A Metasurface Unit Structure Inverse Design Method Based on Improved Generative Adversarial Networks

Abstract

A metasurface unit structure inverse design method based on an improved generative adversarial network (GAN) belongs to the field of electromagnetic metasurface design. The method includes: constructing a metasurface dataset based on the metasurface unit structure, its corresponding electromagnetic response, and its category; inputting the dataset in groups into a generator model G and a discriminator model D for model training; for the trained algorithm model, the electromagnetic response and normal Gaussian noise are used as inputs, and the metasurface unit structure is used as the output. This metasurface unit structure inverse design method can directly obtain the metasurface unit structure that conforms to the electromagnetic response from the electromagnetic response, reducing the relevant professional knowledge required by design engineers and the trial-and-error time in designing metasurface unit structures, thus significantly improving design efficiency. Furthermore, by changing the distribution of Gaussian noise, different metasurface unit structures can be obtained, increasing the diversity of generated structures, allowing engineers to choose from a variety of metasurface unit structures.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic metasurface design, and in particular to a method for inverse design of metasurface unit structures based on an improved generative adversarial network. Background Technology

[0002] Metasurfaces are two-dimensional metamaterials composed of subwavelength structural units. Their unique characteristic lies in their ability to manipulate electromagnetic waves; by altering the unit structure of the metasurface, different wavelength bands of electromagnetic waves can be controlled. Currently, the main targets for manipulation are the amplitude, phase, polarization, and angular momentum of electromagnetic waves. However, in metasurface design, even with simple patterned unit structures, the corresponding electromagnetic response characteristics can be complex. Therefore, accurately calculating and obtaining the electromagnetic response characteristics of a specific metasurface unit structure is quite difficult. For a long time, metasurface design and optimization have relied primarily on researchers' accumulated design experience and robust electromagnetic theory to guide a series of electromagnetic simulations and solve Maxwell's equations until a locally optimized solution is obtained.

[0003] Traditional metasurface design methods typically involve extensive full-wave numerical simulations (such as the finite element method (FEM), finite-difference time-domain method (FDTD), and finite integration technique (FIT)). These methods require complex modeling processes and numerous simulation tests. Using electromagnetic simulation software for metasurface design and optimization often requires hundreds or even thousands of electromagnetic simulation cycles, which is extremely time-consuming and computationally resource-intensive. Meanwhile, as research progresses, the patterns of metasurface unit structures become increasingly complex, further increasing the design difficulty. Final verification also requires repeated experiments.

[0004] With the rapid development of artificial intelligence (AI) technologies in recent years, deep learning, one of the disciplines within AI, has achieved unprecedented breakthroughs. Deep learning algorithms use neural networks to infer the correspondence between input and output pairs, showing particularly good fitting results for mappings that lack precise functions or mathematical correspondences. Therefore, introducing deep learning to address the problems in metasurface design is currently one of the most popular research topics.

[0005] 1. Patent 201910344708.1, "An Electromagnetic Metasurface Design Method Based on Support Vector Machine Algorithm," describes a deep learning algorithm model based on an autoencoder generative network. However, it does not collect a realistic dataset, which may result in poor generalization performance.

[0006] 2. Patent 202010260816.3, "Deep Learning-Based Electromagnetic Metasurface Design Method and Apparatus," describes a deep learning-based electromagnetic metasurface design method and apparatus. This method constructs both a forward prediction model and a reverse design model. However, its input-output diversity is significantly limited, constrained by the geometric parameters of the metasurface unit structure.

[0007] 3. Li Jiang et al. from Nanjing University of Posts and Telecommunications reported a neural network model based on a multilayer perceptron for designing nanostructured phase-manipulated metasurfaces. This network model accurately predicts phase values ​​by processing six geometric parameters and addresses the phase discontinuity problem in the reverse design of phase-manipulated metasurfaces by inserting a sigmoid function between the input layer and the hidden layers and using MAE as the loss function. However, this neural network model is only applicable to nanostructured phase-manipulated metasurfaces with six geometric parameters, exhibiting low generalization and portability. (Jiang L et al., “Neural network enabled metasurface design for phase manipulation”. Optics Express, 2021, 29(2):2521.)

[0008] 4. Zhao Cheng Liu et al. from Georgia Institute of Technology reported a deep neural network model based on generative adversarial networks (GANs). The proposed GAN model can effectively design metasurface unit patterns based on the input spectrum and has good performance. However, the metasurface patterns in the dataset used by the network are relatively simple, and the network cannot solve the design of one-to-many correspondences in metasurface design. (Liu Z et al., “A Generative Model for Inverse Design of Metamaterials Supplementary Information”. Nano Letters, 2018, 18(10): 6570-6576.)

[0009] In summary, the existing inverse design problem for metasurface unit structures based on deep learning is as follows:

[0010] 1. Limited Network Structure: Most networks use the electromagnetic response of metasurfaces as input and the metasurface unit structure as output, typically either patterned output or quantized structural parameter output. However, due to the limited network structure and insufficient model depth, their learning and generalization abilities are restricted, limiting their ability to handle only simple metasurface structures. Therefore, there is an urgent need to find a sufficiently deep neural network model to predict and generate metasurface unit structures, aiming to learn more complex correspondences.

[0011] 2. Limited Metasurface Unit Structure Design: Currently, for a given electromagnetic response input, neural networks typically output only one specific result. However, there is often a one-to-many collision relationship between metasurface unit structures and electromagnetic responses. When a metasurface designed by a neural network meets the electromagnetic response requirements, but fails to meet design requirements in other aspects such as excessive fabrication difficulty or low light transmittance, the neural network model is powerless, and traditional design methods must still be used to design a suitable metasurface unit structure. Therefore, there is an urgent need to find a network model capable of one-to-many mapping, so that metasurfaces with the same electromagnetic response but different unit structures can adapt to different scenarios.

[0012] 3. Conventional generative models often struggle to train on metasurface datasets: Existing generative adversarial networks (GANs) still cannot solve the problem of training difficulties, easily suffering from mode collapse and network crashes during training, especially evident in the design of metasurface unit structures. This is due to the complex relationship between metasurface unit structures and their corresponding absorption properties, and the high difficulty in obtaining and designing datasets for metasurface unit structures. Therefore, there is an urgent need to find a generative model that can be stably trained and eliminates the mode collapse problem. Summary of the Invention

[0013] This invention provides a method for inverse design of metasurface unit structures based on an improved generative adversarial network, characterized in that the method includes:

[0014] An improved generative adversarial network (GAN) architecture is constructed, consisting of a discriminator model D, a generator model G, and a training dataset. Data from the dataset is extracted, combined, and input into the discriminator model D and the generator model G. Adversarial training is then performed on both models. The training process is as follows:

[0015] I. Take a set of data from the training set;

[0016] II. Concatenate the electromagnetic response, true category, and m-dimensional random Gaussian noise in this set of data, where 20 ≤ m ≤ 50;

[0017] Ⅲ. Input the data after splicing in step Ⅱ into the generator model G. The generator model G undergoes x dual-channel convolutions and k upsamplings to obtain a fake metasurface unit structure, where the values ​​of x and k depend on the size of the desired metasurface unit structure.

[0018] IV. The real metasurface unit structure, the fake metasurface unit structure and the electromagnetic response are spliced ​​together and input into the discriminator model D. After the discriminator model D obtains two sets of outputs, the classification loss and Wasserstein distance of the two sets of outputs are obtained respectively, and the parameters of the discriminator model D are updated.

[0019] V. Input the data after concatenation in step IV into the generator model G. The generator model G undergoes x dual-channel convolutions and k upsamplings to obtain a new pseudo metasurface unit structure, where the values ​​of x and k depend on the size of the desired metasurface unit structure.

[0020] VI. The spurious metasurface unit structure is spliced ​​with the electromagnetic response and input into the discriminator model D to obtain the output classification loss and Wasserstein distance, and the parameters of the generator model G are updated.

[0021] VII. After multiple rounds of training, the Wasserstein distance between the generator model G and the discriminator model D will tend to stabilize, and the classification loss will tend to 0. At this point, the model training is complete.

[0022] The electromagnetic response of the input requirement is used to reverse design the metasurface unit structure of the trained generator model G, resulting in multiple sets of metasurface unit structures that meet the requirements. The generator model G and the discriminator model D use a dual-channel convolutional network, specifically a dual-channel convolutional network with upsampling and a dual-channel convolutional network with downsampling. One channel is the concatenation of the input and output residuals, and the other channel is the concatenation of the input and output channels. A self-attention mechanism is added to enable the network to obtain information about the entire metasurface.

[0023] Furthermore, the metasurface unit structure inverse design method based on improved generative adversarial networks includes a training dataset that includes the category of the metasurface unit structure, the metasurface unit structure, and its corresponding electromagnetic response.

[0024] Furthermore, in the improved generative adversarial network-based metasurface unit structure inverse design method, the generator model G is input to the true category of the metasurface unit structure, m-dimensional random Gaussian noise, and the true electromagnetic response corresponding to the metasurface unit structure, and outputs a false metasurface unit structure; the discriminator model D is input to the false metasurface unit structure generated by the generator model G, the true metasurface unit structure, and the true category, and outputs the prediction of the categories of the false metasurface unit structure and the true metasurface unit structure, as well as the Wasserstein distance between the discriminator model D and the generator model G, where 20≤m≤50.

[0025] Furthermore, the training dataset for the aforementioned metasurface unit structure inverse design method based on improved generative adversarial networks is obtained through the following methods:

[0026] The metasurface unit structure is divided into n × n squares. "1" in the squares indicates that the region is covered by the material required by the metasurface unit, while "0" indicates that the region is not covered. Electromagnetic simulation software is used to simulate k groups of metasurface unit structures to obtain their corresponding electromagnetic responses, where 8≤n≤64 and 10000≤k≤40000.

[0027] The metasurface unit structures and their corresponding electromagnetic responses are combined one by one as the labels and electromagnetic response inputs of the dataset. The metasurface unit structures are classified according to their patterns, which serve as the category inputs for the network model.

[0028] Furthermore, the metasurface unit structure inverse design method based on the improved generative adversarial network adds m-dimensional random Gaussian noise to the input of the generator model G, enabling it to output multiple sets of metasurface unit structures under the same electromagnetic response input.

[0029] Furthermore, in the aforementioned metasurface unit structure inverse design method based on improved generative adversarial networks, the parameters of the algorithm model are updated during training by referring to the Wasserstein distance and classification loss respectively. Specifically, the Wasserstein distance is:

[0030]

[0031] in, and These represent the electromagnetic response generated by the generator model G and the actual electromagnetic response in the training set, respectively; E represents the expectation, and D represents the discriminator model D. The Wasserstein distance must satisfy the Lipschitz continuity condition.

[0032] The classification objective function is the probability that the true metasurface unit structure given by the discriminator model D and the metasurface unit structure generated by the generator model G correspond to the class.

[0033]

[0034] Where c represents the true category to which the current metasurface unit structure belongs. The discriminator model D gives the category to which the actual metasurface unit structure belongs. The discriminator model D gives the category to which the metasurface unit structure generated by the generator model G belongs.

[0035] Furthermore, the proposed inverse design method for metasurface unit structures based on improved generative adversarial networks defines a stochastic geometric interpolation structure as a gradient penalty for the Wasserstein distance, ensuring that the Wasserstein distance satisfies the Lipschitz continuity condition. The objective function with stochastic geometric interpolation is:

[0036]

[0037] Where D represents the discriminator model D, The pseudo-metasurface unit structure generated by the generator model G. For the real metasurface unit structures in the training set, The metasurface unit structure is obtained after random geometric interpolation. The weights are for gradient penalty.

[0038] The innovativeness and good effects of this invention are:

[0039] 1. Based on the generative adversarial network architecture, this invention proposes a novel dual-channel supervised generative model. Its generative model is subject to more constraints, which enables the generated metasurface unit structures to have the required electromagnetic response. Its speed for designing metasurface structures far exceeds that of traditional trial-and-error methods.

[0040] 2. This invention proposes a stochastic geometric interpolation method to enable the network to adapt to metasurface unit structures and continuously explore new metasurface unit structures, thus avoiding network collapse due to the inability of the network to meet continuity conditions.

[0041] 3. This invention introduces m (20≤m≤50) dimensional Gaussian noise as a variable on the basis of a supervised generative model, so that the network can generate multiple sets of different metasurface unit structures for a single electromagnetic response input, giving designers more choices when there are different structural requirements. Attached Figure Description

[0042] To more clearly illustrate the technical solution adopted in this invention, the following is a brief description of the accompanying drawings used in the technical methods adopted or proposed in this invention:

[0043] Figure 1 This is an overall flowchart of the method described in this invention.

[0044] Figure 2 This is a flowchart of the generative adversarial network training process described in this invention.

[0045] Figure 3 This is a structural diagram of the generator model G in the generative adversarial network described in this invention.

[0046] Figure 4This is a structural diagram of the discriminator model D in the generative adversarial network described in this invention.

[0047] Figure 5 It is the dual-channel block with upsampling and downsampling described in this invention.

[0048] Figure 6 It is the dual-channel block without upsampling or downsampling described in this invention.

[0049] Figure 7 A schematic diagram of the random geometric interpolation described in the invention.

[0050] Figure 8 A diagram illustrating the dataset preparation process described in this invention.

[0051] Figure 9 This is a comparison diagram of the electromagnetic response of the metasurface unit structure generated by this invention and the required electromagnetic response.

[0052] Figure 10 This is a schematic diagram of the one-to-many generated metasurface unit structure described in this invention.

[0053] Figure 11 These are the absorption characteristics of the three sets of examples of metasurface unit structures generated by this invention. Detailed Implementation

[0054] The neural network model and new technology proposed in this invention will be described in general below with reference to the accompanying drawings. A transparent absorbing metasurface is used as an example. The overall requirements for implementing this example are as follows:

[0055] 1. The proposed inverse design method for metasurface unit structures based on improved generative adversarial networks can generate corresponding absorbing metasurface unit structures according to the electromagnetic response characteristics required by the designer.

[0056] 2. For the same electromagnetic response characteristic requirement, multiple different absorption metasurface unit structures can be obtained for designers to choose from, eliminating metasurface unit structures that are too difficult to process or have too low light transmittance.

[0057] 3. The electromagnetic response characteristics of the designed metasurface unit structure are close to or highly coincide with the electromagnetic response characteristics required in the actual application at the absorption frequency.

[0058] To address the aforementioned needs, this invention proposes a method for inverse design of metasurface unit structures based on an improved generative adversarial network. The overall process of the method is as follows: Figure 1 As shown. Furthermore, this invention proposes a dual-channel generative adversarial network structure, and the overall network training process is as follows: Figure 2As shown, the generator model G takes the electromagnetic response, Gaussian noise, and the true class corresponding to the electromagnetic response as input, and outputs the generated metasurface unit structure. The discriminator model D takes the metasurface unit structure and its corresponding electromagnetic response as input, and outputs predictions of the generated unit structure, the true unit structure class, and the Wasserstein distance.

[0059] The network's objective function consists of two parts: classification loss and Wasserstein distance. The Wasserstein distance is:

[0060]

[0061] in Let D represent the expectation, and D be the discriminator model D. The pseudo-metasurface unit structure generated by the generator model G. For the real metasurface unit structures in the training set, The metasurface unit structure is obtained after random geometric interpolation. The weights are for gradient penalty.

[0062] The classification loss is:

[0063]

[0064] Where E represents the expectation. This indicates the true category to which the current metasurface unit structure belongs. The discriminator model D gives the category to which the actual metasurface unit structure belongs. The discriminator model D gives the category to which the metasurface unit structure generated by the generator model G belongs.

[0065] Therefore, the overall objective function of the network is:

[0066] and L

[0067] In the process of minimizing the objective function, both the generator model G and the discriminator model D adjust their parameters to approximate the actual distribution of metasurface unit structure data.

[0068] Generator model G such as Figure 3 As shown, the upsampling and downsampling dual-channel block is as follows: Figure 5 As shown, a dual-channel block without upsampling or downsampling is as follows: Figure 6As shown, the generator model G takes as input 501 frequency points discretized from the electromagnetic response, a 50-dimensional random Gaussian noise, and a one-dimensional class vector. After receiving the input, the generator model G processes features through multiple dual-channel blocks and gradually upsamples to obtain a 16×16 binary metasurface unit structure image. Specifically, adding Gaussian noise to the input addresses the problem that ordinary neural networks cannot generate metasurface unit structures in a one-to-many manner.

[0069] Discriminator model D, such as Figure 4 As shown, the upsampling and downsampling dual-channel block is as follows: Figure 5 As shown, a dual-channel block without upsampling or downsampling is as follows: Figure 6 As shown, the input to the discriminator model D is mainly a matrix composed of the electromagnetic response and the metasurface unit structure. The purpose is to enable the discriminator model D to learn the matching relationship between the electromagnetic response of the absorbing metasurface and the metasurface unit structure. After receiving the input, features are extracted through multiple dual-channel blocks, and then gradually downsampled to obtain two 1×1 vectors representing the probability and class, respectively.

[0070] Dual-channel blocks, such as Figure 5 , Figure 6 As shown, both types of dual-channel modules, excluding the upsampling and downsampling portions, maintain consistency in the rest, exhibiting good symmetry and enabling better feature extraction. The input is summed and concatenated with the output separately to ensure gradient propagation downwards.

[0071] This invention proposes a gradient penalty term for the Wasserstein distance using stochastic geometric interpolation, such that... Figure 7 As shown, satisfying the Lipschitz continuity condition allows the model to converge. For metasurface unit structure data, "1" represents the material part and "0" represents the substrate part; any other data cannot be effectively converted into physical meaning. Therefore, randomly combining the metasurface unit structures generated by the generative adversarial network with the real metasurface unit structures is necessary to obtain physically meaningful penalty terms, enabling the network to converge.

[0072] This invention provides a method for constructing a metasurface dataset, such as... Figure 8 As shown, the EMNIST alphabet dataset was used as the reference pattern for the metasurface unit structure, which includes 16 uppercase and lowercase letters, ensuring the diversity and richness of the metasurface unit structure dataset. Full-wave simulations were performed on 100,000 data sets in the dataset, and the 12,800 sets with the largest inter-class variance were selected as the training dataset.

[0073] Three sets of tests were performed on the trained network. The results of the full-wave simulation of the generated metasurface unit structure are compared with the required electromagnetic response, as shown in the figure below. Figure 9As shown, it can be proven that the proposed generative adversarial network model can successfully identify and construct the correct metasurface unit structure pattern with only a small deviation from the actual electromagnetic response. Furthermore, by changing the concatenated noise vector, the following can be obtained: Figure 10 The metasurface unit structures shown have the same electromagnetic response but different properties, which can meet different design requirements.

[0074] Three sets of metasurface unit structures were fabricated and their TE and TM response tests were performed, such as Figure 11 As shown, for TE linearly polarized plane waves, the absorption frequencies of the three samples are 9.03 GHz, 13.04 GHz, and 14.72 GHz, with corresponding absorptivity of 92.61%, 99.03%, and 97.56%, respectively; for TM linearly polarized plane waves, the absorption frequencies of the three samples are 15.81 GHz, 13.3 GHz, and 12.8 GHz, with corresponding absorptivity of 98.05%, 93.34%, and 97.65%, respectively.

[0075] In summary, the proposed generative adversarial network (GAN) model, after adjustment, can be stably trained and is adapted to the characteristics of metasurface data. It can design structures for various metasurfaces at a speed far exceeding that of simulation-based trial-and-error methods. In particular, it can obtain outputs with the same electromagnetic response but different unit structures from different noise inputs, thus addressing the aforementioned problem of not being able to handle one-to-many interactions.

Claims

1. A metasurface unit structure inverse design method based on improved generative adversarial network, characterized in that, The method comprises: An improved generative adversarial network architecture is built, a discriminator model D, a generator model G and a training data set are built; Data in the data set is taken out, combined and input into the discriminator model D and the generator model G, and the discriminator model D and the generator model G are adversarially trained, and the training process is as follows: Ⅰ, a group of data is taken out from the training set; Ⅱ, the electromagnetic response, the real category and the m-dimensional random Gaussian noise in the group of data are spliced, 20≤m≤50; Ⅲ, the data after splicing in step Ⅱ is input into the generator model G, the generator model G is subjected to x times of double-channel convolution and k times of upsampling, and a false metasurface unit structure is obtained, wherein the values of x and k depend on the size of the required metasurface unit structure; Ⅳ, the real metasurface unit structure, the false metasurface unit structure and the electromagnetic response are spliced and input into the discriminator model D, the discriminator model D obtains two groups of outputs, respectively obtains the classification loss and the Wasserstein distance of the two groups of outputs, and updates the parameters of the discriminator model D; Ⅴ, the data after splicing in step Ⅳ is input into the generator model G, the generator model G is subjected to x times of double-channel convolution and k times of upsampling, and a new false metasurface unit structure is obtained, wherein the values of x and k depend on the size of the required metasurface unit structure; Ⅵ, the false metasurface unit structure and the electromagnetic response are spliced and input into the discriminator model D, the classification loss and the Wasserstein distance of the output are obtained, and the parameters of the generator model G are updated; After multiple rounds of training, the Wasserstein distance of the generator model G and the discriminator model D tends to be stable, and the classification loss tends to be 0, at which time the model training is completed; The electromagnetic response of the input requirement is input into the trained generator model G for reverse design of the metasurface unit structure, and a plurality of metasurface unit structures meeting the requirements are obtained; the generator model G and the discriminator model D internally adopt a double-channel convolution network, which specifically includes a double-channel convolution network with upsampling and a double-channel convolution network with downsampling; wherein one channel is residual concatenation of input and output, and the other channel is channel concatenation of input and output, and a self-attention mechanism is added therein to enable the network to obtain the overall information of the metasurface.

2. The metasurface unit structure inverse design method based on improved generative adversarial network of claim 1, wherein, The training data set includes the category to which the metasurface unit structure belongs, the metasurface unit structure and the electromagnetic response corresponding thereto.

3. The metasurface unit structure inverse design method based on improved generative adversarial network of claim 1, wherein, The input of the generator model G is the real category to which the metasurface unit structure belongs, the m-dimensional random Gaussian noise and the real electromagnetic response corresponding to the metasurface unit structure, and the output is a false metasurface unit structure; the input of the discriminator model D is the false metasurface unit structure generated by the generator model G, the real metasurface unit structure and the real category, and the output is the prediction of the false metasurface unit structure and the real metasurface unit structure category and the Wasserstein distance between the discriminator model D and the generator model G.

4. The metasurface unit structure inverse design method based on improved generative adversarial network of claim 1, wherein, The training data set is obtained in the following manner: The metasurface unit structure is divided into n×n grids, and "1" in the grid indicates that the area is covered by the required material of the metasurface unit, and "0" indicates that the area is not covered. The electromagnetic simulation software is used to simulate k groups of metasurface unit structures to obtain their corresponding electromagnetic responses, 8≤n≤64, 10000≤k≤40000; The metasurface unit structure and its corresponding electromagnetic response are combined one by one as the label and electromagnetic response input of the data set, and the metasurface unit structure is classified according to the style of the unit structure as the category input of the network model.

5. The metasurface unit structure inverse design method based on improved generative adversarial network of claim 1, wherein, In the input of the generator model G, m-dimensional random Gaussian noise is added, so that it can output multiple groups of metasurface unit structures under the input of the same electromagnetic response.

6. The metasurface unit structure inverse design method based on improved generative adversarial network of claim 1, wherein, In the training process, the parameters of the algorithm model are updated with reference to the Wasserstein distance and the classification loss, specifically, the Wasserstein distance is: where P G and P data are the electromagnetic response generated by the generator model G and the real electromagnetic response in the training set, respectively; E represents expectation, and D represents the discriminator model D; indicates that the Wasserstein distance needs to satisfy the Lipschitz continuity condition; The classification objective function is the possibility that the real metasurface unit structure given by the discriminator model D and the metasurface unit structure generated by the generator model G are of the corresponding category, that is: L C = E[log P(C=c | y)] + E[log P(C=c | y')] Wherein, c represents the real category to which the current metasurface unit structure belongs, y is the category to which the real metasurface unit structure given by the discriminator model D belongs, and y' is the category to which the metasurface unit structure generated by the generator model G belongs.

7. The metasurface unit structure inverse design method based on improved generative adversarial network of claim 1, wherein, The random geometric interpolation structure is defined to be the gradient penalty of the Wasserstein distance, so that the Wasserstein distance satisfies the Lipschitz continuity condition, and the objective function with random geometric interpolation is: where D represents the discriminator model D, x is the real metasurface cell structure in the training set, is the metasurface cell structure interpolated by random geometry, and λ is the weight of gradient penalty.

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