One-to-many fast design method for digital metasurfaces based on nested multilayer perceptron

Abstract

This invention discloses a fast one-to-many digital metasurface design method based on nested multilayer perceptrons. The method involves inputting desired S-parameters at the input of a generator network and outputting a metasurface design with corresponding electromagnetic properties at the output. Compared to traditional metasurface inverse design methods, this method has advantages such as low computational cost, fast design speed, and low user expertise requirements. Furthermore, this method can utilize different noise vectors input to the generator network to find different metasurface structures with the same S-parameters, achieving one-to-many inverse design. Based on this, it is easy to perform secondary screening on the multiple generated metasurfaces that meet the requirements, thereby indirectly improving the accuracy of the inverse design.

Description

Technical Field

[0001] This invention relates to the field of metamaterials technology, specifically a one-to-many rapid design method for digital metasurfaces based on nested multilayer perceptrons. Background Technology

[0002] Metamaterials are man-made materials with unique properties. Due to their specially designed structures, they possess properties not found in natural materials, such as negative refractive index and perfect absorption. Since the 21st century, significant progress has been made in the research and application of metamaterials. Digital metasurfaces, as a special type of metamaterial structure, have geometric structures that can be represented by coded matrices and possess a degree of programmability, making them one of the hot topics in the field of metamaterials research.

[0003] Although metasurfaces possess strong electromagnetic control capabilities, traditional metasurface reverse engineering methods are extremely complex. Reverse engineering refers to deriving the structural parameters of a metasurface based on the desired electromagnetic properties. Commonly used reverse engineering methods, such as genetic algorithms and adjoint methods, require significant computational time and resources. Furthermore, metasurface design demands a thorough understanding of electromagnetics. Since designed metasurfaces lack self-adjustment capabilities, fine-tuning their functionality during practical applications necessitates redesign by specialized personnel. These inherent limitations of traditional metasurface design significantly raise the design threshold, severely restricting their widespread application.

[0004] Currently, some deep learning algorithms, such as AMID and REACTIVE, are also applied to the research of digital metasurface reverse engineering. However, the same S-parameter can often be represented by digital metasurfaces with different structures, and in more design application scenarios, it provides researchers with multiple feasible solutions. Therefore, selecting the solution with higher feasibility in processing and manufacturing the size and structure is very important in reverse engineering. Summary of the Invention

[0005] This invention provides a one-to-many rapid design method for digital metasurfaces based on nested multilayer perceptrons, which solves the problems of large computational load, slow design speed, high user expertise requirements, and low accuracy of reverse design in metasurface reverse design methods.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a one-to-many rapid design method for digital metasurfaces based on nested multilayer perceptrons, comprising the following steps:

[0007] S1. A dataset consisting of 40,000 digital metasurface-S-parameter pairs was obtained through CST-Python co-simulation, and the S-parameter labels of the simulation dataset were compressed.

[0008] S2. Conduct network design and use a multilayer perceptron to establish a direct mapping from the real and imaginary parts of the S-parameters to the pixels of the metasurface image matrix to complete the reverse design network of the metasurface.

[0009] S2. Train the network model, keep the parameters of the forward prediction network constant, and continuously update the weight parameters of the generator network iteratively. The input noise follows a standard normal distribution. During the training of the neural network, continuously change the noise input to ensure that the generator network has a fixed input label.

[0010] S4. After the network is trained, it receives the real and imaginary parts of the S-parameters to generate the corresponding preliminary metasurface image. After binarization, the final metasurface design is obtained.

[0011] Preferably, the digital metasurface comprises a three-layer structure consisting of a top metal patch, a middle insulating dielectric substrate, and a bottom metal substrate. The digital metasurface corresponds to a symmetrical structure with a matrix size of 16×16, represented by a matrix encoding composed of discrete values ​​of 0 and 1, where 1 represents the presence of a metal patch and 0 represents the absence of a metal patch.

[0012] Preferably, the S-parameters obtained from the CST simulation of a single digital metasurface are represented by 1001-dimensional complex numbers, and the real and imaginary parts of the S-parameters are represented by 41-dimensional vectors, respectively.

[0013] Preferably, the compression process obtains new S-parameter labels by sampling the features of the S-parameters of the dataset at equal intervals in 41 dimensions.

[0014] Preferably, the output layer of the generator network uses the Sigmoid activation function, and the hidden layer uses the ReLU activation function, with the following formulas:

[0015]

[0016] Preferably, the overall framework of the reverse design network includes a generator network G and a forward prediction network D, wherein the forward prediction network D receives a metasurface image generated from the reverse network and predicts its S-parameters. The training of the generated network follows the basic training method of convolutional neural networks. It utilizes a gradient-based optimization method, updating the parameters of the neural network by differentiating the error function L and using backpropagation. The optimization process is as follows:

[0017]

[0018] Among them W t W represents the new parameters after the neural network is updated. t-1 The original parameters are represented by lr, the learning rate is l, and m represents m. t For first-order momentum, Vt It is a second-order momentum.

[0019] Preferably, the error function L for network training is obtained by the MSE of the S-parameters output by the forward network and the S-parameters input by the generator network. To improve the network's generalization ability and prevent overfitting, L2 regularization is also added to the error function.

[0020]

[0021] Among them, y re ,y im The input S-parameters are the real and imaginary parts, G and D are the generator and predictor networks in the inverse network, respectively, N is the vector dimension, γ is the regularization coefficient, and W... i This refers to the weight information for a fully connected network.

[0022] Preferably, the forward network uses a ResNet convolutional neural network to achieve convergence, with an MSE error of 10⁻⁶. 5 The error is controlled by the MSE of the S-parameters output by the forward network and the S-parameters input by the generator network, so that the generator network generates a metasurface image that meets the requirements of the input S-parameters. By inputting the same S-parameters, a one-to-many mapping from S-parameters to metasurface images is achieved.

[0023] Preferably, the generating network employs the adaptive optimizer Adam, which combines the first-order momentum of SGDM and the second-order momentum of RMSProp.

[0024] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0025] 1. In this invention, the method has the advantages of low computational load, fast design speed, and low requirements for user expertise.

[0026] 2. This invention can use different noise vectors input to the generator network input terminal to find different metasurface structures with the same S-parameter, realizing one-to-many reverse design. On this basis, it is easy to perform secondary screening on multiple qualified metasurfaces, thereby indirectly improving the accuracy of reverse design.

[0027] 3. The reverse-designed network in this invention has good generalization ability. Attached Figure Description

[0028] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0029] In the attached diagram:

[0030] Figure 1This is a schematic diagram of the partial restoration and reconstruction result of the present invention;

[0031] Figure 2 This is a diagram showing the two computation methods of ResNet in this invention;

[0032] Figure 3 This is a schematic diagram of the forward prediction network structure of the present invention;

[0033] Figure 4 This is a partial test result diagram of the positive prediction model of this invention;

[0034] Figure 5 This is a schematic diagram of the overall framework structure of the reverse engineering of this invention;

[0035] Figure 6 This is a schematic diagram of the one-to-many mapping process from S-parameters to metasurface images in this invention;

[0036] Figure 7 This is a schematic diagram of the process for generating a preliminary metasurface design according to the present invention;

[0037] Figure 8 This is a schematic diagram showing the results of the training set error and the test set error of this invention;

[0038] Figure 9 This is a flowchart of the experimental results verification for this invention;

[0039] Figure 10 This is a schematic diagram of some of the digital metasurface results of this invention;

[0040] Figure 11 These are schematic diagrams of several different digital metasurface results of the present invention;

[0041] Figure 12 This is a schematic diagram of 500 sets of MSE error statistics of the present invention. Detailed Implementation

[0042] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0043] Example: A fast one-to-many design method for digital metasurfaces based on nested multilayer perceptrons. The desired S-parameters are input to the generator network, and the metasurface design with corresponding electromagnetic properties is output. Step 1: Dataset acquisition and processing.

[0044] The construction of the dataset mainly involves simulating the digital metasurface structure parameters to their corresponding S-parameters. The digital metasurface structure is symmetric about the x and y axes and can be represented by a matrix of discrete 0 and 1 values. The digital metasurface simulated in this experiment consists of three layers: a top metal patch, a middle insulating dielectric substrate, and a bottom metal substrate. The dielectric layer is 10 mm long and wide, and 2 mm thick. Each individual metal patch unit at the top is 0.5 mm. Therefore, the matrix size corresponding to the digital metasurface is 16×16, where 1 represents the presence of a metal patch and 0 represents its absence. The S-parameters of the digital metasurface were obtained through simulation by the CST Microwave Studio. This software utilizes electromagnetic simulation methods such as the finite element method (FEM) and finite integral method (FI) to quickly and effectively simulate and calculate electromagnetic parameters.

[0045] The dataset for this invention consists of 40,000 digital metasurface-S-parameter pairs. Given the large size of the dataset, manually simulating each digital metasurface individually would be time-consuming. Therefore, the training dataset for this work was generated through a joint simulation using CST and Python. CST supports relevant Python libraries, greatly improving data acquisition efficiency and reducing manpower requirements. By storing 40,000 randomly generated digital metasurface images in a specific folder, using Python to set the CST simulation environment parameters, and then automatically simulating each digital metasurface image in a loop, the resulting S-parameter results are stored in the dataset.h5 file, thus constructing the dataset required for this experiment.

[0046] The S-parameters obtained from CST simulation of a single digital metasurface are represented by 1001-dimensional complex numbers. When constructing the mapping between the digital metasurface and the S-parameters using an artificial neural network, the size of the network parameters is significantly affected by the dimension of the S-parameters. A 1001-dimensional label may lead to problems such as excessively large neural network parameters, slow training, and poor convergence. Therefore, the S-parameter labels of the simulation dataset need to be compressed. Considering the characteristics of the S-parameters in this dataset, this invention directly samples them at equal intervals to obtain new S-parameter labels in 41 dimensions. To demonstrate that equidistant sampling of 41-dimensional S-parameters can retain all the information of the original 1001-dimensional data, a reconstruction network from 41-dimensional S-parameters to 1001-dimensional S-parameters is trained using an artificial neural network. Its convergence performance is good, proving the effectiveness of equidistant sampling. Partial reconstruction results are shown below. Figure 1 As shown.

[0047] Step 2: Network Design

[0048] (1) Forward prediction model framework

[0049] In the reverse design of metamaterials, a method is needed to quickly predict the forward spectrum of the encoded metasurface to assist in the training of the reverse design network. Therefore, constructing an artificial neural network to predict the forward spectrum is crucial. After the network is trained, its S-parameters can be calculated immediately by inputting the matrix information of the metasurface image into the neural network.

[0050] This invention employs a ResNet convolutional neural network to perform the above mapping function. Proposed by Microsoft Labs in 2015, ResNet significantly alleviates the degradation problem in deep network training. It utilizes residual structures to allow the neural network to skip connections between certain layers and the next layer, weakening the strong connections between layers and ensuring that each layer receives at least the network features extracted from the previous layer. The core modules of ResNet include... Figure 2 The diagram shows two computational methods: The input features of the previous layer are shown in the diagram, and is the convolution operation. When the dimensions of the input features of the previous layer are the same as the dimensions after convolution processing in this layer, they are directly added to obtain the input of the next layer; if the dimensions are different, the dimensions are adjusted through convolution before being added to obtain the input for the next layer.

[0051] H(x) = x + W(x)

[0052] To accelerate network convergence and prevent gradient vanishing, each convolution operation in ResNetBlock is followed by a BN layer for normalization, transforming the extracted image features into a standard normal distribution, and ReLU is chosen as the activation function.

[0053] Forward prediction network structure such as Figure 3 As shown, it mainly consists of two parts, which correspond to the prediction of the real part and the imaginary part of the S-parameters, respectively.

[0054] The training of the prediction network follows the basic training method of convolutional neural networks, utilizing gradient-based optimization. This involves differentiating the error function L and updating the network's parameters using backpropagation. The optimization process is as follows:

[0055]

[0056] Among them W t W represents the new parameters after the neural network is updated. t-1 represents the original parameters, and lr represents the learning rate. m t For first-order momentum, V t This represents second-order momentum. The network's loss function is defined as the mean squared error (MSE), which is the sum of squares of the differences between the predicted and target values. The specific formula is:

[0057]

[0058] like Figure 4As shown, the average error of the trained forward prediction network is on the order of 10⁻⁶. 5 The system can quickly predict the spectral response of the input metasurface while maintaining a low error. Compared to electromagnetic simulation using CST software, which takes about ten minutes, the machine learning model, although requiring some time for the entire training process, can predict the spectral response of the input digital metasurface within seconds once training is complete, representing a significant speed improvement.

[0059] (2) Reverse engineering overall framework

[0060] Compared to traditional metasurface inverse design methods, neural networks can obtain the specific structure of a metasurface more quickly and easily. The inverse design network constructed in this invention can generate corresponding digital metasurfaces based on the real and imaginary parts of the input S-parameters, and then obtain a discrete digital metasurface matrix through subsequent simple optimization. Compared to traditional metasurfaces, which have a certain geometric structure, digital metasurfaces have a more complex structure, composed of randomly distributed metal sheets. Therefore, the image matrix input to the neural network consists of random 0 and 1 discrete values, making the generation of the inverse network more difficult. Currently, mainstream generative network models such as GAN and CGAN tend to generate images of different categories, while digital metasurfaces, due to their randomness, do not have obvious type distinctions. If different encoded metasurfaces are classified into different categories, then the 16×16 symmetric digital metasurface used in this invention theoretically has 2 64 Because there are different categories, the current mainstream generative models cannot be well used for reverse engineering.

[0061] This invention utilizes a multilayer perceptron (MLP) to establish a direct mapping from the real and imaginary parts of the S-parameters to the pixels of the metasurface image matrix to complete the reverse design of the metasurface. Since the MLP establishes a one-to-one mapping, while digital metamaterials exhibit a one-to-many mapping characteristic (i.e., different metasurface structures correspond to the same S-parameters), the input of the MLP needs to receive not only the S-parameters but also noise terms to increase the diversity of the reverse generation network.

[0062] The dataset used in this invention has a 16×16 symmetric metasurface structure, and the real and imaginary parts of the S-parameters are represented by 41-dimensional vectors. Taking the first 8 rows and 8 columns of the 16×16 matrix can represent the original metasurface structure information; therefore, the objects of the mapping are 82-dimensional S-parameter information and 64-dimensional metasurface structure information, such as... Figure 5 As shown.

[0063] The overall framework of the reverse design network consists of a generator network G and a forward prediction network D. The generator network receives three sets of inputs: noise n following a normal distribution, and the real part information of the S-parameters y. re S-parameter imaginary part information yim The network generates a metasurface image x. The forward prediction network takes the metasurface image generated from the inverse network and predicts its S-parameters. In this training framework, the forward prediction network is the network added in the previous section. During the training of the inverse generative network, the forward network does not undergo parameter iteration. Therefore, during model training, error control is obtained by the MSE of the S-parameters output by the forward network and the S-parameters input to the generative network. This forces the generative network to generate a metasurface image that meets the input S-parameter requirements. Furthermore, due to the presence of noise n, the generative network can obtain different metasurface images with the same input S-parameters, thus completing a one-to-many mapping from S-parameters to metasurface images. Figure 6 and 7 As shown.

[0064] The generative network consists of two paths. It receives the real or imaginary parts of the S-parameters and independently generates 64-dimensional metasurface structure information that satisfies the S-parameter requirements. These are then concatenated into a 128-vector by the matrix concatenation module. Finally, the MLP module extracts the 64-dimensional structure parameters that meet the requirements. Based on the symmetry characteristics of the metasurface, the matrix dimension adjustment module Reshapes the model to obtain the initial metasurface design. The linear generative network of the branch uses a hybrid model of fully connected layers and BN layers to improve the convergence speed of the network and alleviate neural network training problems such as overfitting and gradient vanishing. The activation functions of the network follow these principles: the hidden layers use the ReLU activation function, and the output layer uses the Sigmoid activation function. On the one hand, the ReLU activation function is simple to differentiate and has a fast training speed; on the other hand, the Sigmoid activation function in the output layer ensures that the output metasurface structure parameter information is within the range [0, 1], facilitating the subsequent binarization optimization process.

[0065]

[0066] The training of the network follows the basic training method of convolutional neural networks, utilizing gradient-based optimization. This involves differentiating the error function L and updating the network's parameters using backpropagation. The optimization process is as follows:

[0067]

[0068] Among them W t W represents the new parameters after the neural network is updated. t-1 represents the original parameters, and lr represents the learning rate. m t For first-order momentum, V t It is a second-order momentum.

[0069] The error function L for network training is obtained by the MSE of the S-parameters output by the forward network and the S-parameters input by the generator network. To improve the network's generalization ability and prevent overfitting, L2 regularization is also added to the error function.

[0070]

[0071] Among them, y re ,y im The input S-parameters are the real and imaginary parts, G and D are the generator and predictor networks in the inverse network, respectively, N is the vector dimension, γ is the regularization coefficient, and W... i This represents the weight information for a fully connected network. The addition of L2 regularization prevents the neural network parameters from becoming too large, alleviating the problem of overfitting the training set and improving the generalization ability of the generative network.

[0072] In addition, this network employs the adaptive optimizer Adam, which combines the first-order momentum of SGDM and the second-order momentum of RMSProp. This allows it to automatically adjust the learning rate during neural network training, resulting in faster convergence. The optimized network expression is as follows:

[0073]

[0074]

[0075]

[0076] (3) Network training and hyperparameters

[0077] During network training, the parameters of the forward prediction network are kept constant, while the weight parameters of the generator network are iteratively updated. The input noise follows a standard normal distribution. During neural network training, the noise input is continuously changed to ensure that the generator network's error remains within a certain range even with a fixed input label and varying noise levels. The hyperparameters of the generator network are as follows:

[0078]

[0079] During training, it's crucial to simultaneously ensure the diversity and accuracy of the generative network. Excessive training iterations can lead to overfitting and reduce the network's diversity, causing the weights for noise-related operations to be too small, resulting in insensitivity to or even ignoring of noise input. Conversely, insufficient training iterations can lead to underfitting, where the generated images fail to meet the predetermined S-parameter requirements. Furthermore, adjusting the dimension of the input noise can also help regulate the network's diversity to some extent.

[0080] Due to the introduction of Batch Normalization (BN) layers and the ReLU activation function, the training speed of the inverse generative network is relatively fast, and the final training set error and test set error both reach approximately 0.002, as recorded below. Figure 8 As shown.

[0081] (4) Binarization

[0082] After the inverse network is trained, inputting the real and imaginary parts of the S-parameters and noise into it yields the corresponding encoded metasurface image. This output, after passing through the forward prediction network, produces the expected S-parameters. Since the network uses the sigmoid activation function, the inverse network output is a decimal between 0 and 1. However, the metasurface image matrix should consist of discrete 0 and 1 values. Therefore, the inverse design result needs to be binarized to convert the resulting structural parameters into discrete values ​​of 0 or 1. Experimental results show that using a single discriminant method to binarize the output matrix of the inverse network by setting a threshold for each element may lead to significant errors. Therefore, this study seeks a method to find an optimal discrete matrix near the output matrix in 64-dimensional space, representing a metasurface that maps to the expected S-parameters.

[0083] This paper proposes an optimization algorithm to control errors and obtain the final metasurface design. Let M be the parameter matrix obtained by the inverse network. g The S-parameter label is y re Let yim be the noise level n, the generator network be G(x,y,z), the forward prediction network be D(x), and the error function be MSE(x,y). The execution flow of this algorithm is as follows:

[0084]

[0085] The above algorithm can convert all continuous values ​​of the structural parameter matrix obtained by the reverse design network into discrete values ​​of 0 or 1, which is the final metasurface design.

[0086] Step 3: Experiment and Results Analysis

[0087] like Figure 9As shown, after training, the inverse generative network can accept the real and imaginary parts of the S-parameters to generate the corresponding preliminary metasurface image. After binarization, the final metasurface design is obtained. This study primarily verifies the accuracy and diversity of the inverse generative model: whether the expected S-parameters of the generated metasurface are accurate, and whether different generated metasurfaces can have the same S-parameters while keeping the input S-parameters constant. During the verification process, the CST electromagnetic simulation platform is used. First, S-parameters are arbitrarily selected from the test set and input into the inverse generative network. After discretization, the metasurface design generated by the neural network is obtained. Then, this metasurface is input into CST to obtain the simulated S-parameters, which are compared with the S-parameters input to the inverse generative network to verify its accuracy.

[0088] By selecting S-parameters not learned by the inverse network from the test set, multiple experimental results were easily obtained. Analysis of the results shows that the proposed inverse generative network exhibits good design and generalization capabilities, and can complete the design of metasurfaces with predetermined S-parameters in most cases. However, the design capability of this inverse generative network needs further improvement when designing a small number of metasurfaces with abrupt changes in S-parameters. Some results are shown below. Figure 10 As shown;

[0089] To verify the diversity of the results from the inverse generator network, for a one-to-many case, the S-parameters of the input inverse network are kept constant while the input noise is changed. This allows us to obtain multiple different digital metasurfaces that, after CST simulation, have the same S-parameters, such as... Figure 11 As shown;

[0090] like Figure 12 As shown in the results, the reverse design network exhibits good generalization ability. It can extract S-parameters not learned by the reverse generation network from the test set and feed them into the reverse network to obtain digital metasurface designs that meet the requirements. Due to the presence of noise terms, the neural network results in diversity; for the same S-parameters, it can generate multiple metasurface designs with different structures that meet the requirements. To more comprehensively test the performance of the neural network, 500 sets of S-parameters were randomly selected from the test set and fed into the reverse generation network to generate corresponding metasurface designs. The forward prediction network then estimated the S-parameters corresponding to the generated metasurface designs. Finally, 500 sets of MSE errors were calculated with the labels, and the resulting statistics are shown in the following graph. It can be seen that the MSE error between the S-parameters and the labels for 95.5% of the digital metasurface designs is less than 0.01, and the MSE error between the S-parameters and the labels for 72.2% of the digital metasurface designs is less than 0.001. This sufficiently demonstrates that the reverse generation network of this invention has good digital metasurface design capabilities for the vast majority of S-parameters.

[0091] This method can use different noise vectors input to the generator network to find different metasurface structures with the same S-parameters, realizing one-to-many reverse design. Furthermore, it is easy to perform secondary screening on the multiple qualified metasurfaces generated, thereby indirectly improving the accuracy of reverse design.

[0092] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A one-to-many rapid design method for digital metasurfaces based on nested multilayer perceptrons, characterized in that... This includes the following steps: S1. A dataset consisting of 40,000 digital metasurface-S-parameter pairs was obtained through CST-Python co-simulation, and the S-parameter labels of the simulation dataset were compressed. S2. Conduct network design and use a multilayer perceptron to establish a direct mapping from the real and imaginary parts of the S-parameters to the pixels of the metasurface image matrix to complete the reverse design network of the metasurface. S2. Train the network model, keep the parameters of the forward prediction network constant, and continuously update the weight parameters of the generator network iteratively. The input noise follows a standard normal distribution. During the training of the neural network, continuously change the noise input to ensure that the generator network has a fixed input label. S4. After the network is trained, it receives the real and imaginary parts of the S-parameters to generate the corresponding preliminary metasurface image. After binarization, the final metasurface design is obtained. The output layer of the generator network uses the Sigmoid activation function, and the hidden layer uses the ReLU activation function, as shown in the formulas below: The overall framework of the reverse design network includes a generator network G and a forward prediction network D. The forward prediction network D receives the metasurface image generated from the reverse network and predicts its S-parameters. The training of the generated network follows the basic training method of convolutional neural networks. It utilizes a gradient-based optimization method, updating the parameters of the neural network by differentiating the error function L and using backpropagation. The optimization process is as follows: Among them W t W represents the new parameters after the neural network is updated. t-1 The original parameters are represented by lr, the learning rate is l, and m represents m. t For first-order momentum, V t It is second momentum; The error function L for network training is obtained by the MSE of the S-parameters output by the forward network and the S-parameters input by the generator network. To improve the network's generalization ability and prevent overfitting, L2 regularization is also added to the error function. Among them, y re ,y im The input S-parameters are the real and imaginary parts, G and D are the generator and predictor networks in the inverse network, respectively, N is the vector dimension, γ is the regularization coefficient, and W... i This refers to the weight information for a fully connected network.

2. The one-to-many rapid design method for digital metasurfaces based on nested multilayer perceptrons according to claim 1, characterized in that: The digital metasurface comprises a three-layer structure consisting of a top metal patch, a middle insulating dielectric substrate, and a bottom metal substrate. The digital metasurface corresponds to a symmetrical structure with a matrix size of 16×16, and is represented by a matrix encoding composed of discrete values ​​of 0 and 1, where 1 represents the presence of a metal patch and 0 represents the absence of a metal patch.

3. The one-to-many rapid design method for digital metasurfaces based on nested multilayer perceptrons according to claim 1, characterized in that: The S-parameters obtained from the CST simulation of a single digital metasurface are represented by 1001-dimensional complex numbers, and the real and imaginary parts of the S-parameters are represented by 41-dimensional vectors.

4. The one-to-many rapid design method for digital metasurfaces based on nested multilayer perceptrons according to claim 1, characterized in that: The compression process obtains new S-parameter labels by sampling the features of the S-parameters of the dataset at equal intervals in 41 dimensions.

5. The one-to-many rapid design method for digital metasurfaces based on nested multilayer perceptrons according to claim 1, characterized in that: The forward network uses a ResNet convolutional neural network to achieve convergence, with an MSE error of 10. -5 The error is controlled by the MSE of the S-parameters output by the forward network and the S-parameters input by the generator network, so that the generator network generates a metasurface image that meets the requirements of the input S-parameters. By inputting the same S-parameters, a one-to-many mapping from S-parameters to metasurface images is achieved.

6. The one-to-many rapid design method for digital metasurfaces based on nested multilayer perceptrons according to claim 5, characterized in that: The generating network employs the adaptive optimizer Adam, which combines the first-order momentum of SGDM and the second-order momentum of RMSProp.

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