Reflection metasurface reverse design method based on deep learning

Abstract

The invention discloses a reflection metasurface reverse design method based on deep learning, and the method comprises the steps: generating a corresponding metasurface geometrical shape image according to a given target reflection characteristic through employing a generative adversarial network and combining a conditional generative adversarial network with a Wharisstein generative adversarial network with gradient penalty; and a forward network based on the convolutional neural network is trained to predict reflection characteristics of the metasurface structure, and the reflection characteristics are used as verification of a reverse design result. According to the method, the circular polarization reflection metasurface is designed, time-consuming electromagnetic simulation calculation is avoided, consumption of calculation resources is reduced, and design efficiency is improved.

Description

Technical Field

[0001] This invention belongs to the field of antenna technology, specifically relating to a deep learning-based reverse design method for reflective metasurfaces. Background Technology

[0002] Metasurfaces possess unique electromagnetic control properties, low loss, low profile, and ease of fabrication, making them promising for applications in various fields such as communications, radar, and imaging. However, traditional metasurface design typically relies on complex electromagnetic simulations and optimization algorithms. While these methods can accurately calculate the electromagnetic response characteristics of metasurface units, they are extremely time-consuming for complex unit structures. Furthermore, designing a metasurface structure that meets specific requirements heavily depends on the designer's experience, requiring continuous trial and error to adjust the model structure, further increasing time costs.

[0003] The rapid development of artificial intelligence, especially deep learning technology, has provided new approaches to solving complex electromagnetic problems. By learning from a large number of metasurface structures and their corresponding electromagnetic response characteristics, deep learning can establish complex nonlinear mapping relationships between structural parameters and electromagnetic response characteristics. This mapping relationship greatly simplifies the design process, allowing for the direct acquisition of corresponding metasurface structures based on specific electromagnetic response requirements. This process requires no human intervention, breaking through the traditional design methods' heavy reliance on experience and intuition, reducing a significant amount of repetitive work, and greatly improving design efficiency. Summary of the Invention

[0004] The purpose of this invention is to provide a deep learning-based reverse design method for reflective metasurfaces. By leveraging the learning and optimization capabilities of deep learning models, the reflective metasurface structure is directly derived from the desired electromagnetic response, thereby significantly shortening the design cycle and improving design efficiency. This method overcomes the limitations of traditional design methods, enabling fast, accurate, and efficient design of reflective metasurfaces.

[0005] The objective of this invention is achieved through the following technical solution: a deep learning-based reverse design method for reflective metasurfaces, comprising the following steps:

[0006] The structure and operating frequency of the metasurface unit were determined, the reflection coefficients of metasurface units with different structures were collected, the dataset was collected, and the dataset was divided into training set and test set;

[0007] A network model is constructed, including a generator, a discriminator, and a predictor. The generative adversarial network composed of the generator and discriminator enables the reverse design of metasurfaces, while the predictor forward predicts the reflection coefficient of the generated metasurface structure to verify the accuracy of the reverse-designed metasurface structure.

[0008] The network model is trained using the collected training set samples, and the trained network model is tested and analyzed using the test set samples.

[0009] Furthermore, the centralized metasurface unit structure of the data includes a metal layer, a dielectric substrate, and a metal ground, with a unit period of 8 mm; the dielectric substrate is Rogers RT5880 material with a dielectric constant of 2.2 and a loss tangent of 0.0009, and a thickness of 1.57 mm; the metal layer and the metal ground are made of copper.

[0010] Furthermore, various regular shapes such as cross shapes, rectangular rings with rectangular patches, circular rings with circular patches, fan shapes, and arc shapes, as well as irregular shape images from the database of the National Institute of Standards and Technology, are used as the metal layer of the metasurface structure. The metal layer is divided into a 32×32 pixel binary encoding matrix, where a pixel value of 1 represents the part covered by metal and a pixel value of 0 represents the area without metal coverage. The side length of each pixel is 0.25 mm, and the pixel at the outermost position of the unit is set to 0.

[0011] Furthermore, the predictor model consists of convolutional layers, four ResNet residual blocks, pooling layers, and four fully connected layers. The input is a two-dimensional image of a metasurface unit structure with a size of (1, 32, 32), and the output is reflectance coefficient data with a size of (1, 84). The generator model has six hidden layers consisting of fully connected layers, batch normalization layers, and LeakyReLU activation functions. The output layer uses the Tanh function as its activation function. The input is (1, 128), consisting of Gaussian noise (1, 44) and reflectance coefficients (1, 84), and the output is (1, 1024). The discriminator model has three hidden layers consisting of fully connected layers and LeakyReLU activation functions. The input is (1, 1108), consisting of pixel values ​​(1, 1024) and reflectance coefficients (1, 84) of the two-dimensional image of the unit structure, and the output is (1, 1).

[0012] Furthermore, the dataset for model training consists of 9866 sets of two-dimensional images of metasurface unit structures and the real and imaginary parts of the x-polarization and y-polarization reflection coefficients in the corresponding 15-25 GHz frequency band, divided into training and test sets of sizes 7893 and 1973, respectively.

[0013] Furthermore, the predictor model has a batch size of 128, a learning rate of 0.0001, an optimizer of Adam, an activation function of ReLU, and a loss function of mean squared error (MSE). The generative adversarial network model has a batch size of 64, a learning rate of 0.0002 for the generator, a learning rate of 0.0004 for the discriminator, an optimizer of Adam, and a gradient penalty term coefficient of 10. The generator and discriminator are cross-trained, with the generator trained once after every 5 training iterations of the discriminator.

[0014] Furthermore, by using the inverse design network model obtained from the training, 2-bit circularly polarized reflective metasurface units are designed, and these units are arranged according to the phase distribution to obtain the desired circularly polarized metasurface structure.

[0015] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method described above.

[0016] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of the above-described method.

[0017] A computer program product includes a computer program that, when executed by a processor, implements the steps of the above-described method.

[0018] Compared to existing methods, the deep learning-based reverse design method for reflective metasurfaces of this invention offers significant advantages: the deep learning model, through learning from a large number of samples, can capture the complex relationship between the reflective metasurface structure and its electromagnetic response. This capability allows the model to directly deduce the metasurface structure from the desired electromagnetic response, greatly reducing the number of design iterations and thus significantly shortening the design cycle. By adjusting the input electromagnetic response parameters of the deep learning model, reflective metasurfaces that meet the needs of different application scenarios can be flexibly designed. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of a metasurface unit structure.

[0020] Figure 2 This is a schematic diagram of a portion of the metasurface unit structure in the dataset.

[0021] Figure 3 A framework for an overall network model for reverse engineering of metasurfaces.

[0022] Figure 4 The diagram shows the structure of the predictor network model and the residual block network.

[0023] Figure 5 The loss graph is used to train the predictor network model.

[0024] Figure 6 This is a comparison chart of the test results and simulation results for a single sample predictor in the test set.

[0025] Figure 7 To generate the adversarial network model structure.

[0026] Figure 8 To generate the training loss map for the adversarial network model.

[0027] Figure 9 A comparison chart showing the reflectance coefficients of a sample generator design result and the target reflectance coefficients in the test set.

[0028] Figure 10 The design results of a 2-bit reflective metasurface unit with a phase difference of 90° and the simulation pattern of the reflective metasurface at 20 GHz are presented.

[0029] Figure 11 The design results of 2-bit reflective metasurface units with equal phase and the simulation radiation pattern of the reflective metasurface at 20 GHz are presented.

[0030] Figure 12 The design results of a 2-bit reflective metasurface unit with a phase difference of 180° and the simulation pattern of the reflective metasurface at 20 GHz are shown. Detailed Implementation

[0031] This invention proposes a deep learning-based reverse design method for reflective metasurfaces. This method utilizes a Generative Adversarial Network (GAN), combining a Conditional Generative Adversarial Network (CGAN) and a Gradient-Penalized Wasserstein Generative Adversarial Network (WGAN-GP) to generate a corresponding metasurface geometry image based on given target reflection characteristics. A forward network based on a Convolutional Neural Network (CNN) is then trained to predict the reflection characteristics of the metasurface structure, which serves as a verification of the reverse design results. This invention designs a circularly polarized reflective metasurface using this method, avoiding time-consuming electromagnetic simulation calculations, reducing computational resource consumption, and improving design efficiency.

[0032] The technical solution of the present invention will be described in detail below.

[0033] First, a database containing a large number of reflective metasurface samples was constructed. These samples include various shapes and structures such as cross-shaped, rectangular rings with rectangular patches, circular rings with circular patches, sector-shaped, arc-shaped, and handwritten digits from the National Institute of Standards and Technology (MNIST) database, along with their corresponding electromagnetic response characteristics. The real and imaginary parts of the x-polarized and y-polarized reflection coefficients of these samples from 15 GHz to 25 GHz were obtained through full-wave electromagnetic simulation using the CST electromagnetic simulation software, providing rich data support for the training of deep learning models.

[0034] A deep learning model is then constructed, comprising a generative adversarial network (GAN) consisting of a generator and a discriminator to perform inverse design of metasurface units and a predictor to perform forward prediction of the unit's electromagnetic response. The generator takes Gaussian random noise and the real and imaginary parts of the unit's reflection coefficients as input, and outputs a two-dimensional image of the unit structure after passing through six hidden layers. Generated samples (unit structure images generated by the generator) or real samples (unit structure images corresponding to the dataset) are combined with the reflection coefficients and input into the discriminator, which approximates the Wasserstein distance between the real and generated samples after passing through three hidden layers. The predictor takes the two-dimensional image of the unit structure as input, extracts features through a series of convolutional, pooling, and fully connected layers, and outputs the predicted reflection coefficients.

[0035] The model is trained using training set samples. The predictor's loss function is the average error, which is the squared difference between the predicted and true reflection coefficients. The overall network parameters are updated using a backpropagation algorithm. The gradients of each variable in each network are calculated based on the overall network loss function, and these gradients are fed into the Adam optimizer to update the model's network parameters using gradient descent. After the predictor model is trained, its network parameters are fixed, and a generative adversarial network (GAN) is trained. The GAN's loss function is the Wasserstein distance. The generator aims to make the generated image as close to the real image as possible, i.e., to minimize the Wasserstein distance through training. The discriminator aims to distinguish between real and generated samples; therefore, the Wasserstein distance between real and generated samples should be as large as possible. Similar to the predictor model training, the overall network parameters are updated using a backpropagation algorithm.

[0036] After training, this invention utilizes a deep learning model for the reverse design of circularly polarized reflective metasurfaces. By inputting the target reflection amplitude and phase, the generator model quickly outputs an image of the reflective metasurface unit structure that meets the requirements. This generated image is then input into a predictor to obtain its predicted amplitude and phase values. The predicted results are compared with the design target, and the metasurface unit structure that best meets the requirements is selected. Arranging these units according to their phase distribution yields the desired circularly polarized metasurface structure.

[0037] The present invention will be further described below with reference to the accompanying drawings and specific examples.

[0038] Example

[0039] The unit structure designed in this invention is as follows: Figure 1 As shown. The centralized metasurface unit structure of the dataset includes a metal layer, a dielectric substrate, and a metal ground, with a unit cell period of 8 mm. The dielectric substrate is made of Rogers RT5880 material with a dielectric constant of 2.2 and a loss tangent of 0.0009, and has a thickness of 1.57 mm. The metal layer and metal ground are made of copper.

[0040] Various regular shapes, including cross-shaped, rectangular rings with rectangular patches, circular rings with circular patches, fan-shaped, and arc-shaped, along with handwritten digits from the National Institute of Standards and Technology (MNIST) database, were used as the metal layer of the metasurface structure. The metal layer was divided into a corresponding 32×32 pixel binary encoding matrix, where a pixel value of 1 represented a metal-covered area, and a pixel value of 0 represented an area without metal coverage. Each pixel had a side length of 0.25 mm. To reduce the coupling effect between adjacent units, the outermost pixel of each unit was set to 0, thus limiting the overall effective length of the metal layer pattern to within 7.5 mm. The real and imaginary parts of the x-polarization and y-polarization reflection coefficients of these unit structures from 15 GHz to 25 GHz were obtained using the electromagnetic simulation software CST full-wave simulation, providing rich data support for the training of deep learning models. Figure 2 This is a schematic diagram of a portion of the metasurface unit structure in the dataset.

[0041] Figure 3 The overall network model framework for metasurface inverse design consists of three network structures: a generator, a discriminator, and a predictor. The generative adversarial network (GAN) formed by the generator and discriminator enables the inverse design of the metasurface, while the predictor forward-predicts the reflection coefficient of the generated metasurface structure to verify the accuracy of the inverse-designed metasurface structure.

[0042] Predictor network model structure as follows Figure 4 As shown in (a), the network consists of convolutional layers, four ResNet residual blocks, pooling layers, and four fully connected layers. Each convolutional layer is followed by a batch normalization layer and a ReLU activation function to ensure the stability of network training and its nonlinear mapping capability. Figure 4 Figure (b) illustrates the specific structure of the residual block. The sum of the results from the residual branch and the main branch ensures information flow during network training, effectively avoiding the vanishing and exploding gradient problems. Following the residual block, an average pooling layer is used to reduce the dimensionality of the feature map, which is then flattened into a one-dimensional vector. The predicted reflection coefficient values ​​are then output through a fully connected layer. Except for the last output layer, each fully connected layer uses the ReLU activation function. Furthermore, to prevent overfitting, a Dropout layer is used to randomly deactivate some neurons, improving the model's generalization ability.

[0043] Figure 5 The changes in the loss function of the predictor during training are shown. After 800 iterations, the mean square error of the training and test sets converged to 0.003 and 0.03, respectively. A set of samples was randomly selected from the test set, and the reflection coefficients of these samples were predicted using the trained predictor model. The comparison between the prediction results and the actual reflection coefficients obtained through CST simulation software is shown in the figure below. Figure 6As shown, the overall predictor model has a high accuracy rate, while the MSE remains at a low level.

[0044] Generative Adversarial Network (GAN) model structure as follows Figure 7 As shown, both the generator and discriminator are composed of fully connected neural networks. The generator uses six fully connected neural network layers as hidden layers, such as... Figure 7 As shown in (a), the output of each hidden layer passes through a batch normalization layer and a LeakyReLU activation function to improve the network's generalization ability and training stability. Finally, the output layer's Tanh activation function generates samples. The discriminator network structure is as follows: Figure 7 As shown in (b), the number of hidden layers is reduced to a three-layer fully connected neural network and the batch normalization layer is no longer used in the hidden layers, but the activation function is still the LeakyReLU function. The discriminator approximates the Wasserstein distance between the real sample and the generated sample instead of judging the authenticity of the input sample, so the output layer no longer uses the Sigmoid activation function.

[0045] Figure 8 The loss curves of the generator and discriminator during training are shown. As the number of training iterations increases, the generator loss decreases, and the generated images become increasingly closer to real images, while the discriminator loss increases. The reflectance coefficients of a set of samples in the test set are combined with random Gaussian noise and input into the generator to obtain the corresponding metasurface structure design. To accurately reflect whether the generated metasurface structure meets the expected reflectance coefficient, the generated metasurface structure is simulated in CST software. The simulated reflectance coefficient is compared with the input reflectance coefficient, and the MSE is calculated. Figure 9 As shown, the generated samples can well satisfy the input characteristics, and the difference between the generated samples and the original test set samples also indicates that the generator model has a certain degree of generalization ability.

[0046] Using the trained network model, three sets of 2-bit circularly polarized reflective metasurface units were designed at 20 GHz, with the amplitude and phase combinations of the y-polarized reflectivity coefficient S11 and x-polarized reflectivity coefficient S22 as design objectives. For each design objective, a series of two-dimensional pixel images of the metasurface unit structure were first generated using a generator. These images were then input into a predictor to obtain the predicted amplitude and phase values. The predicted results were compared with the design objectives, and the metasurface unit structure that best met the requirements was selected. Corresponding circularly polarized reflective metasurfaces were constructed based on the three sets of 2-bit circularly polarized reflective metasurface units, and simulation analysis was performed. Figure 10 , Figure 11 and Figure 12For each design scenario, the simulation results obtained through the reverse design network model in CST software are basically consistent with the target requirements, and the amplitude and phase errors are within acceptable ranges. The reflective metasurfaces constructed from the 2-bit circularly polarized reflective metasurface units obtained based on the reverse design network model all exhibit good circular polarization performance and beam pointing, verifying the effectiveness and practicality of the deep learning-based reverse design method for reflective metasurfaces in this invention.

[0047] The above embodiments are only used to illustrate the principles and effects of the present invention and do not limit its application scope. While maintaining the core spirit and scope of the present invention, experts in the art can make flexible adjustments and innovations. Therefore, any equivalent modifications or changes guided by the spirit and technical ideas of the present invention are within the protection scope of the present invention.

Claims

1. A deep learning-based reverse design method for reflective metasurfaces, characterized in that, Includes the following steps: The metasurface unit structure and operating frequency were determined, the reflection coefficients of metasurface units with different structures were collected, the dataset was collected, and the dataset was divided into training set and test set; Build a network model, including a generator, discriminator, and predictor; A generative adversarial network consisting of a generator and a discriminator enables the reverse design of metasurfaces, while a predictor forward-predicts the reflection coefficient of the generated metasurface structure to verify the accuracy of the reverse-designed metasurface structure. The network model is trained using the collected training set samples, and the trained network model is tested and analyzed using the test set samples.

2. The deep learning-based reverse design method for reflective metasurfaces according to claim 1, characterized in that, The centralized metasurface unit structure of the data set includes a metal layer, a dielectric substrate, and a metal ground, with a unit period of 8 mm. The dielectric substrate is made of Rogers RT5880 material with a dielectric constant of 2.2 and a loss tangent of 0.0009, and has a thickness of 1.57 mm. The metal layer and the metal ground are made of copper.

3. The deep learning-based reverse design method for reflective metasurfaces according to claim 1, characterized in that, Images of various regular shapes, such as cross shapes, rectangular rings with rectangular patches, circular rings with circular patches, fan shapes, and arc shapes, as well as irregular shapes from the database of the National Institute of Standards and Technology, are used as the metal layer of the metasurface structure. The metal layer is divided into a 32×32 pixel binary encoding matrix, where a pixel value of 1 represents the part covered by metal and a pixel value of 0 represents the area without metal coverage. The side length of each pixel is 0.25 mm, and the pixel at the outermost position of the unit is set to 0.

4. The deep learning-based reverse design method for reflective metasurfaces according to claim 1, characterized in that, The predictor model consists of convolutional layers, four ResNet residual blocks, pooling layers, and four fully connected layers. The input is a two-dimensional image of a metasurface unit structure with a size of (1, 32, 32), and the output is reflectance coefficient data with a size of (1, 84). The generator model has six hidden layers consisting of fully connected layers, batch normalization layers, and LeakyReLU activation functions. The output layer has Tanh activation function, with an input size of (1, 128) consisting of Gaussian noise (1, 44) and reflectance coefficients (1, 84), and an output size of (1, 1024). The discriminator model has three hidden layers consisting of fully connected layers and LeakyReLU activation functions, with an input size of (1, 1108) consisting of pixel values ​​(1, 1024) and reflectance coefficients (1, 84) of the two-dimensional image of the unit structure, and an output size of (1, 1).

5. The deep learning-based reverse design method for reflective metasurfaces according to claim 1, characterized in that, The dataset for model training consists of 9866 sets of two-dimensional images of metasurface unit structures and the real and imaginary parts of the x-polarization and y-polarization reflection coefficients in the corresponding 15-25 GHz frequency band, divided into training and test sets of sizes 7893 and 1973, respectively.

6. The deep learning-based reverse design method for reflective metasurfaces according to claim 5, characterized in that, The predictor model has a batch size of 128, a learning rate of 0.0001, an optimizer of Adam, an activation function of ReLU, and a loss function of mean squared error (MSE). The generative adversarial network (GAN) model has a batch size of 64, a learning rate of 0.0002 for the generator, a learning rate of 0.0004 for the discriminator, an optimizer of Adam, and a gradient penalty term coefficient of 10. The generator and discriminator are cross-trained, with the generator trained once after every 5 training iterations of the discriminator.

7. The deep learning-based reverse design method for reflective metasurfaces according to claim 1, characterized in that, Using the inverse design network model obtained from training, 2-bit circularly polarized reflective metasurface units are designed, and these units are arranged according to phase distribution to obtain the desired circularly polarized metasurface structure.

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of any of the methods described in claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method described in any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the method described in any one of claims 1-7.

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