A task-target-based generative electromagnetic metasurface structure design method and system

Abstract

The application discloses a kind of based on task target's generative electromagnetic super surface structure design method and system, it is related to electromagnetic super surface technical field, establishes task target, deduces the characteristic frequency response amplitude and phase characteristic that super surface needs to have for different functions of super surface.The KAE network of condition variation generative network model KAE network improved by this task-oriented design Kolmogorov-Arnold network is used as structure generation network.Improved deep neural network model is used as forward prediction network to predict frequency response amplitude and phase characteristic.The distance difference between quantitative calculation and target frequency response amplitude, target phase is retrieved to the super surface structure closest to task characteristic.Improves the precision of encoder and decoder network, alleviates the edge oscillation problem caused by fourier low frequency subspace.Solves the problem that one-to-many mapping in traditional neural network is difficult to accurately train, and has the advantages of high precision, high design efficiency.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic metasurface technology, and more particularly to a task-objective-based generative electromagnetic metasurface structure design method and system. Background Art

[0002] Metasurfaces are composed of periodic or aperiodic subwavelength unit structures. By designing these unit structures, the amplitude, phase, and polarization of electromagnetic waves can be effectively controlled. Due to their unique electromagnetic properties, metasurfaces are widely used to design various electromagnetic functional structures, such as frequency-selective metasurfaces and artificial magnetic conductors, with applications in stealth, focusing lenses, and absorbers.

[0003] Traditional methods for determining the structural parameters of metasurfaces with specific functional objectives often require time-consuming simulations and complex optimization processes. In recent years, deep learning has been widely used as an effective method to solve complex problems in this field.

[0004] Forward prediction infers electromagnetic properties from physical parameters and solves a one-to-one mapping. The spectral response is often a high-dimensional output at equally spaced frequency points, which increases the computational complexity of artificial neural networks and makes them more difficult to train. The dominance of a few dimensions also leads to memory waste. A common solution is to extract a small portion of the low-frequency components from the Fourier spectrum, predicting the Fourier low-frequency subspace, and then restore the curve using the inverse discrete Fourier transform (IDFT) to optimize this problem. However, the restored curve using this method exhibits edge oscillations, resulting in reduced prediction accuracy.

[0005] Unlike forward optimization methods, inverse design often involves multiple solutions to meet given design requirements. The non-unique mapping from input to output makes training neural networks difficult. Currently, inverse design of metasurfaces with frequency-response amplitude and phase characteristics involves either combining heuristic algorithms such as genetic algorithms (GAs) with forward prediction models (deep convolutional neural networks (CNNs) / deep neural networks (DNNs)). This approach is currently applied to metasurfaces with random discrete grid structures, and each inverse search requires iteration, resulting in computational loss. Alternatively, two traditional fully connected neural networks—a forward network (FN) and an inverse network (IN)—are used to design metasurfaces. Using the IN, a metasurface design with the desired frequency-response amplitude and phase characteristics can be retrieved. However, this traditional fully connected neural network approach has poor generalization capabilities and struggles to accurately predict structures with a limited distribution of amplitude and phase characteristics. Furthermore, the total loss is a weighted sum of the losses between the frequency-response amplitude and phase, making it difficult to reconcile the two, leading to inaccurate predictions of the more important phase information.

[0006] Therefore, how to provide a generative electromagnetic metasurface structure design method and system based on mission objectives, eliminate edge oscillations, improve prediction network performance and prediction accuracy, and retrieve the metasurface structure with the frequency response amplitude characteristics closest to the mission objectives is an urgent problem that technicians in this field need to solve. Summary of the Invention

[0007] In view of this, the present invention provides a generative electromagnetic metasurface structure design method and system based on mission objectives, which overcomes the shortcomings of the existing frequency-response amplitude-phase metasurface structural design, eliminates edge oscillations, improves the prediction network performance and prediction accuracy, and retrieves the metasurface structure that is closest to the mission objective frequency-response amplitude characteristics.

[0008] To achieve the above objectives, the present invention adopts the following technical solutions: a generative electromagnetic metasurface structure design method based on mission objectives, comprising: establishing mission objectives, and extracting target frequency response amplitude and target phase characteristics of the metasurface based on metasurface functions;

[0009] Based on the variational generative network, a Kolmogorov-Arnold network is added to the variational generative network for improvement to obtain a KAE network. Based on the KAE network, a structural parameter library with a target phase response is generated;

[0010] Constructing a forward prediction network, the forward prediction network comprising a deep neural network improved based on a Fourier leaf space-smoothing filter layer;

[0011] Inputting the structural parameter library into the forward prediction network, predicting the frequency response amplitude and phase characteristics, and obtaining predicted frequency response amplitude and predicted phase characteristics;

[0012] The distance difference between the predicted frequency response amplitude and the target frequency response amplitude, and the distance difference between the predicted phase feature and the target phase feature are calculated to obtain the metasurface structure closest to the task characteristics.

[0013] Preferably, the method further comprises: constructing a training data set;

[0014] The training data set includes structural parameters of different metasurfaces and their corresponding frequency response amplitude and phase characteristics;

[0015] The KAE network and the forward prediction network are trained respectively using the training data set.

[0016] Preferably, training the KAE network includes:

[0017] Taking the structural parameters as input and the corresponding phase features as conditions, the KAE network is trained to generate a structural parameter library with target phase response;

[0018] Training the forward prediction network includes:

[0019] The forward prediction network is trained using the structural parameters as input and the corresponding frequency response amplitude and phase characteristics as output. After the training is completed, the network model parameters of the forward prediction network are fixed.

[0020] Preferably, the Kolmogorov-Arnold network is added to the variational generative network for improvement, including: designing the encoder and / or decoder network using the Kolmogorov-Arnold network framework;

[0021] Among them, a learnable activation function is used at the edge of the Kolmogorov-Arnold network, so that each weight parameter in the Kolmogorov-Arnold network can be replaced by a univariate function and parameterized in the form of a B-spline function.

[0022] Preferably, the variational generative network consists of an encoder and a decoder. The encoder input is the structural parameters of the metasurface, and the output is a latent vector. The decoder input is the latent vector and phase response, and the output is the reconstructed structural parameters of the metasurface. Both the encoder and decoder are designed using the Kolmogorov-Arnold network framework and employ the reparameterization technique to obtain the gradient.

[0023] Preferably, during the training of the variational autoencoder, the algorithm model parameters are updated based on the total loss value, which is composed of the reconstruction loss MSE and KL divergence:

[0024] ;

[0025] in, represents the ratio between KL divergence and reconstruction loss, represents the mean square error, represents the variance vector of the i-th normal distribution output by the encoder, represents the mean vector of the i-th normal distribution of the encoder output.

[0026] Preferably, the forward prediction network comprises a deep neural network based on an improved Fourier leaf space-smoothing filter layer, comprising:

[0027] Embedding the Fourier leaf space-smoothing filter layer into the last layer of a deep neural network, wherein the Fourier leaf space-smoothing filter layer receives the output of the last layer of a fully connected layer in the deep neural network;

[0028] The Fourier leaf space-smoothing filter layer includes adding a variable window exponential weighted smoothing filter method and matrixing it, and performing different smoothing processes on the middle and edge oscillation parts.

[0029] Preferably, the variable window exponential weighted smoothing filter method is expressed as follows in each window:

[0030] ;

[0031] in, represents the tth value in the window, represents the weighted average of the t-th value in the window, is the weighted weight value;

[0032] Slide the window in sequence to obtain the filtering sliding effect of the entire curve;

[0033] According to the different degrees of edge and middle oscillation, it is divided into three parts: M1, M2, and M3;

[0034] The concatenated matrix is ​​expressed as: ;

[0035] The smoothed curve is expressed as: ,in v is the original curve.

[0036] Preferably, a generative electromagnetic metasurface structure design system based on a task objective comprises:

[0037] The mission target establishment module is used to establish the mission target and extract the target frequency response amplitude and target phase characteristics of the metasurface based on the metasurface function;

[0038] A structural parameter library generation module is used to generate a structural parameter library with a target phase response based on a variational generative network by adding a Kolmogorov-Arnold network to the variational generative network for improvement to obtain a KAE network;

[0039] A forward prediction network construction module, used to construct a forward prediction network, wherein the forward prediction network includes a deep neural network improved based on the Fourier leaf space-smoothing filter layer;

[0040] A frequency response feature prediction module, configured to input the structural parameter library into the forward prediction network, predict the frequency response amplitude and phase features, and obtain predicted frequency response amplitude and predicted phase features;

[0041] The metasurface structure generation module is used to calculate the distance difference between the predicted frequency response amplitude and the target frequency response amplitude, and between the predicted phase feature and the target phase feature, to obtain the metasurface structure that is closest to the task characteristics.

[0042] Through the above technical solutions, it can be seen that compared with the existing technology, the present invention provides a generative electromagnetic metasurface structure design method and system based on task objectives. 1. The present invention addresses the edge oscillation problem after Fourier transform subspace curve restoration in the forward prediction network. A variable window exponential weighted smoothing filter is added and matrixed as a layer and embedded into the neural network, which can eliminate the edge oscillation problem and improve the prediction network performance and prediction accuracy. 2. The present invention proposes a KAE network for the reverse retrieval network. The generative network solves the problem that one-to-many mapping in traditional neural networks is difficult to train. The encoder and decoder networks are represented by the Kolmogorov-Arnold network KAN framework. KAN can approximate the activation function of any continuous function through training, which can improve the accuracy of the encoder and decoder networks. 3. The present invention targets different metasurface task orientations: the conditional variational generative network KAE improved by the Kolmogorov-Arnold network is used as the structure generation network, and the deep neural network model FFDNN improved by the Fourier leaf space-smoothing filter layer is used as the forward prediction network to retrieve the metasurface structure that is closest to the frequency response amplitude characteristics of the task objective. 4. The network designed in this invention is helpful for the research on phase control of broadband / narrowband transmission / reflection metasurfaces, and can be applied to the fields of metasurface focusing, deflection, frequency-selective metasurface phase compensation, etc. It has the advantages of generating structural diversity, high precision, and high design efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0044] Figure 1 A diagram of the overall network implementation framework provided for an embodiment of the present invention;

[0045] Figure 2 A diagram of a metasurface structure used for frequency selective surface self-cloaking according to an embodiment of the present invention;

[0046] Figure 3 A diagram of a KAE network framework generated by an embodiment of the present invention;

[0047] Figure 4 A diagram of the forward prediction network (FFDNN) framework provided by an embodiment of the present invention;

[0048] FIG5( a ) is a graph showing the change in loss value of the forward prediction network FFDNN training model provided by an embodiment of the present invention;

[0049] FIG5( b ) is a diagram showing the prediction effect of the first frequency response amplitude (transmission coefficient) of the forward prediction network FFDNN training model provided by an embodiment of the present invention;

[0050] FIG5( c ) is a diagram showing the prediction effect of the second frequency response amplitude (transmission coefficient) of the forward prediction network FFDNN training model provided by an embodiment of the present invention;

[0051] FIG5( d ) is a diagram showing the first frequency response phase prediction effect of the forward prediction network FFDNN training model provided by an embodiment of the present invention;

[0052] FIG5( e ) is a diagram showing the second frequency response phase prediction effect of the forward prediction network FFDNN training model provided by an embodiment of the present invention;

[0053] FIG6 (a) is a comparison diagram of the predicted results of the metasurface structure designed by KAE and the transmission coefficient simulation results of the electromagnetic software under the condition of 9-13 GHz transmission bandwidth for the mission target provided by an embodiment of the present invention;

[0054] FIG6( b ) is a comparison diagram of the predicted results of the metasurface structure designed by KAE and the phase simulation results of the electromagnetic software under the condition of 9-13 GHz transmission bandwidth for the mission target provided by an embodiment of the present invention;

[0055] FIG6 (c) is a comparison diagram of the predicted results of the metasurface structure designed by KAE and the transmission coefficient simulation results of the electromagnetic software under the condition of 8-16 GHz transmission bandwidth for the mission target provided by an embodiment of the present invention;

[0056] FIG6 (d) shows a comparison between the predicted results of the metasurface structure designed by KAE and the phase simulation results of the electromagnetic software under the condition of 8-16 GHz transmission bandwidth for the mission target provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0057] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0058] Embodiments of the present invention disclose a task-oriented, generative electromagnetic metasurface structure design method and system. By establishing a task objective and deriving the required characteristic frequency response amplitude and phase characteristics of the metasurface based on its different functions, this task-oriented approach employs a KAN (KAN-conditional Variational Auto Encoder) network, a conditional variational generative network model based on an improved Kolmogorov-Arnold network (KAN), as the structure generation network. An improved deep neural network model, FFDNN (Fourier filter Deep Neural Network), is used as the forward prediction network, replacing electromagnetic simulation software to predict the frequency response amplitude and phase characteristics of the generated structural parameter library. By quantitatively calculating the distance difference between the target frequency response amplitude and target phase, the metasurface structure that best matches the task characteristics is retrieved. This embodiment of the present invention utilizes a learnable activation function at the edges of the KAN framework to improve the accuracy of the encoder and decoder networks. A variable window exponentially weighted smoothing filter is added to the FFDNN network and its matrixed form is embedded as a layer in the neural network to mitigate edge oscillation caused by the Fourier low-frequency subspace. The metasurface structure generated based on the embodiment of the present invention is diverse, which solves the problem that one-to-many mapping in traditional neural networks is difficult to train accurately, and has the advantages of high precision and high design efficiency.

[0059] In a specific embodiment of the present invention, a generative electromagnetic metasurface structure design method based on task objectives is provided. Figure 1 As shown, it includes: S1, establishing a mission goal, and extracting the target frequency response amplitude and target phase characteristics of the metasurface according to the metasurface function;

[0060] Specifically, mission objectives are set based on the different functional requirements of the metasurface, and its characteristic frequency response amplitude and phase characteristics are derived from the mission requirements. The specific mission requirement derivation method is determined according to the task, including the metasurface focusing phase formula, generalized Snell's law, and equal air layer phase accumulation.

[0061] Mission types include applications such as beam focusing / deflection control based on transmissive / reflective metasurfaces, and transmission, reflection, and absorption control of frequency selective surfaces.

[0062] In a specific embodiment of the present invention, the metasurface structure in S1 realizes the frequency selective surface self-cloaking function, that is, the phase accumulation amount at a specific frequency point is consistent with the air layer. Figure 2As shown, the metasurface structure consists of three metal layers: from top to bottom, a first U-shaped metal layer, a first dielectric layer, a second U-shaped metal layer, a second dielectric layer, and a third U-shaped metal layer. The second metal layer is located at the periodic boundary. The first and third metal layers have the same shape and size. The first and second dielectric layers are F4B dielectric substrates with a dielectric constant of 2.2. The thickness h of the F4B dielectric substrate is fixed at 1.5 mm, and the total thickness is approximately 3 mm. The frequency response amplitude and phase curves are simulated by varying the structural dimension parameters [s, m, b, l1]. s represents the vertical distance between the outer boundary of the first metal layer and the boundary of the metasurface structure; l1 represents the distance between the large and small diameters of the U-shaped structure in the first or third metal layer; m represents the distance between the large and small diameters of the U-shaped structure in the second metal layer; and b represents half the side length of the inner diameter in the first or third U-shaped metal layer. This structure exhibits frequency-selective broadband transmission characteristics. Phase control can be achieved by varying the structural dimensions. At a single frequency, the phase accumulation is consistent with that of an air layer of equal thickness, thus achieving self-cloaking. Electromagnetic simulations were performed using randomized values ​​in the parameter space [s, m, b, l1]. Within the 2-18 GHz frequency range, 501 frequency points were selected at 0.032 GHz intervals. The phase and amplitude response dimensions corresponded to the number of frequency points.

[0063] S2. Based on the variational generative network, a Kolmogorov-Arnold network is added to the variational generative network for improvement to obtain a KAE network, and based on the KAE network, a structural parameter library with a target phase response is generated;

[0064] S3. Constructing a forward prediction network, wherein the forward prediction network includes a deep neural network improved based on a Fourier leaf space-smoothing filter layer;

[0065] S4. Inputting the structural parameter library into the forward prediction network, predicting the frequency response amplitude and phase characteristics, and obtaining predicted frequency response amplitude and predicted phase characteristics;

[0066] S5. Calculate the distance difference between the predicted frequency response amplitude and the target frequency response amplitude, and the distance difference between the predicted phase feature and the target phase feature, and obtain the metasurface structure closest to the task feature.

[0067] Specifically, based on the calculated distance difference, the predicted frequency response amplitude with the smallest difference and the corresponding structural parameters are obtained to generate the metasurface structure closest to the task characteristics.

[0068] Specifically, it also includes: building a training data set;

[0069] The training data set includes structural parameters of different metasurfaces and their corresponding frequency response amplitude and phase characteristics;

[0070] The KAE network and the forward prediction network are trained respectively using the training data set.

[0071] In a specific embodiment of the present invention, a task objective is determined and a data set is collected. Based on the metasurface function, the amplitude and phase characteristics of the metasurface are extracted;

[0072] By varying the metasurface's structure and related dimensional parameters and inserting them into the simulation software, the corresponding frequency response amplitude and phase characteristic curves were obtained as a dataset. The input and output of the KAE network were both structural parameters, and the frequency response phase characteristics served as the conditional input of the KAE network. The dataset was divided into 90% training and 10% testing.

[0073] Specifically, training the KAE network includes:

[0074] Taking the structural parameters as input and the corresponding phase features as conditions, the KAE network is trained to generate a structural parameter library with target phase response;

[0075] Training the forward prediction network includes:

[0076] The forward prediction network is trained using the structural parameters as input and the corresponding frequency response amplitude and phase characteristics as output. After the training is completed, the network model parameters of the forward prediction network are fixed.

[0077] Specifically, the Kolmogorov-Arnold network is added to the variational generative network for improvement, including: designing the encoder and / or decoder network using the Kolmogorov-Arnold network framework;

[0078] Among them, a learnable activation function is used at the edge of the Kolmogorov-Arnold network, so that each weight parameter in the Kolmogorov-Arnold network can be replaced by a univariate function and parameterized in the form of a B-spline function.

[0079] For variational generative networks, adding the KAN framework can improve design accuracy and efficiency.

[0080] Specifically, the variational generative network consists of two parts: an encoder and a decoder. The encoder input is the structural parameters of the metasurface, and the output is a latent vector. The decoder input is the latent vector and phase response, and the output is the reconstructed structural parameters of the metasurface. Both the encoder and decoder are designed using the Kolmogorov-Arnold network framework and employ the reparameterization technique to obtain gradients.

[0081] Specifically, the input variable x is input to the KAE network, and the encoder is used to determine the posterior distribution of the latent variable z , the decoder is used to determine the phase response c and the latent variable z, and the generation distribution of the design parameter x ,in and They are the parameters of the posterior and generative distribution functions, respectively. Their specific values ​​are obtained during the training of the network, and the total loss value is calculated.

[0082] Specifically, during the training of the variational autoencoder, the algorithm model parameters are updated based on the total loss value. The total loss value is composed of the reconstruction loss MSE (mean square error) and KL divergence:

[0083] ;

[0084] in, represents the ratio between KL divergence and reconstruction loss, represents the mean square error, represents the variance vector of the i-th normal distribution output by the encoder, represents the mean vector of the i-th normal distribution output by the encoder;

[0085] In a specific embodiment of the present invention, the KAE network takes the structural parameters in the data set as input and the phase as a condition, and uses the KAN improved conditional variational generative network KAE for training to generate a structural parameter library with a target phase response. The structural parameters are represented as x, the phase response is represented as c, and the latent variable is represented as z. Given the input variable x, the encoder defines the posterior distribution of the latent variable z , the decoder defines the generative distribution of the design parameter x given the phase response c and the latent variable z , the total loss value is composed of the reconstruction loss MSE (mean square error) and KL divergence.

[0086] Specifically, the Kolmogorov-Arnold network uses a learnable activation function at the edge of the network, so that each weight parameter in the KAN can be replaced by a single variable function and parameterized in the form of a B-spline function. Using the KAN network to improve cVAE can take advantage of the advantages of both models. The specific structure is as follows Figure 3 Shown, including:

[0087] 1. Encoder: Designed by the KAN framework, the input x passes through multiple layers of single variable functions Processing. The output is the latent variable (mean and variance).

[0088] 2. Keep the cVAE method and use the reparameterization trick to sample z from the latent space.

[0089] 3. Decoder: Designed by the KAN framework, the latent variable z and the condition y are passed through multiple layers of univariate functions Processing. The output is the reconstructed x.

[0090] Specifically, the forward prediction network includes a deep neural network based on an improved Fourier leaf space-smoothing filter layer, including:

[0091] Embedding the Fourier leaf space-smoothing filter layer into the last layer of a deep neural network, wherein the Fourier leaf space-smoothing filter layer receives the output of the last layer of a fully connected layer in the deep neural network;

[0092] The Fourier leaf space-smoothing filter layer includes adding a variable window exponential weighted smoothing filter method and matrixing it, and performing different smoothing processes on the middle and edge oscillation parts.

[0093] For FFDNN networks, adding smoothing filters and embedding them as layers into the neural network matrix can alleviate the edge oscillation problem caused by the Fourier low-frequency subspace. Smoothing filters include variable window exponential weighted filters, sliding average filters, low-pass filters, Savitzky-Golay filters, and other smoothing filter algorithms.

[0094] In a specific embodiment of the present invention, the FFDNN network is composed of three fully connected layers, a Fourier space transform layer, and a smoothing filter layer. The Fourier space transform layer receives the output of the third fully connected layer in the deep neural network.

[0095] The structural parameters [s, m, b, l1] are used as input, and the frequency response amplitude and phase curves are used as output. Since the phase and amplitude responses are 501-dimensional respectively, high-dimensional output will be generated, which increases the computational complexity of the neural network. The above problems can be optimized by predicting and restoring the curves through the Fourier low-frequency subspace. Specifically, a Fourier layer is added to the forward network. This layer accepts the output of the previous fully connected layer and performs the inverse discrete Fourier transform (IDFT) function. The Fourier transform FourierLayer is embedded in the neural network, as shown in the figure. Figure 4 As shown in Figure 2, high-frequency components are removed by controlling the Fourier series.

[0096] Furthermore, since the inverse discrete Fourier transform (IDFT) in the Fourier low-frequency space will inevitably bring about edge oscillation problems, the prediction accuracy will be reduced. A variable window exponential weighted smoothing filter method is added to achieve different smoothing treatments for the intermediate and edge oscillation parts by giving different weights to the average method of recent data, thereby alleviating the edge oscillation problem on the basis of ensuring the accuracy of the intermediate data. The filter Emalayer is embedded in the last layer of the FourierLayer, that is, the last layer of the neural network for training, as shown in the figure. Figure 4 shown.

[0097] Specifically, the variable window exponential weighted smoothing filter method is expressed in each window as:

[0098] ;

[0099] in, represents the tth value in the window, represents the weighted average of the t-th value in the window, is the weighted weight value, which can be expanded to obtain:

[0100] ;

[0101] By sliding the window in this way, the filtering sliding effect of the entire curve can be obtained. In order to reduce iterations and improve calculation speed, the process is replaced by matrix M. According to the different degrees of oscillation at the edge and in the middle, M is divided into three parts: M1, M2, and M3. Take M1 as an example:

[0102] Take M1 as an example:

[0103] ;

[0104] The concatenated matrix is ​​expressed as: ; M1 represents the first edge portion, M2 represents the middle portion, and M3 represents the second edge portion;

[0105] The smoothed curve is expressed as: ,in v is the original curve.

[0106] , N is the total number of points on the curve, N=501.

[0107] Specifically, the structural parameter library is fed into a trained forward prediction network model to predict the frequency response amplitude and phase characteristics, obtaining frequency response amplitude and phase frequency spectrum curves. Based on the target frequency response amplitude characteristics, the distance between the predicted data and the target frequency response is minimized.

[0108] In a specific embodiment of the present invention, a task-goal-based generative electromagnetic metasurface structure design system includes:

[0109] The mission target establishment module is used to establish the mission target and extract the target frequency response amplitude and target phase characteristics of the metasurface based on the metasurface function;

[0110] A structural parameter library generation module is used to generate a structural parameter library with a target phase response based on a variational generative network by adding a Kolmogorov-Arnold network to the variational generative network for improvement to obtain a KAE network;

[0111] A forward prediction network construction module, used to construct a forward prediction network, wherein the forward prediction network includes a deep neural network improved based on the Fourier leaf space-smoothing filter layer;

[0112] A frequency response feature prediction module, configured to input the structural parameter library into the forward prediction network, predict the frequency response amplitude and phase features, and obtain predicted frequency response amplitude and predicted phase features;

[0113] The metasurface structure generation module is used to calculate the distance difference between the predicted frequency response amplitude and the target frequency response amplitude, and between the predicted phase feature and the target phase feature, to obtain the metasurface structure that is closest to the task characteristics.

[0114] In a specific embodiment of the present invention, a metasurface structure is constructed, such as Figure 2 As shown, the circuit consists of three metal layers: from top to bottom, a first U-shaped metal layer, a first dielectric layer, a second U-shaped metal layer, a second dielectric layer, and a third U-shaped metal layer. The second U-shaped metal layer is located at the period boundary. The first and third U-shaped metal layers have the same structure and dimensions. The first and second dielectric layers are F4B dielectric substrates with a dielectric constant of 2.2. The thickness h of the F4B dielectric substrate is fixed at 1.5 mm, for a total thickness of approximately 3 mm. Frequency response amplitude and phase curves were obtained by simulation by varying the structural dimensional parameters [s, m, l, b].

[0115] The forward prediction network (FFDNN) takes structural parameters as input and the predicted values ​​of the frequency response amplitude and phase curves as output. It embeds the Fourier transform and smoothing filter layers into the neural network. Each curve is divided into three parts: edge / middle / edge according to the number of data points (60:38:1:60). The two edge windows have a size of 20 and a β value of 0.2, and the middle window has a size of 5 and a β value of 0.9. The Fourier transform-smoothing filter layer is embedded in the neural network for training. The performance improvement is measured by the average mean square error of N curves in the test set. The performance improvement is defined as

[0116] ;

[0117] The training results show that the performance has been improved by 18%. is the mean square error between the unfiltered prediction and the original curve, is the mean square error between the filtered prediction and the original curve. At this point, the filtered test_loss decreases from 0.00255 to 0.00239. The test results of the FFDNN network training model are shown in Figures 5(a) to 5(e).

[0118] The inverse training network takes the structural parameters in the dataset as input and the phase as a condition, and uses the improved conditional variational generation network KAE for training to generate a structural parameter library with the target phase response. The structural parameters are represented as x, the phase response is represented as c, the latent variable is represented as z, and the latent variable dimension latent_size=5. Given the input variable x, the encoder defines the posterior distribution of the latent variable z , the decoder defines the generative distribution of the design parameter x given the phase response c and the latent variable z , the total loss value is composed of the reconstruction loss MSE (mean square error) and KL divergence;

[0119] ;

[0120] in, represents the ratio between KL divergence and reconstruction loss, The size of is 0.001, represents the variance vector of the i-th normal distribution output by the encoder, represents the mean vector of the i-th normal distribution of the encoder output.

[0121] The Kolmogorov-Arnold network (KAN) uses a learnable activation function at the edge of the network, so that each weight parameter in the KAN can be replaced by a single variable function and parameterized in the form of a B-spline function. Using the KAN network to improve cVAE can take advantage of the advantages of both models. For any continuous function , there exists a continuous function 、 and . The output of the three-layer KAN network is:

[0122] ;

[0123] Where n represents the number of structural parameters, n=4, m=20, , 、 and They represent the kth, ith, and jth continuous functions (k=1,2,...l; i=1,2,...m; j=1,2,...n), respectively, and can all be represented by B-splines, such as Here the initial value of the grid size of the B-spline basis function is set to grid_size=5, and the initial value of the grid size of the B-spline basis function is spline_order=3, then p=grid_size+spline_order-1=7, It is trainable. Using the KAN architecture further improves its accuracy, with Test_Loss and MSE values ​​reaching 0.0099 and 0.0023, respectively. A comparison of the test results using the MLP framework is shown in Table 1.

[0124] Table 1

[0125]

[0126] Taking the frequency selective surface self-stealth task as an example, the task goal is: under the condition of normal incidence of a single-frequency 10Ghz electromagnetic wave, the frequency selective surface has a self-stealth function, and the phase accumulation is consistent with the equal-thickness air layer at this time, which is -36°; at the same time, a certain transmission bandwidth must be met (with a transmission coefficient of 0.8 as the basis for transmission evaluation). A large number of structural parameter libraries that meet -36°@10Ghz are generated using the KAE network. -36°@10Ghz means that the phase value at the 10GHz frequency point is -36 degrees. The trained forward prediction model FFDNN is used instead of the electromagnetic simulation software to predict the frequency response amplitude and phase curve. By quantitatively calculating the distance between the target value and the predicted value, the metasurface structure closest to the target frequency response characteristics is retrieved. In the case of a 9-13GHz transmission bandwidth, the distance between the target value and the predicted value is:

[0127] ;

[0128] When Ds is minimized, the most suitable structural parameters [s, l1, b, m] are [0.42mm, 0.26mm, 1.52mm, 0.40mm]. To verify whether the designed structure meets the mission requirements, Figures 6(a) and (b) show the predicted results of the metasurface structure designed by KAE and the electromagnetic software simulation results. It is found that the phase and frequency response amplitude curves of the two are consistent and consistent with the designed target transmission bandwidth of 9-13GHz. The phase accumulation meets the requirement of -36°@10GHz. In addition, considering the mission target of 8-16GHz transmission bandwidth and the phase change meeting -36°@10GHz, the structural parameter design is [0.67mm, 0.39mm, 1.27mm, 0.16mm]. The predicted results and electromagnetic software simulation results are shown in Figures 6(c) and (d), which can meet the mission requirements.

[0129] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0130] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A generative electromagnetic metasurface structure design method based on task objectives, characterized in that: include: Establish mission objectives and extract the target frequency response amplitude and target phase characteristics of the metasurface based on its functions; Based on the variational generative network, a Kolmogorov-Arnold network is added to the variational generative network for improvement to obtain a KAE network. Based on the KAE network, a structural parameter library with a target phase response is generated; Constructing a forward prediction network, the forward prediction network comprising a deep neural network improved based on a Fourier leaf space-smoothing filter layer; Inputting the structural parameter library into the forward prediction network, predicting the frequency response amplitude and phase characteristics, and obtaining predicted frequency response amplitude and predicted phase characteristics; Calculate the distance difference between the predicted frequency response amplitude and the target frequency response amplitude, and between the predicted phase feature and the target phase feature to obtain the metasurface structure closest to the task characteristics; The forward prediction network includes a deep neural network based on an improved Fourier leaf space-smoothing filter layer, including: Embedding the Fourier leaf space-smoothing filter layer into the last layer of a deep neural network, wherein the Fourier leaf space-smoothing filter layer receives the output of the last layer of the fully connected layer in the deep neural network; The Fourier leaf space-smoothing filter layer includes adding a variable window exponential weighted smoothing filter method and matrixing it to perform different smoothing treatments on the middle and edge oscillation parts; The variable window exponential weighted smoothing filter method is expressed in each window as: ； in, represents the tth value in the window, represents the weighted average of the t-th value in the window, is the weighted weight value; Slide the window in sequence to obtain the filtering sliding effect of the entire curve; According to the different degrees of edge and middle oscillation, it is divided into three parts: M1, M2, and M3; The concatenated matrix is ​​expressed as: ; The smoothed curve is expressed as: ,in v is the original curve.

2. The method for designing a generative electromagnetic metasurface structure based on a task objective according to claim 1, wherein: Also includes: Build a training dataset; The training data set includes structural parameters of different metasurfaces and their corresponding frequency response amplitude and phase characteristics; The KAE network and the forward prediction network are trained respectively using the training data set.

3. The method for designing a generative electromagnetic metasurface structure based on a task objective according to claim 2, wherein: The KAE network is trained, including: Taking the structural parameters as input and the corresponding phase features as conditions, the KAE network is trained to generate a structural parameter library with target phase response; Training the forward prediction network includes: The forward prediction network is trained using the structural parameters as input and the corresponding frequency response amplitude and phase characteristics as output. After the training is completed, the network model parameters of the forward prediction network are fixed.

4. The method for designing a generative electromagnetic metasurface structure based on a task objective according to claim 1, wherein: Improve the variational generative network by adding a Kolmogorov-Arnold network, including: designing the encoder and / or decoder network using the Kolmogorov-Arnold network framework; Among them, a learnable activation function is used at the edge of the Kolmogorov-Arnold network, so that each weight parameter in the Kolmogorov-Arnold network can be replaced by a univariate function and parameterized in the form of a B-spline function.

5. The method for designing a generative electromagnetic metasurface structure based on a task objective according to claim 4, wherein: The variational generation network consists of two parts: an encoder and a decoder. The encoder input is the structural parameters of the metasurface, and the output is a latent vector. The decoder input is the latent vector and phase response, and the output is the structural parameters of the reconstructed metasurface.

6. The method for designing a generative electromagnetic metasurface structure based on a task objective according to claim 5, wherein: The total loss value is composed of the reconstruction loss MSE and KL divergence: ； in, represents the ratio between KL divergence and reconstruction loss, represents the mean square error, represents the variance vector of the i-th normal distribution output by the encoder, represents the mean vector of the i-th normal distribution of the encoder output.

7. A generative electromagnetic metasurface structure design system based on task objectives, characterized in that: include: The mission target establishment module is used to establish the mission target and extract the target frequency response amplitude and target phase characteristics of the metasurface based on the metasurface function; A structural parameter library generation module is used to generate a structural parameter library with a target phase response based on a variational generative network by adding a Kolmogorov-Arnold network to the variational generative network for improvement to obtain a KAE network; A forward prediction network construction module, used to construct a forward prediction network, wherein the forward prediction network includes a deep neural network improved based on the Fourier leaf space-smoothing filter layer; A frequency response feature prediction module, configured to input the structural parameter library into the forward prediction network, predict the frequency response amplitude and phase features, and obtain predicted frequency response amplitude and predicted phase features; The metasurface structure generation module is used to calculate the distance difference between the predicted frequency response amplitude and the target frequency response amplitude, and between the predicted phase feature and the target phase feature, to obtain the metasurface structure that is closest to the task characteristics; The forward prediction network includes a deep neural network based on an improved Fourier leaf space-smoothing filter layer, including: Embedding the Fourier leaf space-smoothing filter layer into the last layer of a deep neural network, wherein the Fourier leaf space-smoothing filter layer receives the output of the last layer of the fully connected layer in the deep neural network; The Fourier leaf space-smoothing filter layer includes adding a variable window exponential weighted smoothing filter method and matrixing it to perform different smoothing treatments on the middle and edge oscillation parts; The variable window exponential weighted smoothing filter method is expressed in each window as: ； in, represents the tth value in the window, represents the weighted average of the t-th value in the window, is the weighted weight value; Slide the window in sequence to obtain the filtering sliding effect of the entire curve; According to the different degrees of edge and middle oscillation, it is divided into three parts: M1, M2, and M3; The concatenated matrix is ​​expressed as: ; The smoothed curve is expressed as: ,in v is the original curve.

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