Electromagnetic metamaterial design method and system based on deep neural network and genetic algorithm

Abstract

The invention provides an electromagnetic metamaterial design method based on a deep neural network and a genetic algorithm, and relates to the technical field of metamaterial design. Firstly, an initial structure sample for generating the electromagnetic metamaterial is obtained, and a training set is constructed. And constructing and utilizing the training set to train an electromagnetic metamaterial forward prediction network model. And taking a preset electromagnetic metamaterial structure parameter and set frequency information as the input of the model, and utilizing the electromagnetic metamaterial to forward predict the predicted reflection loss of each frequency point in the frequency information output by the network model. The method comprises the following steps: constructing a structure parameter original population of the electromagnetic metamaterial, solving an optimal solution of the structure parameter original population based on a genetic algorithm of neighborhood dynamic evolution regulation, and in the solving process, obtaining an optimal structure parameter of the electromagnetic metamaterial by predicting reflection loss and calculating an individual fitness value so as to design the electromagnetic metamaterial. According to the design method provided by the invention, the design efficiency and precision of the electromagnetic metamaterial are improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of metamaterial design, and more particularly to a method and system for designing electromagnetic metamaterials based on deep neural networks and genetic algorithms. BACKGROUND

[0002] With the rapid development of modern electronic information, wireless communication and radar systems, higher requirements are placed on metamaterials with specific electromagnetic response characteristics. Electromagnetic metamaterials are a class of functional materials that achieve specific electromagnetic properties through artificial structure design, and their functional characteristics are closely related to structural parameters. Due to the diversity of shape and structural parameters, the design is very complex. Therefore, how to accurately design the structural parameters to meet the expected electromagnetic response has become a key problem in the field of metamaterial design.

[0003] To design metamaterial structures that meet electromagnetic responses, it is necessary to establish a mapping relationship between metamaterial structures and electromagnetic responses. Traditional design methods mainly include numerical simulation such as finite element method or finite difference time domain method, and adjustment of structural parameters combined with the experience of designers. Although such methods can obtain high-precision simulation results, they are time-consuming and difficult to meet the actual needs of people for rapid iteration and high-performance optimization of metamaterial structures.

[0004] To overcome the above problems, researchers have gradually introduced machine learning techniques into the field of metamaterial design, using proxy modeling techniques to replace high-computational-cost simulations to speed up design optimization. For example, support vector regression (SVR) is used to model the reflectarray unit of an antenna to improve antenna design efficiency; a prediction model is constructed based on Gaussian process (GP) to quickly obtain optimal design parameters; and an integrated learning algorithm (XGBoost) is used to design a transmission coding super surface structure to achieve super surface structure design. However, as the amount of training data, design variables and constraints increases, the training time of machine learning methods increases dramatically. And the model needs to be retrained for different design tasks.

[0005] In contrast, deep neural networks (DNNs) have received increasing attention in the field of electromagnetic metamaterial design in recent years due to their superior non-linear fitting and automatic feature extraction capabilities. For example, multilayer perceptron (MLP) is used to predict the electromagnetic absorption performance of metamaterials to optimize the geometry of the wave absorber. The use of pre-trained convolutional neural networks (CNNs) for forward prediction and inverse design of metamaterial sensors significantly reduces the cost of manual parameter tuning; the use of series neural networks successfully applied in the design of electromagnetic metamaterials avoids complex electromagnetic simulation processes. However, although deep learning models have shown great potential in electromagnetic metamaterial design, the end-to-end design method inevitably has a non-unique problem, which may lead to difficulty in model convergence, decreased prediction stability, and reduced efficiency and accuracy of electromagnetic metamaterial design in the multi-solution design scenario. SUMMARY

[0006] In order to solve the problems of low design efficiency and low accuracy of the current electromagnetic metamaterial design method, the present application provides an electromagnetic metamaterial design method and system based on deep neural networks and genetic algorithms, which improves the efficiency and accuracy of electromagnetic metamaterial design.

[0007] In order to achieve the above technical effects, the technical solutions of the present application are as follows: S1: obtaining an initial structure sample of the generated electromagnetic metamaterial, and constructing a training set according to the initial structure sample; S2: constructing an electromagnetic metamaterial forward prediction network model, and training the electromagnetic metamaterial forward prediction network model using the training set to obtain a trained electromagnetic metamaterial forward prediction network model; S3: using the preset electromagnetic metamaterial structure parameters and the set frequency information as the input of the trained electromagnetic metamaterial forward prediction network model, and using the electromagnetic metamaterial forward prediction network model to output the predicted reflection loss of each frequency point in the frequency information; S4: constructing an original population of structure parameters of the electromagnetic metamaterial, and solving the optimal solution of the original population of structure parameters based on a genetic algorithm with neighborhood dynamic evolution regulation, wherein the predicted reflection loss is used to calculate the individual fitness value to obtain the optimal structure parameters of the electromagnetic metamaterial for electromagnetic metamaterial design.

[0008] Further, the electromagnetic metamaterial forward prediction network model comprises a first encoder module, L first feature fusion modules connected in sequence, and a first decoder module connected in sequence. The first encoder module comprises a first structure parameter encoder layer and a first frequency information encoder layer. The first feature fusion module comprises a first multi-head cross attention layer, a first residual connection and layer normalization layer, a first feedforward subnetwork layer and a second residual connection and layer normalization layer connected in sequence; the output ends of the first structure parameter encoder layer and the first frequency information encoder layer are connected to the first multi-head cross attention layer and the first residual connection and layer normalization layer; and the output end of the first residual connection and layer normalization layer is connected to the input end of the second residual connection and layer normalization layer. The first decoder module comprises a first full connection layer, a second full connection layer and a first GELU activation function layer connected in sequence.

[0009] Further, in the first encoder module, it is assumed that X S ∈ represents a preset structure parameter; the structure parameter is mapped to a high-dimensional space through linear transformation, layer normalization and GELU activation function to obtain a structure feature, and the expression is as follows:

[0010] In the formula, represents a structure feature, represents an activation function, and LayerNorm represents layer normalization, represents a weight matrix, represents a weight matrix, and B represents a batch size. In the first frequency information encoder layer, it is assumed that X P ∈ represents a preset frequency information; a frequency embedding matrix is obtained through point-by-point encoding, frequency position encoding is introduced, and element addition is performed to obtain a frequency domain feature, and the expression is as follows:

[0011] In the formula, represents a frequency domain feature, represents a frequency embedding matrix, represents frequency position encoding.

[0012] Further, in the first multi-head cross attention layer, it is assumed that SP ext ∈ represents a global feature generated by dimension expansion of the structure feature; through feature projection, a query matrix Q, a key matrix K and a value matrix V are generated by using the global feature and the frequency domain feature, and the expression is as follows:

[0013] In the formula, l represents the number of layers of the multi-head cross attention layer, , denotes a learnable parameter matrix, Q denotes a query vector matrix, K denotes a key matrix, V a value matrix; The query vector matrix Q, the key matrix K, and the value matrix V are split into multi-head attentions along the feature dimension, dot products are calculated and scaled to obtain each head attention score, and the expression is:

[0014] In the formula, d k denotes a scaling factor, denotes a head attention score, denotes a normalized exponential function.

[0015] Further, the process of step S4 is: S41: using Latin hypercube sampling method, constructing the original population of electromagnetic metamaterial structure parameters; the original population includes m individuals, and each individual corresponds to a set of electromagnetic metamaterial design parameters; S42: generating the field individuals of the original population individuals based on a dynamic neighborhood disturbance mechanism, and forming an exploration elite population including the original population individuals and the field individuals; S43: calculating the fitness values of the individuals in the exploration elite population by using the predicted reflection loss, screening the individuals in the exploration elite population based on the fitness of the individuals in the exploration elite population, and obtaining a new generation of exploration elite population; S44: based on a hybrid crossover strategy, hybrid crossover is performed on the original population and the new generation of exploration elite population to generate a child population; S45: setting the number of iterations, taking the child population generated in step S44 as the original population, repeating steps S41 to S44 until the set number of iterations is reached, selecting the optimal individual from the child population, and obtaining the optimal structure parameters of the electromagnetic metamaterial for electromagnetic metamaterial design.

[0016] Further, based on the dynamic neighborhood disturbance mechanism, the expression for generating the field individuals of the original population individuals is:

[0017] In the formula, denotes a field individual, and Δ denotes a uniformly distributed disturbance vector, denotes an original population individual, denotes a dynamic adjustment coefficient, denotes the upper bound of the electromagnetic metamaterial structure parameters, denotes the lower bound of the electromagnetic metamaterial structure parameters.

[0018] ​Further, the expression for calculating the fitness value of the individual of the exploration elite population by using the predicted reflection loss is:

[0019] wherein, represents the fitness function, represents the weight coefficient, represents the return loss, represents the constraint penalty term, represents the maximum value of the working frequency, represents the minimum value of the working frequency, i represents the working frequency.

[0020] Further, the specific process of S43 is: The expression for calculating the crowding degree of the individual of the exploration elite population is:

[0021] wherein, represents the crowding degree, represents the i-th individual of the exploration elite population, represents the j-th individual of the exploration elite population, represents the k-th dimension of the i-th individual of the exploration elite population, represents the k-th dimension of the j-th individual of the exploration elite population, represents the dimension; The expression for calculating the comprehensive score of each individual of the exploration elite population by using the crowding degree and the fitness of the individual of the exploration elite population is:

[0022] wherein, represents, represents the diversity weight, represents the standardized value of the crowding degree, represents the standardized value of the fitness.

[0023] ​Further, based on the hybrid crossover strategy, the original population and the new generation of exploration elite population are hybridly crossed to generate the offspring population, the process being: a crossover probability threshold CT is set, and a random probability u is generated in the crossover process; when the crossover probability threshold CT is greater than the generated random probability u, a roulette wheel selection method is used to select one individual from the new generation of exploration elite population and the original population as a parent individual, and a crossover operation is performed to generate the offspring population; when the crossover probability threshold CT is less than or equal to the generated random probability u, two individuals are selected from the original population to perform a crossover operation to generate the offspring population.

[0024] A deep neural network and genetic algorithm-based electromagnetic metamaterial design system, comprising: A data acquisition module is configured to acquire an initial structure sample of an electromagnetic metamaterial, and construct a training set according to the initial structure sample. A model construction and training module is configured to construct an electromagnetic metamaterial forward prediction network model, and train the electromagnetic metamaterial forward prediction network model using the training set to obtain a trained electromagnetic metamaterial forward prediction network model. A prediction module is configured to use a preset electromagnetic metamaterial structure parameter and a set frequency information as an input of the trained electromagnetic metamaterial forward prediction network model, and use the electromagnetic metamaterial forward prediction network model to output a predicted reflection loss of each frequency point in the frequency information. A design module is configured to construct an original population of structure parameters of the electromagnetic metamaterial, solve an optimal solution of the original population of structure parameters based on a genetic algorithm of neighborhood dynamic evolution regulation, calculate an individual fitness value using the predicted reflection loss in the solving process, obtain an optimal structure parameter of the electromagnetic metamaterial, and design the electromagnetic metamaterial.

[0025] Compared with the prior art, the method has the following beneficial effects: The method and system for designing electromagnetic metamaterials based on a deep neural network and a genetic algorithm are proposed, the initial structure sample of the electromagnetic metamaterial is first acquired, and a training set is constructed, then the electromagnetic metamaterial forward prediction network model is constructed and trained, the reflection loss can be efficiently predicted through the forward prediction network model, and accurate calculation basis is provided for the genetic algorithm. The trained model is used to output the predicted reflection loss of each frequency point using the preset electromagnetic metamaterial structure parameter and the set frequency information, finally, the original population of structure parameters of the electromagnetic metamaterial is constructed, the genetic algorithm of neighborhood dynamic evolution regulation is used to solve the optimal solution by combining the predicted reflection loss to calculate the individual fitness value, the optimal structure parameter of the electromagnetic metamaterial is obtained, and the electromagnetic metamaterial is designed. The genetic algorithm of neighborhood dynamic evolution regulation is integrated, the efficiency and accuracy of solving the optimal structure parameter are improved, and the efficiency and precision of the electromagnetic metamaterial design are improved when the forward prediction network model is used. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 Figure 1 shows a flow chart of the electromagnetic metamaterial design method based on the deep neural network and the genetic algorithm according to an embodiment of the present application; Figure 2 Figure 2 shows a structure diagram of the electromagnetic metamaterial forward prediction network model according to an embodiment of the present application; Figure 3 Figure 3 shows a schematic diagram of the electromagnetic metamaterial design method based on the deep neural network and the genetic algorithm according to an embodiment of the present application; Figure 4 Figure 4 shows a schematic diagram of the hybrid crossover strategy according to an embodiment of the present application; Figure 5 Figure 5 shows a comparison diagram of the average convergence curves of the genetic algorithm and the existing algorithm according to an embodiment of the present application; Figure 6 Figure 6 shows a comparison diagram of the population diversity variation curves of the genetic algorithm and the existing algorithm according to an embodiment of the present application; Figure 7 Figure 7 shows a comparison diagram between the prediction results and the simulation results under the wideband response according to an embodiment of the present application; Figure 8 Figure 8 shows an RL curve diagram under different thicknesses of the ultra-thin structure design according to an embodiment of the present application; Figure 9 Figure 9 shows a comparison diagram between the prediction results and the simulation results under the ultra-thin structure design according to an embodiment of the present application; Figure 10 Figure 10 shows a comparison diagram between the prediction results and the simulation results under the fixed parameter design according to an embodiment of the present application; Figure 11 Figure 11 shows a structure diagram of the electromagnetic metamaterial design system based on the deep neural network and the genetic algorithm according to an embodiment of the present application. DETAILED DESCRIPTION

[0027] The accompanying drawings are only used for illustrative description and cannot be understood as a limitation of the present patent; In order to better illustrate the present embodiment, some parts of the drawings are omitted, enlarged or reduced, and do not represent the actual size; It is understandable for those skilled in the art that some known content in the drawings can be omitted.

[0028] The technical solutions of the present application will be further described below in combination with the drawings and embodiments.

[0029] The positional relationship described in the drawings is only used for illustrative description and cannot be understood as a limitation of the present patent; Embodiment 1 The present embodiment proposes an electromagnetic metamaterial design method based on a deep neural network and a genetic algorithm, as shown inFigure 1 As shown in the flowchart of the method, the method proposed in this embodiment includes the following steps in whole: S1: obtaining an initial structure sample of generating electromagnetic metamaterial, and constructing a training set according to the initial structure sample; S2: constructing an electromagnetic metamaterial forward prediction network model, and training the electromagnetic metamaterial forward prediction network model by using the training set to obtain a trained electromagnetic metamaterial forward prediction network model; S3: taking preset electromagnetic metamaterial structure parameters and set frequency information as inputs of the trained electromagnetic metamaterial forward prediction network model, and outputting, by using the electromagnetic metamaterial forward prediction network model, a predicted reflection loss of each frequency point in the frequency information; S4: constructing an original population of structure parameters of the electromagnetic metamaterial, solving an optimal solution of the original population of structure parameters based on a genetic algorithm of neighborhood dynamic evolution regulation, calculating an individual fitness value by using the predicted reflection loss in the solving process, obtaining optimal structure parameters of the electromagnetic metamaterial, and designing the electromagnetic metamaterial.

[0030] The structure design of the electromagnetic metamaterial is essentially an optimization problem with a high-dimensional parameter space and multiple constraint conditions. The core objective is to find the optimal metamaterial structure configuration from a set of structure parameters to be adjusted (such as resistance, dielectric layer thickness, etc.) while meeting specific electromagnetic performance objectives.

[0031] In this embodiment, Latin hypercube sampling (LHS) is used to uniformly sample in the electromagnetic metamaterial design variable space to obtain an initial structure sample of generating the electromagnetic metamaterial, and a training set is constructed according to the initial structure sample.

[0032] For example, the initial structure sample is set to 60000 groups.

[0033] The reflection loss RL is obtained by using the (HFSS) platform for electromagnetic simulation, and the training set is constructed. Based on the training set, the electromagnetic metamaterial forward prediction network model FPETNet is trained to establish the mapping relationship between the structure parameters and the frequency domain response. After the prediction model is trained, it is used for individual fitness value calculation in the genetic algorithm, and finally the electromagnetic metamaterial parameter design scheme with optimal absorption performance within the working frequency is obtained.

[0034] In this embodiment, as shown in the structure diagram of the model, Figure 2 The electromagnetic metamaterial forward prediction network model includes: a first encoder module, L first feature fusion modules connected in sequence, and a first decoder module connected in sequence; The first encoder module includes a first structure parameter encoder layer and a first frequency information encoder layer; The first feature fusion module comprises a first multi-head cross attention layer, a first residual connection and layer normalization layer, a first feedforward subnetwork layer and a second residual connection and layer normalization layer connected in sequence; the output ends of the first structure parameter encoder layer and the first frequency information encoder layer are connected to the first multi-head cross attention layer and the first residual connection and layer normalization layer; and the output end of the first residual connection and layer normalization layer is connected to the input end of the second residual connection and layer normalization layer. The first decoder module comprises a first full connection layer, a second full connection layer and a first GELU activation function layer connected in sequence.

[0035] The electromagnetic metamaterial design parameters include arrangement period p, square ring outer size a1, square ring outer size a2, square ring outer size a3, square ring width w, surface resistance r1, surface resistance r2, surface resistance r3, thickness of each layer of dielectric d1, thickness of each layer of dielectric d2 and thickness of each layer of dielectric d3.

[0036] The electromagnetic metamaterial forward prediction network model adopts a typical encoder-decoder structure. The structure parameters are mapped to a high-dimensional space through a first structure parameter encoder layer to obtain a structure feature vector SP. The frequency information is discretized into 17 sampling points in the frequency range of 2-18 GHz, and the input dimension is [B, 17]. After the first frequency information encoder layer, it is mapped to [B, 17, 64], and the learnable position encoding is fused to obtain the frequency feature vector F, so as to retain the sequence relationship and position information between the frequency points. The structure feature vector SP and the frequency feature vector F are input into the cross attention module to establish the dynamic dependence relationship between the structure and the frequency.

[0037] In the first encoder module: let X S ∈ , which represents the preset structure parameter; the structure parameter is mapped to a high-dimensional space through linear transformation, layer normalization and GELU activation function to obtain the structure feature, and the expression is:

[0038] In the formula, , which represents the structure feature, , which represents the activation function, LayerNorm represents layer normalization, , which represents the weight matrix, , which represents the weight matrix, and B represents the batch size; In the first frequency information encoder layer: let X P ∈ , which represents the preset frequency information; the frequency embedding matrix is obtained by point-by-point encoding, the frequency position encoding is introduced, and the frequency domain feature is obtained by element-wise addition, and the expression is:

[0039] wherein, represents a frequency domain feature, represents a frequency embedding matrix, represents a frequency position encoding.

[0040] In the embodiment, the multi-head cross-attention layer is composed of L=3 layers stacked, each layer containing a multi-head attention mechanism and a feed-forward subnetwork (FFN), and introducing a residual connection and a layer normalization operation. In the attention mechanism, the frequency embedding F is taken as the query vector (Query, Q), and the structure feature vector SP is taken as the key and value (Key, K / Value, V) to perform cross-modal attention calculation.

[0041] In the first multi-head cross-attention layer: let SP ext ∈ represents a global feature generated by dimension expansion of the structure feature; through feature projection, the global feature and the frequency domain feature are used to generate a query vector matrix Q, a key matrix K, and a value matrix V, and the expression is:

[0042] wherein, l represents the number of layers of the multi-head cross-attention layer, 、 、 represents a learnable parameter matrix, Q represents a query vector matrix, K represents a key matrix, V a value matrix; The query vector matrix Q, the key matrix K, and the value matrix V are divided into multi-head attention along the feature dimension, the dot product is calculated and scaled to obtain the attention score of each head, and the expression is:

[0043] wherein, d k represents a scaling factor, represents a head attention score, represents a normalized exponential function. Wherein d k =8 is a scaling factor for stabilizing gradient calculation.

[0044] In the embodiment, the feature dimension is set to 8. The self-attention score of each group is calculated, the output result of the obtained self-attention score is spliced, and then multiplied by the weight vector W l O ∈ to obtain the final output vector of the first multi-head cross-attention layer, and the expression is:

[0045] wherein, MultiHead represents an output vector, represents a concatenation operation, represents the output of the first attention head in the l-th layer.

[0046] In the first feedforward subnetwork layer, the expression is:

[0047] wherein, W 1∈ represents a weight matrix, W 2∈ represents a weight matrix, represents the output of the first feedforward subnetwork layer, represents the input of the first feedforward subnetwork layer, represents a bias, represents a bias.

[0048] Different frequency points are dynamically screened by attention weights to select the most relevant structural parameters. Compared with the traditional self-attention, the computational complexity is reduced from O(B·172·64) to O(B·17·64), which improves the computational efficiency of the model.

[0049] In the decoder part, the output features are mapped in the frequency domain through two layers of fully connected network. First, the features are mapped from [B, 17, 64] to [B, 17, 128] using a feedforward network, and nonlinearity is introduced through a GELU activation function; then it is mapped to the final output shape [B, 17, 1], i.e. the predicted reflection loss RLi at each frequency point.

[0050] In the training process, the Adam optimizer is used, the learning rate is 2e-4, the Batch Size is 64, and the model is trained for 100 rounds. The loss value of the model on the training set and the validation set continues to decrease, and finally converges (the training loss is 0.012; the validation loss is 0.007). Finally, iterative optimization is performed, and the surrogate model is constantly updated until the maximum iteration requirement is met, and the iteration is stopped.

[0051] Embodiment 2 In this embodiment, the process of solving the optimal solution of the original population of structural parameters by genetic algorithm based on neighborhood dynamic evolution regulation is described in detail.

[0052] Genetic Algorithm (GA) is a heuristic algorithm commonly used to find the global optimal solution of multi-dimensional objective function in a given parameter space. Traditional Genetic Algorithm (GA) often faces premature convergence and local optimal trap. Based on the dynamic evolution regulation of neighborhood, the dynamic neighborhood disturbance mechanism, the elite diversity selection and the dynamic crossover strategy are introduced to realize the efficient exploration of the design parameter space, effectively expand the search range and avoid premature convergence, and help the algorithm jump out of the local optimal solution.

[0053] In this embodiment, as shown in the schematic diagram of Figure 3 The process of step S4 is: S41: Latin hypercube sampling method is used to construct the original population of electromagnetic metamaterial structure parameters; the original population contains m individuals, and each individual corresponds to a set of electromagnetic metamaterial design parameters; S42: Based on the dynamic neighborhood disturbance mechanism, the field individuals of the original population individuals are generated, and the exploration elite population including the original population individuals and the field individuals is constructed; S43: The fitness value of the individuals in the exploration elite population is calculated by using the predicted reflection loss, and the individuals in the exploration elite population are screened by using the fitness of the individuals in the exploration elite population, to obtain a new generation of exploration elite population; S44: Based on the hybrid crossover strategy, the original population and the new generation of exploration elite population are hybrid crossed to generate a child population; S45: Set the number of iterations, take the child population generated in step S44 as the original population, repeat steps S41 to S44 until the set number of iterations is reached, select the optimal individual from the child population to obtain the optimal structure parameters of the electromagnetic metamaterial, and design the electromagnetic metamaterial.

[0054] In this embodiment, the initial population S0 is generated by binary coding and contains m individuals. For each structure parameter, the coding length is determined according to its value range, and the parameters are spliced in order to form a complete binary chromosome. Finally, each row of the binary coding matrix corresponds to a parameter combination of an individual.

[0055] Based on the dynamic neighborhood disturbance mechanism, the expression for generating the field individuals of the original population individuals is:

[0056] In the formula, represents the field individual, Δ represents a uniformly distributed disturbance vector, represents the original population individual, represents a dynamic adjustment coefficient, represents the upper bound of the electromagnetic metamaterial structure parameter, represents the lower bound of the electromagnetic metamaterial structure parameter. Δ~U(-0.5,0.5)11 represents a uniformly distributed disturbance vector. ∈ [0.5-t / 2T, 0.5+t / 2T] is a dynamic adjustment coefficient. As the iteration number t increases, The disturbance interval of achieves the adaptive conversion from early wide-area exploration to late local search. ∘ represents the Hadamard product, t represents the current iteration number, and T represents the maximum iteration number.

[0057] The expression for calculating the fitness value of the individual in the exploration elite population is:

[0058] In the formula, represents the fitness function, represents the weight coefficient, represents the return loss, represents the constraint penalty term, represents the maximum value of the working frequency, represents the minimum value of the working frequency, i represents the working frequency.

[0059] The specific process of S43 is: The expression for calculating the crowding degree of the individual in the exploration elite population is:

[0060] In the formula, represents the crowding degree, represents the i th individual in the exploration elite population, represents the j th individual in the exploration elite population, represents the k th dimension of the i th individual in the exploration elite population, represents the k th dimension of the j th individual in the exploration elite population, represents the dimension; Using the crowding degree and fitness of the individual in the exploration elite population, the comprehensive score of each individual is calculated, and the individuals are sorted according to the comprehensive score. The m individuals with the highest scores are selected to obtain a new generation of exploration elite population; The expression for calculating the comprehensive score of the individual in the exploration elite population is:

[0061] In the formula, represents, represents the diversity weight, represents the standardized value of the crowding degree, represents the standardized value of the fitness.

[0062] The expression for calculating the standardized value of the crowding degree is:

[0063] wherein, denotes the normalized value of crowding degree, denotes the minimum value of crowding degree, denotes the maximum value of crowding degree, = 10-6, to prevent division by zero.

[0064] The expression of the normalized value of fitness is:

[0065] denotes the normalized value of fitness, denotes the minimum value of fitness, denotes the maximum value of fitness.

[0066] The sum of crowding degrees considers the Euclidean distance of all individuals in the population (parameter dimension D = 11), quantifying the dispersion degree of individuals in the parameter space. Then the same maximum-minimum normalization processing is performed to obtain. Finally, the comprehensive score is calculated, and the m individuals with the highest score are selected to form the new generation of exploration elite population EPt.

[0067] As shown in the schematic diagram shown in Figure 4 , based on the hybrid crossover strategy, the original population and the new generation of exploration elite population are hybrid crossed to generate the process of the offspring population: set the crossover probability threshold CT, generate a random probability u in the crossover process; when the crossover probability threshold CT is greater than the generated random probability u, a roulette wheel method is used to select one individual from the new generation of exploration elite population and the original population as the parent individual, and the crossover operation is performed to generate the offspring population; when the crossover probability threshold CT is less than or equal to the generated random probability u, two individuals are selected from the original population to perform the crossover operation to generate the offspring population.

[0068] The algorithm flow of the genetic algorithm based on neighborhood dynamic evolution regulation is as follows: Input: original population S, fixed crossover probability threshold CT; original population individual number m; iteration number T; Output: optimal structure parameters x* of electromagnetic metamaterials; 1. for t = 1 to T do 2. generate exploration elite population EP t ’ ; 3. calculate the individual fitness value Fitness of the exploration elite population by using the predicted reflection loss; 4. use the crowding degree and the fitness of the exploration elite population individual; 5. Calculate the overall score of each individual, sort them according to their overall scores, and select the m individuals with the highest scores to obtain the new generation of elite explorer population EPt; 6. for i = 1 to m do 7. If Pd ≥ CT then 8.parents ← roulette_select( S t , 2) ; 9.else 10.parents← [roulette_select( S t , 1), random_choice( EP t , 1)] 11. Perform the intersection of two points → child1, child2; 12. end for 13. Update the population S t+1 = new_population 14. end for 15.return x* = argmin(Fitness (ST)).

[0069] In this embodiment, a genetic algorithm based on neighborhood dynamic evolution control is used to solve for the optimal solution of the original population of structural parameters, and its effectiveness in electromagnetic metamaterial design is verified. To ensure the stability and robustness of the results, the algorithm is run independently 30 times, with the number of iterations T set to 100 and the population size uniformly set to 40. In the comparative experiment, the performance of the method proposed in this embodiment is compared with traditional genetic algorithms (GA), particle swarm optimization (PSO), differential evolution (DE), and quantum particle swarm optimization (QPSO). The optimization objective is to reduce reflection loss near low frequency 4 GHz and high frequency 10 GHz. RL i ≤-30dB, the crossover probability of the method in this embodiment ( P c ) and mutation probability ( P m Set them to 0.8 and 0.01 respectively. For example... Figure 5 The comparison of average convergence curves shown illustrates that the fitness value steadily decreases during iteration, reaching its lowest point in the later stages of iteration, effectively avoiding getting trapped in local optima. Figure 6The comparison of population diversity curves shown in the figure evaluates the trend of population diversity changes during the iteration process of each algorithm by calculating the Euclidean distance between individuals in the population. The results show that the algorithm proposed in this embodiment has high diversity in the early stage, which is beneficial for global search, and the diversity gradually decreases in the later stage, ensuring the convergence of the final solution. In contrast, GA, PSO, and DE show a rapid decrease in diversity in the early stage, making them prone to premature convergence. Although QPSO has high diversity, it lacks a convergence trend in the later stage. Overall, the genetic algorithm proposed in this embodiment effectively balances exploration ability and convergence performance.

[0070] Example 3 In this embodiment, to verify the performance of the electromagnetic metamaterial design methods based on deep neural networks and genetic algorithms proposed in Embodiments 1 and 2, three electromagnetic metamaterial optimization tasks with different objective requirements were set up. Finite element models were established using HFSS to compare the experimental results with simulation results, thus verifying the effectiveness of the proposed electromagnetic metamaterial design methods based on deep neural networks and genetic algorithms.

[0071] In this embodiment, the experimental platform uses an Intel(R) Core(TM) i7-12400F processor with a CPU frequency of 2.50GHz, 32GB of memory, and an NVIDIA GTX4060 graphics card, and is implemented on a Win10 system based on the Python language.

[0072] In the "wideband" design, for the electromagnetic metamaterial design, the following target specifications are selected: frequency range of 2GHz~18GHz, minimum reflectivity RLi=-10dB, and the same electromagnetic metamaterial material as before. For example... Figure 7 The graph shown compares the predicted and simulated results under wideband response, with the reflection loss calculated by HFSS simulation and the electromagnetic metamaterial forward prediction network model at a threshold of -10 dB. RL i The simulation results show good agreement with the predicted results, and the experiments further verify the feasibility of the method. Table 1 shows the average reflection loss and minimum reflection loss across the entire frequency band of the electromagnetic metamaterial at low frequencies (2–10 GHz) and high frequencies (10–18 GHz). The designed optimal structure has an effective absorption bandwidth of 100% in the 2–18 GHz frequency range, an average RL of -18.237 dB, and a minimum RL of -35.012 dB, which fully meets the pre-design objectives. Table 2 shows the optimal solution parameters of the electromagnetic metamaterial under broadband response.

[0073] Table 1

[0074] Table 2

[0075] Thinning is a key objective in the optimization of electromagnetic metamaterial structures. To meet the design requirements of lightweighting, this study explores the impact of different thicknesses on the microwave absorption performance of electromagnetic metamaterials. Taking a "wide" bandgap design as an example, keeping other structural parameters constant, the sum of the thicknesses of each layer, dsum, is further optimized, where dsum = d1 + d2 + d3. Figure 8 The RL curves shown below illustrate the effects of different dsum thicknesses. As the dsum thickness decreases, the average reflection loss continuously increases in the low-frequency range of 2–4 GHz, with dsum2–dsum5 failing to meet the threshold value. The design requirement is <-10dB. To achieve efficient absorption while minimizing thickness, a penalty function for thickness dsum is introduced into the fitness function. The following target specifications are selected: frequency range of 2GHz to 18GHz, and minimum reflectivity. RL i =-10dB, the fitness function further considers the minimum medium thickness dsum, which is 16.4mm. For example... Figure 9 The comparison chart shown shows the difference between the predicted and simulated results for the ultrathin structure design. Compared to the broadband response design, the thickness is significantly reduced by 24.4% (from 21.7 mm to 16.4 mm).

[0076] The expression for the fitness function is:

[0077] Table 3 shows the optimal solution parameters for electromagnetic metamaterials in ultrathin structure design.

[0078] Table 3

[0079] For a design with fixed parameters, the following objectives are selected: frequency range of 2GHz to 18GHz, and minimum reflectivity. RL i =-10dB, the electromagnetic metamaterial is the same material as in the previous example and the total thickness dsum = 20mm is fixed (d1+d2+d3). For example... Figure 10 The comparison chart shown here, which compares the predicted and simulated results under the fixed parameter design, demonstrates the comparison between the HFSS simulation and the predicted RL curve of the model proposed in this embodiment with structural parameters of thickness dsum=20mm. The simulated and predicted return loss curves are basically fitted.

[0080] Table 4 shows the optimal solution parameters for electromagnetic metamaterials designed with fixed parameters.

[0081] Table 4

[0082] Through the above three tasks, the electromagnetic metamaterial design method based on deep neural network and genetic algorithm can meet the design requirements, and the three groups of structure parameters RL i The predicted value and the simulation value are compared, the prediction and simulation results of the model are compared by calculating the mean absolute percentage error (MAPE) between them, and the expression is:

[0083] In the formula, represents the mean absolute percentage error, represents the predicted value, represents the simulation value. The MAPE of the three groups of optimal solutions is 4.42%, 7.99%, and 4.75%, respectively.

[0084] Example 4 In this embodiment, as shown in the structural diagram shown in Figure 11 , a deep neural network and genetic algorithm-based electromagnetic metamaterial design system is provided, which includes: A data acquisition module is configured to acquire an initial structure sample of an electromagnetic metamaterial, and construct a training set according to the initial structure sample. A model construction and training module is configured to construct an electromagnetic metamaterial forward prediction network model, and train the electromagnetic metamaterial forward prediction network model using the training set to obtain a trained electromagnetic metamaterial forward prediction network model. A prediction module is configured to use a preset electromagnetic metamaterial structure parameter and a set frequency information as an input of the trained electromagnetic metamaterial forward prediction network model, and use the electromagnetic metamaterial forward prediction network model to output a predicted reflection loss of each frequency point in the frequency information. A design module is configured to construct an original population of structure parameters of an electromagnetic metamaterial, solve an optimal solution of the original population of structure parameters based on a genetic algorithm of neighborhood dynamic evolution regulation, calculate an individual fitness value using the predicted reflection loss in the solving process, obtain optimal structure parameters of the electromagnetic metamaterial, and design the electromagnetic metamaterial.

[0085] The embodiments are only examples for clearly illustrating the present application, and are not intended to limit the embodiments of the present application. Based on the above description, other different forms of changes or variations can be made by those of ordinary skill in the art. Here, it is not necessary or possible to exhaust all embodiments. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the claims of the present application.

Claims

1. A method for designing electromagnetic metamaterials based on deep neural networks and genetic algorithms, characterized in that, The method comprises the following steps: S1: obtaining an initial structure sample of an electromagnetic metamaterial, and constructing a training set according to the initial structure sample; S2: constructing an electromagnetic metamaterial forward prediction network model, and training the electromagnetic metamaterial forward prediction network model by using the training set to obtain a trained electromagnetic metamaterial forward prediction network model; S3: taking preset electromagnetic metamaterial structure parameters and set frequency information as inputs of the trained electromagnetic metamaterial forward prediction network model, and outputting, by using the electromagnetic metamaterial forward prediction network model, a predicted reflection loss of each frequency point in the frequency information; S4: constructing a structure parameter original population of the electromagnetic metamaterial, solving an optimal solution of the structure parameter original population based on a genetic algorithm of a neighborhood dynamic evolution regulation, calculating, in the solving process, an individual fitness value by using the predicted reflection loss, obtaining optimal structure parameters of the electromagnetic metamaterial, and designing the electromagnetic metamaterial. 2.The electromagnetic metamaterial design method based on deep neural network and genetic algorithm according to claim 1, wherein, The electromagnetic metamaterial forward prediction network model comprises a first encoder module, L first feature fusion modules connected in sequence, and a first decoder module connected in sequence. The first encoder module comprises a first structure parameter encoder layer and a first frequency information encoder layer. The first feature fusion module comprises a first multi-head cross attention layer, a first residual connection and layer normalization layer, a first feedforward subnetwork layer, and a second residual connection and layer normalization layer connected in sequence; the output ends of the first structure parameter encoder layer and the first frequency information encoder layer are connected to the first multi-head cross attention layer and the first residual connection and layer normalization layer; and the output end of the first residual connection and layer normalization layer is connected to the input end of the second residual connection and layer normalization layer. The first decoder module comprises a first full connection layer, a second full connection layer, and a first GELU activation function layer connected in sequence.

3. The method of claim 2, wherein, In the first encoder module: set X S ∈ represents a preset structure parameter; the structure parameter is mapped to a high-dimensional space through linear transformation, layer normalization and a GELU activation function to obtain a structure feature, and the expression is as follows: wherein denotes a structural feature, denotes an activation function, LayerNorm denotes a layer normalization, denotes a weight matrix, denotes a weight matrix, B denotes a batch size; In the first frequency information encoder layer: set X P ∈ represents the preset frequency information; the frequency embedding matrix is obtained by encoding each frequency point, the frequency position encoding is introduced, and the frequency domain features are obtained by element-wise addition, and the expression is: wherein denotes a frequency domain feature, denotes a frequency embedding matrix, denotes a frequency position encoding.

4. The method of claim 2, wherein, In the first multi-head cross-attention layer: let SP ext ∈ The global feature generated by dimension expansion of the structural features By feature projection, a query vector matrix Q, a key matrix K, and a value matrix V are generated by using global features and frequency domain features, and an expression is as follows: In the formula, l represents the number of multi-head cross attention layers, , , represents a learnable parameter matrix, Q represents a query vector matrix, K represents a key matrix, and V represents a value matrix. The query vector matrix Q, the key matrix K, and the value matrix V are divided into multiple attention heads along the feature dimension, a dot product is calculated and scaled to obtain a score of each head attention, and an expression is as follows: wherein d k denotes a scaling factor, denotes a head attention score, denotes a normalized exponential function.

5. The method of claim 1, wherein, The process of step S4 is as follows: S41: a Latin hypercube sampling method is used to construct a structure parameter original population of the electromagnetic metamaterial; the original population comprises m individuals, and each individual corresponds to a set of electromagnetic metamaterial design parameters; S42: a dynamic neighborhood disturbance mechanism is used to generate a field individual of an original population individual, and an exploration elite population comprising the original population individual and the field individual is constructed; S43: the predicted reflection loss is used to calculate an individual fitness value of the exploration elite population, the individuals in the exploration elite population are screened by using the fitness of the individuals in the exploration elite population, and a new generation of exploration elite population is obtained; S44: a hybrid crossover strategy is used to perform hybrid crossover on the original population and the new generation of exploration elite population to generate a child population; and S45: the child population is used to construct the electromagnetic metamaterial. S45: set the number of iterations, take the offspring population generated in step S44 as the original population, repeat steps S41 to S44 until the set number of iterations is reached, select the optimal individual from the offspring population to obtain the optimal structure parameter of the electromagnetic metamaterial, and perform electromagnetic metamaterial design.

6. The method of claim 5, wherein, Based on the dynamic neighborhood disturbance mechanism, the expression of the neighborhood individual of the original population individual is: wherein denotes the field individuals, Δ denotes a uniformly distributed disturbance vector, denotes the original population individuals, denotes a dynamic adjustment coefficient, denotes an upper bound of the electromagnetic metamaterial structure parameters, denotes a lower bound of the electromagnetic metamaterial structure parameters.

7. The method of claim 5, wherein the method further comprises: The expression for calculating the fitness value of the exploration elite population individual using the predicted reflection loss is: In the formula, denotes a fitness function, denotes a weight coefficient, denotes a return loss, denotes a constraint penalty term, denotes a maximum value of an operating frequency, denotes a minimum value of an operating frequency, i denotes an operating frequency.

8. The method of claim 7, wherein, The specific process of S43 is: The crowding degree of the exploration elite population individual is calculated, and the expression is: In the formula, denotes the crowding degree, denotes the i-th individual of the exploration elite population, denotes the j-th individual of the exploration elite population, denotes the k-th dimension of the i-th individual of the exploration elite population, denotes the k-th dimension of the j-th individual of the exploration elite population, D denotes the dimension; Using the crowding degree and fitness of the exploration elite population individual, the comprehensive score of each individual is calculated, and the individuals are sorted according to the comprehensive score, and the m individuals with the highest score are selected to obtain a new generation of exploration elite population; The expression for calculating the comprehensive score of the exploration elite population individual is: In the formula, represents, represents a diversity weight, represents a standardized value of crowding, represents a standardized value of fitness. 9.The electromagnetic metamaterial design method based on deep neural network and genetic algorithm of claim 5, wherein, Based on the hybrid crossover strategy, the original population and the new generation of exploration elite population are hybrid crossed to generate the offspring population. The process is as follows: set a crossover probability threshold CT, and generate a random probability u during the crossover process; when the crossover probability threshold CT is greater than the generated random probability u, a roulette wheel method is used to select one individual from the new generation of exploration elite population and the original population as the parent individual, and a crossover operation is performed to generate the offspring population; when the crossover probability threshold CT is less than or equal to the generated random probability u, two individuals are selected from the original population for crossover operation to generate the offspring population.

10. A deep neural network and genetic algorithm based electromagnetic metamaterial design system for implementing the deep neural network and genetic algorithm based electromagnetic metamaterial design method of any one of claims 1-9, characterized in that, It comprises: A data acquisition module is configured to acquire an initial structure sample of the electromagnetic metamaterial, and construct a training set based on the initial structure sample; A model construction and training module is configured to construct an electromagnetic metamaterial forward prediction network model, and train the electromagnetic metamaterial forward prediction network model using the training set to obtain a trained electromagnetic metamaterial forward prediction network model; A prediction module is configured to input a preset electromagnetic metamaterial structure parameter and a set frequency information into the trained electromagnetic metamaterial forward prediction network model, and output a predicted reflection loss of each frequency point in the frequency information using the electromagnetic metamaterial forward prediction network model; A design module is configured to construct an original population of structure parameters of the electromagnetic metamaterial, and solve the optimal solution of the original population of structure parameters based on a neighborhood dynamic evolution regulation genetic algorithm. In the solving process, the fitness value of the individual is calculated using the predicted reflection loss to obtain the optimal structure parameter of the electromagnetic metamaterial, and the electromagnetic metamaterial is designed.

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