[0020] The electromagnetic response is decomposed into a real part Re and an imaginary part Im. The real part Re and the imaginary part Im are sampled at a uniform frequency with a sampling interval of 0.1 GHz. The real part Re and the imaginary part Im are represented as 41-dimensional vectors and used as labels for the dataset to construct a positive prediction dataset.

[0021] 4) Represent the real part Re and the imaginary part Im as 41-dimensional vectors and use them as both input and label to construct the reverse design dataset.

[0022] Furthermore, in step two:

[0023] The input to the forward prediction dataset is a 32×32 encoding matrix, and the corresponding labels are 41-dimensional real part Re vectors and 41-dimensional imaginary part Im vectors. The input to the reverse design dataset is a 41-dimensional real part Re vector and a 41-dimensional imaginary part Im vector, and the corresponding labels are the same as the input, which are also 41-dimensional real part Re vectors and 41-dimensional imaginary part Im vectors.

[0024] Furthermore, in step three:

[0025] The constructed positive prediction network model uses identical network structures for its real part network RNet and imaginary part network INet. The output of the real part network RNet is a real part vector, which fits the real part of the electromagnetic response; the output of the imaginary part network INet is an imaginary part vector, which fits the imaginary part of the electromagnetic response. Both the real part network RNet and the imaginary part network INet use the ResNet18 structure. The optimizer for the real part network RNet is set to Adam with a learning rate of 1e-3; the optimizer for the imaginary part network INet is set to Adam with a learning rate of 1e-3.

[0026] use Let represent the network loss function, where y is the true value. Let m be the predicted value, and m be the dimension. The positive prediction dataset is fed into the positive prediction network model for training. The total loss value of the positive prediction network is defined as... Among them, Re f For the real part of the positive prediction dataset response, For the real part predicted by the positive prediction network, Im f For the imaginary part of the response of the positive prediction dataset, For the positive prediction network to predict the imaginary part, A f To predict the response magnitude of the dataset in a positive direction, To calculate the predicted magnitude of the prediction network, the parameters of the forward prediction network model are fixed after training.

[0027] Furthermore, in step four:

[0028] The real part generator network R-Generator and the imaginary part generator network I-Generator use the same network structure. The real part generator network R-Generator is composed of deconvolution layers. After the input 41-dimensional real part vector Re is deconvolved, a 64×64×1 real part pre-permutation matrix will be generated. The imaginary part generator network I-Generator is also composed of deconvolution layers. After the input 41-dimensional imaginary part vector Im is deconvolved, a 64×64×1 imaginary part pre-permutation matrix will be generated.

[0029] Furthermore, in step five, the iterative calculation process for each round is as follows:

[0030] Step 5.1: Feed the real part training subset of the reverse design dataset into the real part generator network R-Generator, and feed the imaginary part training subset of the reverse design dataset into the imaginary part generator network I-Generator to obtain the real part pre-permutation matrix and the imaginary part pre-permutation matrix, respectively.

[0031] Step 5.2: Concatenate the real part pre-permutation matrix and the imaginary part pre-permutation matrix according to the channel dimension, fuse the channels through a 1×1 convolutional layer, and then pass the Gumbel-sinkhorn operator to obtain the permutation matrix;

[0032] Step 5.3: Introduce structural variables in the form of discrete vectors; indirectly obtain the generated metasurface arrangement pattern by performing vector product calculations on the structural variables and the permutation matrix obtained in Step 5.2.

[0033] Step 5.4: Feed the metasurface arrangement pattern generated in Step 5.3 into the forward prediction network constructed in Step 3 to obtain the real part prediction value, imaginary part prediction value and magnitude prediction value respectively;

[0034] Step 5.5: Calculate the error using the real part prediction, imaginary part prediction, and magnitude prediction, and then use the backpropagation algorithm to update the parameters of the real part generator network R-Generator, the imaginary part generator network I-Generator, and the 1×1 convolutional fusion layer.

[0035] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0036] The beneficial effects of this invention are that it accelerates the forward prediction process by introducing a forward prediction network model, reduces the discrete mapping error in generating metasurface arrangement patterns by introducing the Gumbel-Sinkhorn operator, and further improves the flexibility and accuracy of the final reverse design network model by introducing structural variables. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the electromagnetic metasurface unit structure of the present invention;

[0038] Figure 2 This is a flowchart illustrating the structure and training process of the forward network model of this invention.

[0039] Figure 3 This is a flowchart illustrating the structure and training process of the reverse-engineered network model of this invention.

[0040] Figure 4 This is a graph showing the decreasing trend of the loss function during the forward network training process of this invention.

[0041] Figure 5 This invention reverse-engineers a network training process loss function descent trend diagram;

[0042] Figure 6 The difference between the predicted and simulated values ​​of the forward network;

[0043] Figure 7 This section describes the differences between the design values ​​and simulation values ​​of the reverse-engineered network. Detailed Implementation

[0044] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings and specific implementation examples.

[0045] This invention proposes an electromagnetic metamaterial design method based on deep learning and structural variables. To improve the accuracy and flexibility of reverse design, structural variables and a discrete mapping method based on the Gumbel-Sinkhorn operator are introduced to indirectly generate the final metasurface arrangement information. Simultaneously, a forward prediction network model is introduced to construct a dual-network cascade system for metasurface reverse design. The dual-network cascade system refers to the cascading of the reverse design network and the forward prediction network.

[0046] The technical solution of the present invention is as follows:

[0047] Step 1: Input the electromagnetic metasurface unit structure design and related parameter periodic arrangement structure into electromagnetic simulation software to obtain the corresponding electromagnetic response, and construct a forward prediction dataset and a reverse design dataset; the forward prediction dataset and the reverse design dataset include the generated electromagnetic response data, which includes the real part simulation value and the imaginary part simulation value.

[0048] The electromagnetic metasurface unit designed for such purposes Figure 1 As shown, Figure 1(a) is a front view, and (b) is a side view. The middle layer dielectric substrate is made of F4B with a dielectric constant of 2.65(1+0.003i), a width l1 = 10 mm, and a thickness t1 = 2 mm. The lower layer is covered entirely with copper, with a conductivity of 5.8e+007 S / m and a thickness t2 = 0.017 mm. The upper layer is divided into a coding pattern area with a width l2 = 8 mm. The coding pattern area is divided into a 16×16 matrix, where 1 represents a copper patch at the corresponding position, and 0 represents air at the corresponding position. The copper patch in the coding pattern has a conductivity of 5.8e+007 S / m, a width l3 = 0.5 mm, and a thickness t2 = 0.017 mm. The electromagnetic response of the electromagnetic metasurface unit of this structure depends on the coding pattern pattern of the upper layer, which adopts a centrally symmetrical design.

[0049] In step one, the steps for constructing the forward prediction dataset and the reverse design dataset are as follows:

[0050] 1) Randomly generate a 16×16 encoding matrix, construct the corresponding electromagnetic metasurface unit, and send it into electromagnetic simulation software to obtain the corresponding electromagnetic response. The frequency range is set to 8-12 GHz.

[0051] 2) The 16×16 encoding matrix is ​​expanded into a 32×32 encoding matrix by horizontal and vertical replication as the network input; this is to increase the input dimension and retain the feature dimension information after downsampling through the neural network;

[0052] 3) Amplitude A and phase of the electromagnetic response The following correspondence exists between the real part Re (real simulated value) and the imaginary part Im (imaginary simulated value) of the electromagnetic response:

[0053]

[0054]

[0055] 4) Based on the above relationships, the electromagnetic response is decomposed into a real part Re and an imaginary part Im. At the same time, the real part Re and the imaginary part Im are sampled at a uniform frequency with a sampling interval of 0.1 GHz. The real part Re and the imaginary part Im are represented as 41-dimensional vectors, which are used as labels for the dataset to construct a forward prediction dataset. The real part Re and the imaginary part Im are represented as 41-dimensional vectors and used as both input and label to construct a reverse design dataset.

[0056] Step 2: Divide the forward prediction dataset and the reverse design dataset constructed in Step 1 into 80% training set and 20% test set, respectively.

[0057] The input to the forward prediction dataset is a 32×32 encoding matrix, with corresponding labels being a 41-dimensional real part Re vector and a 41-dimensional imaginary part Im vector. The input to the reverse design dataset is a 41-dimensional real part Re vector and a 41-dimensional imaginary part Im vector, with corresponding labels being the same as the input, also a 41-dimensional real part Re vector and a 41-dimensional imaginary part Im vector.

[0058] Step 3: Construct as follows Figure 2 The model shown is a forward prediction network. The constructed forward prediction network model uses the same network structure for its real part network RNet and imaginary part network INet. The difference lies in that the output of the real part network RNet is a real vector, fitting the real part of the electromagnetic response; the output of the imaginary part network INet is an imaginary vector, fitting the imaginary part of the electromagnetic response. Both the real part network RNet and the imaginary part network INet use the ResNet18 architecture. The optimizer for the real part network RNet is set to Adam with a learning rate of 1e-3; the optimizer for the imaginary part network INet is also set to Adam with a learning rate of 1e-3.

[0059] use Let represent the network loss function, where y is the true value. Let m be the predicted value, and m be the dimension. The positive prediction dataset is fed into the positive prediction network model for training. The total loss value of the positive prediction network is defined as... Among them, Re f For the real part of the positive prediction dataset response, For the real part predicted by the positive prediction network, Im f For the imaginary part of the response of the positive prediction dataset, For the positive prediction network to predict the imaginary part, A f To predict the response magnitude of the dataset in a positive direction, To calculate the predicted magnitude of the prediction network, the parameters of the forward prediction network model are fixed after training.

[0060] Step 4: Construct the reverse engineering network model, including the real part generator network R-Generator and the imaginary part generator network I-Generator, and initialize the network parameters;

[0061] The real part generator network R-Generator and the imaginary part generator network I-Generator use the same network structure, as shown in the figure below. Figure 3As shown, the real part generator network R-Generator consists of deconvolution layers. By performing a deconvolution operation on the input 41-dimensional real part vector Re, a 64×64×1 real part pre-permutation matrix will be generated. The imaginary part generator network I-Generator also consists of deconvolution layers. By performing a deconvolution operation on the input 41-dimensional imaginary part vector Im, a 64×64×1 imaginary part pre-permutation matrix will be generated.

[0062] Step 5: Feed the real part training subset from the reverse design dataset into the real part generator network R-Generator of the reverse design network model, and feed the imaginary part training subset from the reverse design dataset into the imaginary part generator network I-Generator of the reverse design network model, and perform iterative training.

[0063] The final required metasurface artificial arrangement information It can be represented as a 16×16 matrix, because The central symmetry property, The top left quarter matrix This allows us to represent the entire artificial arrangement information of the metasurface. Right now:

[0064]

[0065] The matrix is ​​8×8 in size, and all its elements are either 0 or 1; we will Perform a stretching operation, Stretched to a 64×1 dimensional vector type

[0066] Introducing a permutation matrix P and a structure variable SV, where P is defined as a square binary matrix of size 64×64, containing only one 1 in each row and column, and zeros elsewhere; and SV is defined as a 64×1 vector containing n 1s, with all other elements being 0.

[0067]

[0068] Different structure variables SV can be generated by changing the size of n.

[0069] By introducing the permutation matrix P and the structural variable SV, the following relationship can be obtained:

[0070]

[0071] The structural variable SV is pre-set by the user, providing ample flexibility. The permutation matrix P is further generated by the real part generator network R-Generator and the imaginary part generator network I-Generator. Therefore, the reverse design method proposed in this invention does not directly utilize the artificial arrangement information of the metasurface. Instead of generating it directly, the artificial arrangement information of the metasurface is indirectly calculated by generating the permutation matrix P.

[0072] In order to generate a permutation matrix P that satisfies the properties of a permutation matrix, this invention uses the Gumbel-Sinkhorn operator to generate a permutation matrix P with discrete properties.

[0073] Due to the artificial arrangement of information matrix on metasurface The elements in the matrix are discrete values ​​of 0 or 1, while the output of the neural network is a continuous value between 0 and 1. Using a deep neural network generative model will generate a continuous value type of metasurface artificial arrangement information matrix. Therefore, a discrete mapping operation is required, that is...

[0074]

[0075] in, To output continuous values ​​for deep neural network generative models, This is a discrete mapping strategy.

[0076] Commonly used discrete mapping strategies One approach is a hard threshold method, which involves setting a fixed threshold to... Each is discretely mapped to either 0 or 1. The form is as follows:

[0077]

[0078] Probabilistic sampling can also be used, but since it cannot be differentiated in the backpropagation algorithm, it cannot be well incorporated into deep neural network models. These methods all introduce significant discrete mapping errors, which are not negligible in deep neural networks. This invention adopts a discrete mapping method that can reduce discrete mapping errors, namely, using the Gumbel-Sinkhorn operator as the discrete mapping method.

[0079] The specific process of the Gumbel-sinkhorn operator is as follows:

[0080] 1) The Sinkhorn operator is defined as follows:

[0081] S 0 (X)=e X

[0082]

[0083]

[0084] Where e is the natural logarithm, X is the input parameter, and S... l (X) represents the result of the l-th sinkhorn transformation on the input variable X. This indicates that a softmax operation is performed on each column of the matrix. This indicates that a softmax operation is performed on each row of the matrix. In order to ensure that the permutation matrix has elements that are either 0 or 1, a softmax temperature coefficient τ is introduced. At the same time, the temperature coefficient τ needs to be close to 0, and in the actual implementation, it is set to a small number.

[0085] The softmax function with a temperature coefficient τ is defined as follows:

[0086]

[0087] in For input variables, This represents the input variable of the c-th dimension.

[0088] 2) Introducing Gumbel distribution sampling to simulate probability sampling reduces the discrete mapping error caused by the discrete mapping strategy. The cumulative distribution function (CDF) of the Gumbel distribution is defined as:

[0089]

[0090] 3) The complete gumbel-sinkhorn operator is defined as follows:

[0091]

[0092] Among them, G i Let be a random variable that follows a Gumbel distribution.

[0093] In step five, the iterative calculation process for each round is as follows:

[0094] Step 5.1: Feed the real part training subset of the reverse design dataset into the real part generator network R-Generator to obtain the real part pre-permutation matrix with a size of 64×64×1; feed the imaginary part training subset of the reverse design dataset into the imaginary part generator network I-Generator to obtain the imaginary part pre-permutation matrix with a size of 64×64×1.

[0095] Step 5.2: Concatenate the real part pre-permutation matrix and the imaginary part pre-permutation matrix according to the channel dimension to generate an intermediate result matrix of size 64×64×2. Then, pass the intermediate result matrix through a convolutional channel fusion layer with a kernel size of 1×1 to generate a pre-permutation matrix of size 64×64×1. Perform Gumbel-sinkhorn operator calculation on the pre-permutation matrix to generate a permutation matrix P with the discrete characteristics of the permutation matrix.

[0096] Step 5.3: Introduce structural variables SV, which are discrete vectors. Perform vector multiplication between structural variables SV and the permutation matrix P obtained in Step 5.2 to indirectly obtain the generated metasurface arrangement pattern.

[0097] Specifically, by setting different values ​​for n, different structural variables SV can be obtained, thus providing great flexibility to the system model. Here, we choose to set n to 32. According to the binomial theorem, when n is 32, the possible types of artificial arrangement information on the metasurface are maximized. The artificial arrangement information vector on the metasurface is calculated using the structural variables SV and the permutation matrix P.

[0098] Step 5.4: Feed the metasurface arrangement pattern generated in Step 5.3 into the forward prediction network constructed in Step 3 to obtain the real part prediction value, imaginary part prediction value and magnitude prediction value respectively;

[0099] Specifically, the metasurface artificial arrangement information vector calculated in step 5.3 is used... Transform to obtain a quarter matrix Then The information matrix of artificial arrangement of metasurface is obtained by performing flip-symmetric filling. Artificially arranged information matrix of metasurface Horizontal and vertical translations are performed to replicate and expand the data, generating a 32×32 quadruple matrix of artificial metasurface arrangement information. Will The predicted value of the real part of the electromagnetic response is obtained by feeding it into a forward prediction network with fixed parameters. Imaginary part prediction value And the predicted amplitude value is calculated.

[0100] Step 5.5: Calculate the error using the real part prediction, imaginary part prediction, and magnitude prediction, and then use the backpropagation algorithm to update the parameters of the real part generator network R-Generator, the imaginary part generator network I-Generator, and the 1×1 convolutional fusion layer.

[0101] Specifically, the overall network loss value is still defined as follows: Where Rei is the real part of the response of the reverse design dataset. Let Imi be the real part of the reverse-engineered network's prediction, and let Imi be the imaginary part of the response to the reverse-engineered dataset. To reverse engineer the network for predicting the imaginary part, A i To reverse engineer the dataset response amplitude, To predict the amplitude of the reverse-engineered network, the overall network loss is calculated using the real part prediction, imaginary part prediction, and amplitude prediction obtained in step 5.4. The error is then used to update the parameters of the real part generator network R-Generator, the imaginary part generator network I-Generator, and the 1×1 convolutional channel fusion layer through backpropagation.

[0102] The electromagnetic material design method based on deep learning and structural variables proposed in this invention employs an indirect generative reverse design network model. It generates a permutation matrix, performs discretization optimization using the Gumbel-Sinkhorn operator, and then combines this with structural variables to obtain the final generated metasurface arrangement information. Compared to conventional deep learning generative models, this method overcomes the errors introduced during discretization, improves the final accuracy of the reverse design network model, and significantly enhances the flexibility and controllability of the reverse design network model through the introduction of structural variables.

[0103] The following examples illustrate the invention:

[0104] Example 1:

[0105] 4000 sets of 16×16 encoding matrices were randomly generated, and the encoding matrices were set to be centrally symmetric. Corresponding electromagnetic metasurface unit structures were constructed and fed into electromagnetic simulation software for numerical simulation. Following implementation step 1, a forward prediction dataset containing 40,000 (encoding matrix, real part, imaginary part) label pairs and a reverse design dataset containing 40,000 (real part, imaginary part, real part, imaginary part) label pairs were constructed. Following implementation step 2, the forward prediction dataset and the reverse design dataset were respectively divided into a training set of size 32,000 and a test set of size 8,000.

[0106] Following step three, a forward prediction network model is built, and the forward prediction dataset is fed into the model for iterative training. The real part network RNet and the imaginary part network INet optimizer are both set to Adam, with an initial learning rate of 1e-3 and a training epoch of 500.

[0107] Figure 4The diagram shows the decrease in the total loss value over 500 training epochs. The loss function of the forward prediction network gradually decreases, and the losses on the training and test sets are similar, eventually converging to a lower value. This demonstrates that the forward prediction network exhibits high accuracy and generalization ability. After 500 training epochs, the training set loss... total-f =2.6e-4, Test set Loss total-f =7.48e-3, Specifically, the specific values ​​of each loss value in the test set are shown in Table 1. After 500 training cycles, the test set approaches convergence and has achieved high accuracy. Randomly selected examples from the test set show the differences between the predicted and simulated values ​​of the forward network as follows: Figure 6 As shown, the similarity between the predicted and simulated values ​​of the forward prediction network is extremely high in the real part, imaginary part, amplitude, and phase. The forward prediction network has achieved high accuracy and can quickly and accurately predict the response of electromagnetic metasurfaces.

[0108] Table 1. Specific values ​​of the loss function during the forward network training process.

[0109]

[0110] The parameters of the trained forward prediction network are fixed. Following step four, a real part generator network (R-Generator) and an imaginary part generator network (I-Generator) are constructed. Further, according to step four, the reverse engineering dataset is fed into the real part generator network (R-Generator) and the imaginary part generator network (I-Generator) for iterative training. The structural variable SV is set to n = 32, the optimizer is set to Adam, the initial learning rate is 1e-3, and the training epochs are set to 200.

[0111] Figure 5 The diagram shows the decrease in the total loss value over 200 training epochs. The loss function of the inverse design network gradually decreases, and the losses on the training and test sets are similar, eventually converging synchronously to a lower value. The inverse design network exhibits high accuracy and generalization ability. After 200 epochs, the training set loss... total =1.51e-2, Test set Loss total =1.32e-2, Specifically, the specific values ​​of each loss in the test set are shown in Table 2. After 200 training cycles, the test set approaches convergence and has achieved a high level of accuracy. A random sample from the test set shows the differences between the designed and simulated values ​​of the reverse-engineered network. Figure 7 As shown, the design values ​​and simulation values ​​of the reverse engineering network are highly similar in real part, imaginary part, phase and amplitude. The reverse engineering network has achieved high accuracy and can meet the requirements of fast and accurate design.

[0112] Table 2. Specific numerical values ​​of the loss function during the reverse engineering network training process.

[0113]

Claims

1. A deep learning and structure variable based electromagnetic metamaterial design method, characterized in that, The method comprises the following steps: Step one: input the electromagnetic super surface unit structure design and related parameter periodic arrangement structure into electromagnetic simulation software to obtain corresponding electromagnetic response, construct a forward prediction dataset and a reverse design dataset; the forward prediction dataset and the reverse design dataset include generated electromagnetic response data, and the electromagnetic response data includes real part simulation values and imaginary part simulation values; Step two: divide the forward prediction dataset and the reverse design dataset constructed in step one into 80% training sets and 20% test sets, respectively; Step three: construct a forward prediction network model, train the segmented forward prediction dataset in the forward prediction network model, and fix the forward prediction network model parameters after the training is completed; Step four: construct a reverse design network model, including a real part generation network R-Generator and an imaginary part generation network I-Generator, and initialize network parameters; Step five: input the real part training subset in the reverse design dataset into the real part generation network R-Generator of the reverse design network model, input the imaginary part training subset in the reverse design dataset into the imaginary part generation network I-Generator of the reverse design network model, and perform iterative cycle training; In step five, the iterative calculation process of each round is as follows: Step 5.1: input the real part training subset in the reverse design dataset into the real part generation network R-Generator, and input the imaginary part training subset in the reverse design dataset into the imaginary part generation network I-Generator, to obtain real part preset permutation matrices and imaginary part preset permutation matrices, respectively; Step 5.2: splice the real part preset permutation matrices and the imaginary part preset permutation matrices according to a channel dimension, fuse channels through a 1×1 convolution layer, and then obtain a permutation matrix through a gumbel-sinkhorn operator; Step 5.3: introduce a structure variable in the form of a discrete vector; perform vector multiplication calculation on the structure variable and the permutation matrix obtained in step 5.2 to indirectly obtain a generated super surface arrangement pattern; Step 5.4: input the super surface arrangement pattern obtained in step 5.3 into the forward prediction network constructed in step three, to obtain real part prediction values, imaginary part prediction values and amplitude prediction values, respectively; Step 5.5: calculate errors through the real part prediction values, the imaginary part prediction values and the amplitude prediction values, and update the real part generation network R-Generator, the imaginary part generation network I-Generator and the 1×1 convolution fusion layer parameters through a back propagation algorithm.

2. The method of claim 1, wherein, In step one, the steps of constructing the forward prediction dataset and the reverse design dataset are as follows: The electromagnetic metasurface unit comprises an upper layer, a middle layer and a lower layer; the upper layer is divided into an encoding pattern region, the width ; the encoding pattern region is divided into a matrix , the conductivity of the encoding pattern metal copper patch is , the width is , and the thickness is ; the encoding pattern style adopts a central symmetry mode; the middle layer is made of F4B, the dielectric constant is , the width is , and the thickness is ; and the lower layer is fully covered with metal copper, the conductivity is , and the thickness is . 1) Randomly generated The encoding matrix is used to construct the corresponding electromagnetic super surface unit, and the corresponding electromagnetic response is obtained by inputting the electromagnetic simulation software, and the frequency range is set to ; 2) the encoding matrix of is transversely and longitudinally replicated to expand it into as network input; 3) magnitude of the electromagnetic response and phase , real part of the electromagnetic response and imaginary part The following correspondences exist: ； ； decomposing the electromagnetic response into real and imaginary parts sampling the real and imaginary parts at uniform frequency samples with a sampling interval of and imaginary parts, respectively, into 41 -dimensional vectors as labels of the dataset, a forward prediction dataset is constructed;​​​​ 4) the real part and the imaginary part are represented as 41-dimensional vectors both as input and label, constructing the inverse design dataset.

3. The method of claim 2, wherein, In step two: Forward prediction dataset input is The encoding matrix, with the corresponding label being a 41-dimensional real part The vector and a 41-dimensional imaginary part The vector; The reverse design dataset input is a 41 dimensional real part The vector sum is 41 dimensional imaginary part The vector, the corresponding label is the same as the input, is also a 41 dimensional real part The vector sum is 41 dimensional imaginary part The vector.

4. The method of claim 3, wherein, In step three: The constructed forward prediction network model has the same network structure for the real part network RNet and the imaginary part network INet, the real part network RNet outputs a real part vector to fit the real part of the electromagnetic response, the imaginary part network INet outputs an imaginary part vector to fit the imaginary part of the electromagnetic response, the real part network RNet and the imaginary part network INet both adopt the ResNet18 structure, the optimizer of the real part network RNet is set to Adam, and the learning rate is 1e-3; the optimizer of the imaginary part network INet is set to Adam, and the learning rate is 1e-3; with denotes the network loss function, where is the real value, is the predicted value, is the dimension, the forward prediction data set is fed into the forward prediction network model for training, and the total loss value of the forward prediction network is defined as , where the real part of the response of the forward prediction data set, is the predicted real part of the forward prediction network, the imaginary part of the response of the forward prediction data set, is the predicted imaginary part of the forward prediction network data set is the calculated predicted amplitude of the prediction network, and the parameters of the forward prediction network model are fixed after training is completed.

5. The method of claim 4, wherein, In the step four, The real part generator network R-Generator and the imaginary part generator network I-Generator use the same network structure. The real part generator network R-Generator consists of deconvolutional layers, which generate the input 41-dimensional real part vector. After deconvolution, it will generate The real part pre-permutation matrix; the imaginary part generator network I-Generator is also composed of deconvolution layers, which transform the input 41-dimensional imaginary part vector. After deconvolution, it will generate The imaginary part of the pre-permutation matrix.

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