Metasurface inverse design method based on residual enhancement neural network

Abstract

The application discloses a metasurface inverse design method based on a residual enhancement neural network, and relates to the technical field of artificial electromagnetic materials and artificial intelligence. The method solves the problems of gradient disappearance and insufficient nonlinear mapping capability in traditional inverse design by constructing a deep fully connected neural network with residual connection and establishing an end-to-end mapping model from electromagnetic response to structure parameters. The network adopts a multi-level cascade architecture, including a feature extraction layer, a residual mapping layer, a feature compression layer and a parameter regression layer, and promotes deep feature propagation through a skip connection. In the training process, logarithmic transformation and standardization preprocessing are introduced, combined with adaptive optimization and regularization strategies, to improve the model convergence speed and generalization capability. The method can efficiently and accurately predict metasurface structure parameters, significantly improve design efficiency, and can be widely applied to intelligent design of multifunctional metasurfaces.

Description

Technical Field

[0001] This application relates to the field of interdisciplinary technology of artificial electromagnetic materials and artificial intelligence, and in particular to a metasurface reverse design method based on residual enhanced neural networks. Background Technology

[0002] Metasurfaces, as artificial electromagnetic structures at the subwavelength scale, can flexibly manipulate the polarization, phase, and amplitude of electromagnetic waves by adjusting the unit structure, and have wide applications in radar stealth, communication systems, imaging technology, and other fields. Traditional metasurface design methods rely on researchers to iterate through 3D modeling, parameterization, mesh generation, and full-wave simulation based on physical principles and experience. This results in long design cycles, high computational costs, and significant challenges in multi-parameter optimization.

[0003] In recent years, deep learning technology has provided a new approach for the reverse design of metasurfaces. Reverse design, by establishing a mapping model from the target electromagnetic response to structural parameters, can directly derive the required metasurface structure, significantly improving design efficiency. Existing research has applied methods such as reversible neural networks, deep neural networks, and generative adversarial networks to metasurface design, but two limitations remain: first, neural networks are prone to gradient vanishing when processing high-spectral features, hindering the propagation of deep features; second, the multi-parameter coupling characteristics of metasurfaces require models with stronger nonlinear mapping capabilities.

[0004] Therefore, there is an urgent need for a metasurface reverse design method that can effectively solve the gradient vanishing problem and improve mapping accuracy. Summary of the Invention

[0005] Therefore, it is necessary to develop a metasurface reverse design method based on residual enhancement neural networks to address the aforementioned technical problems.

[0006] The following technical solution is adopted in this specification: This specification provides a metasurface inverse design method based on residual enhancement neural networks, including: Obtain the correlation dataset of metasurface unit structure parameters and electromagnetic response within the target frequency band; A residual-enhanced deep fully connected neural network model with a multi-layer cascaded architecture for feature extraction, residual mapping, feature compression, and parameter regression is constructed. The residual mapping of the residual-enhanced deep fully connected neural network model contains two or more residual blocks. Each residual block adopts a dual-branch structure of main path and residual path, and feature reuse is achieved through skip connections. The metasurface unit structure parameters of the associated dataset are input into the residual-enhanced deep fully connected neural network model to obtain the predicted value of the electromagnetic response. The mean squared error loss function is used to obtain the loss value between the predicted value and the actual electromagnetic response value in the associated dataset. Based on the loss value, the training parameters of the residual-enhanced deep fully connected neural network model are adjusted by an adaptive moment estimation optimizer combined with a strategy of L2 regularization and Dropout to obtain an inverse mapping model from electromagnetic response to structural parameters. The target electromagnetic response is input into the inverse mapping model to obtain the predicted metasurface structure parameters.

[0007] Furthermore, the metasurface includes, from top to bottom, a metal pattern layer, a dielectric substrate layer, and a metal backplane layer, specifically including: The metal pattern layer consists of a symmetrical, double-arrow-shaped copper base layer with a fixed thickness; The dielectric substrate layer is composed of an F4B board with a fixed side length and thickness; wherein, the diagonal length of the dielectric substrate layer is the same as the length of the double arrow of the metal pattern layer; The metal backplane layer is composed of grounded metal with the same side length as the dielectric substrate layer.

[0008] Furthermore, the structural parameters include the geometric dimensions and rotation angle of the metal pattern in the metal pattern layer.

[0009] Furthermore, the residual-enhanced deep fully connected neural network model of the multi-layer cascaded architecture specifically includes: Input layer: The feature input dimension is consistent with the number of sampling points for the electromagnetic response parameters; Feature extraction layer: A fully connected layer with 512 neurons, equipped with batch normalization and a dropout rate of 0.3; The residual mapping layer consists of two cascaded residual blocks; each residual block consists of a fully connected layer, a ReLU activation function, batch normalization, and Dropout; the fully connected layer of residual block 1 contains 384 neurons, and the fully connected layer of residual block 2 contains 256 neurons. Feature compression layer: It consists of fully connected layers containing 192 units and 128 units respectively, and is equipped with a batch normalization layer with a dropout rate of 0.15; Linear processing layer: consists of two fully connected layers containing 64 units and 32 units respectively; Output layer: The number of neurons is consistent with the number of parameters of the metasurface structure.

[0010] Furthermore, each residual block adopts a dual-branch structure of main path and residual path, specifically including: The main path of the residual block contains two fully connected layers. The first layer uses the ReLU activation function in conjunction with batch normalization and Dropout, and the second layer uses linear activation and is batch normalized. The residual path of the residual block is dimension-aligned through a 1×1 equivalent fully connected layer, and finally superimposed with the main path output through an Add operation and activated by ReLU.

[0011] Furthermore, the training process of the deep fully connected neural network model also includes: The learning rate is dynamically adjusted until the model converges. Overfitting is prevented by using early stopping and dynamic adjustment of the learning rate.

[0012] Furthermore, the metasurface includes a broadband polarization conversion metasurface, a microwave absorber, or a phase-modulated metasurface.

[0013] Furthermore, the acquisition of the correlation dataset of metasurface unit structure parameters and electromagnetic response within the target frequency band specifically includes: The unit structure parameters of the metasurface within the target frequency band and the corresponding electromagnetic response are obtained through full-wave simulation; and the electromagnetic response is subjected to logarithmic transformation and standardization to obtain a dataset relating the metasurface unit structure parameters and the electromagnetic response.

[0014] Furthermore, the logarithmic transformation is expressed as taking the logarithm of the S-parameters; The standardization process uses StandardScaler to make the feature mean 0 and variance 1.

[0015] The above-mentioned technical solutions adopted in this specification can achieve the following beneficial effects: The metasurface reverse design method based on residual enhanced neural networks provided in this specification constructs a multi-layer cascaded architecture residual enhanced deep fully connected neural network model, which directly derives the end-to-end mapping of structural parameters from the target electromagnetic response, replacing traditional manual debugging and iterative simulation, and greatly improving design efficiency and design accuracy.

[0016] Furthermore, the residual augmentation neural network promotes gradient propagation through skip connections, effectively solving the gradient vanishing problem in deep network training and enhancing the fitting ability to the multi-parameter coupling relationship of metasurfaces. Attached Figure Description

[0017] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0018] Figure 1This is a schematic diagram of a residual augmentation neural network architecture provided in this specification; Figure 2 This is a schematic diagram of the training loss comparison curve provided in this manual; Figure 3 This is a diagram showing the comparison of the prediction accuracy of the parameters provided in this manual. Figure 4 Scatter plots and coefficients of determination diagrams for the parameter predictions provided in this manual; Figure 5 This is a schematic diagram of a metasurface structure provided in this specification. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this specification clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments in this specification without creative effort are within the scope of protection of this application.

[0020] This invention aims to provide a metasurface inverse design method based on residual enhanced neural networks. By introducing a residual connection mechanism and optimizing the training strategy, it solves the gradient vanishing problem in deep network training, enhances the model's ability to nonlinearly map multi-parameter coupling relationships, and achieves efficient and accurate metasurface inverse design.

[0021] This invention provides a metasurface inverse design method based on residual enhancement neural networks, which specifically includes the following steps: S1: Based on a preset metasurface unit structure (such as a three-layer metal-dielectric-metal backplate structure), multiple sets of parameter combinations are randomly generated within the range of its structural parameter values. The S-parameters (such as S11) in the target frequency band are obtained through full-wave simulation (such as CST Studio Suite) as electromagnetic response characterization, forming a correlation dataset between structural parameters and electromagnetic response.

[0022] S2: Logarithmic transformation of S-parameters is performed to enhance the discriminative power of low-amplitude features and alleviate gradient vanishing during training; then, standardization is performed to make the feature mean 0 and variance 1, while the structural parameters are standardized in the same way to unify the data scale and accelerate model convergence.

[0023] S3: Construct a deep fully connected neural network with residual enhancement, employing a multi-layered cascaded architecture of "feature extraction - residual mapping - feature compression - parameter regression": Input layer: The dimension is the same as the number of sampling points for the S-parameters (e.g., 200 dimensions); Feature extraction layer: A high-dimensional fully connected layer with 512 neurons, equipped with a batch normalization layer and a dropout layer with a dropout rate of 0.3, used to mine the electromagnetic property patterns hidden in the S-parameters; The residual mapping layer consists of two cascaded residual blocks, employing a pyramid-style dimensionality reduction design (e.g., 384 units → 256 units). Each residual block adopts a dual-branch structure of "main path + residual path". The main path contains two fully connected layers (the first layer is ReLU activation + batch normalization + Dropout, and the second layer is linear activation + batch normalization). The residual path is dimension-aligned through a 1×1 equivalent fully connected layer, and finally, feature fusion and ReLU activation are achieved through the Add operation.

[0024] Feature compression layer: After passing through fully connected layers of 192 units and 128 units in sequence, and with a decreasing Dropout rate (0.15→0), a smooth transition from high-dimensional features to compact representation is achieved; Linear processing layer: Contains 64-unit and 32-unit linear transformations, without using activation functions, and gradually transforms nonlinear features into a linear representation suitable for parametric regression; Output layer: The predicted values ​​of structural parameters are output through a fully connected layer, and the dimension is consistent with the number of geometric parameters of the metasurface to be inverted.

[0025] S4: The Adam adaptive moment estimator is used, with an initial learning rate of 0.0007 and mean squared error (MSE) as the loss function. L2 regularization (λ=1e-5) and Dropout are combined to suppress overfitting. During training, dynamic learning rate adjustment and early stopping are used, with a batch size of 48. The training and validation sets are divided proportionally (e.g., 8:2), and training is iteratively continued until the model converges.

[0026] S5: Input the target electromagnetic response into the trained model and directly output the predicted metasurface structure parameters to complete the reverse design. This method is applicable to various functional metasurfaces, including broadband polarization conversion metasurfaces, absorbers, and phase-tuned metasurfaces.

[0027] The technical solutions provided by the various embodiments of this application are described in detail below with reference to the accompanying drawings.

[0028] 1. Dataset Construction Metasurface unit structure: A three-layer structure is adopted, as shown in the attached diagram. Figure 5 As shown, it includes a double-arrow-shaped metal pattern layer, an F4B dielectric substrate layer, and a metal backplane layer. The structural parameters include eight degrees of freedom: L1, L2, L3, W1, W2, W3, α, and β, and their value ranges are shown in Table 1.

[0029] Table 1 Structural parameters and their ranges Data collection: 4000 sets of parameter combinations were randomly generated within the range of structural parameter values. Full-wave simulation was performed using CST StudioSuite to obtain the S11 parameters for the 2.0-28.0 GHz frequency band. A 200-dimensional feature vector was formed by uniform interpolation within this frequency band and divided into a training set (3200 sets) and a validation set (800 sets) in an 8:2 ratio.

[0030] 2. Data preprocessing.

[0031] Logarithmic transformation: Perform a logarithmic transformation on the S11 parameter, i.e., calculate log(|S11| + 1e-8), to amplify the differences in low-amplitude features.

[0032] Standardization: StandardScaler is used to standardize the S11 parameters and structural parameters so that the feature mean is 0 and the variance is 1.

[0033] 3. Model Building and Training Network architecture: as attached Figure 1 As shown, a residual augmentation neural network with an input dimension of 200 and an output dimension of 8 is constructed. The feature extraction layer has 512 units, the residual mapping layer contains two residual blocks (384 units → 256 units), the feature compression layer has 192 → 128 units, and the linear processing layer has 64 → 32 units.

[0034] Training strategy: Use the Adam optimizer (learning rate 0.0007), batch size 48, 300 iterations. Add L2 regularization (λ=1e-5) and Dropout, and employ early stopping and dynamic learning rate adjustment, such as... Figure 2 As shown, the MSE loss converges faster and has a lower initial loss after the logarithmic transformation.

[0035] Performance evaluation: such as Figure 3 and Figure 4 As shown, using the coefficient of determination R² and prediction accuracy as indicators, the model's prediction R² for all eight structural parameters is greater than 0.9, and the accuracy is improved by an average of more than 4.5%.

[0036] 4. Reverse Design Verification The target S11 curve is input into the trained model, which outputs the predicted structural parameters. The metasurface designed based on the predicted parameters maintains a polarization conversion rate of over 90% in the 8.8-24.4 GHz frequency band, verifying the effectiveness of the method.

[0037] This invention achieves efficient reverse design of metasurfaces through residual enhancement neural networks. The method is flexible and highly accurate, and can be extended to the design of more functional metasurfaces.

[0038] This invention can bring the following beneficial effects: 1. Highly efficient and accurate reverse engineering: Through an end-to-end mapping model, structural parameters are directly derived from the target electromagnetic response, replacing traditional manual debugging and iterative simulation, which greatly improves design efficiency; the model's prediction determination coefficient R² for multiple structural parameters is greater than 0.9, indicating high design accuracy.

[0039] 2. Powerful nonlinear mapping capability: Residual augmentation neural networks promote gradient propagation through skip connections, solving the gradient vanishing problem in deep network training and enhancing the fitting ability to the multi-parameter coupling relationship of metasurfaces.

[0040] 3. Excellent generalization performance: The introduction of logarithmic transformation and normalization preprocessing enhances the model's ability to capture spectral details and improves convergence speed; combined with regularization and dynamic learning rate adjustment, it effectively prevents overfitting and improves the model's adaptability to unseen data.

[0041] 4. Wide range of applications: The method does not depend on a specific metasurface structure and can be extended to the reverse design of different functional metasurfaces by changing the training dataset, which is highly flexible.

[0042] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

Claims

1. A metasurface inverse design method based on residual enhancement neural networks, characterized in that, include: Obtain the correlation dataset of metasurface unit structure parameters and electromagnetic response within the target frequency band; A residual-enhanced deep fully connected neural network model with a multi-layer cascaded architecture for feature extraction, residual mapping, feature compression, and parameter regression is constructed. The residual mapping of the residual-enhanced deep fully connected neural network model contains two or more residual blocks. Each residual block adopts a dual-branch structure of main path and residual path, and feature reuse is achieved through skip connections. The metasurface unit structure parameters of the associated dataset are input into the residual-enhanced deep fully connected neural network model to obtain the predicted value of the electromagnetic response. The mean squared error loss function is used to obtain the loss value between the predicted value and the actual electromagnetic response value in the associated dataset. Based on the loss value, the training parameters of the residual-enhanced deep fully connected neural network model are adjusted by an adaptive moment estimation optimizer combined with a strategy of L2 regularization and Dropout to obtain an inverse mapping model from electromagnetic response to structural parameters. The target electromagnetic response is input into the inverse mapping model to obtain the predicted metasurface structure parameters.

2. The metasurface reverse design method based on residual enhancement neural network as described in claim 1, characterized in that, The metasurface comprises, from top to bottom, a metal pattern layer, a dielectric substrate layer, and a metal backplane layer, specifically including: The metal pattern layer consists of a symmetrical, double-arrow-shaped copper base layer with a fixed thickness; The dielectric substrate layer is composed of an F4B board with a fixed side length and thickness; wherein, the diagonal length of the dielectric substrate layer is the same as the length of the double arrow of the metal pattern layer; The metal backplane layer is composed of grounded metal with the same side length as the dielectric substrate layer.

3. The metasurface reverse design method based on residual enhancement neural network as described in claim 2, characterized in that, The structural parameters include the geometric dimensions and rotation angle of the metal pattern in the metal pattern layer.

4. The metasurface reverse design method based on residual enhancement neural network as described in claim 1, characterized in that, The residual-enhanced deep fully connected neural network model with a multi-layered cascaded architecture specifically includes: Input layer: The feature input dimension is consistent with the number of sampling points for the electromagnetic response parameters; Feature extraction layer: A fully connected layer with 512 neurons, equipped with batch normalization and a dropout rate of 0.3; The residual mapping layer consists of two cascaded residual blocks; each residual block consists of a fully connected layer, a ReLU activation function, batch normalization, and Dropout; the fully connected layer of residual block 1 contains 384 neurons, and the fully connected layer of residual block 2 contains 256 neurons. Feature compression layer: It consists of fully connected layers containing 192 units and 128 units respectively, and is equipped with a batch normalization layer with a dropout rate of 0.15; Linear processing layer: consists of two fully connected layers containing 64 units and 32 units respectively; Output layer: The number of neurons is consistent with the number of parameters of the metasurface structure.

5. The metasurface reverse design method based on residual enhancement neural network as described in claim 1, characterized in that, Each residual block adopts a dual-branch structure of main path and residual path, specifically including: The main path of the residual block contains two fully connected layers. The first layer uses the ReLU activation function in conjunction with batch normalization and Dropout, and the second layer uses linear activation and is batch normalized. The residual path of the residual block is dimension-aligned through a 1×1 equivalent fully connected layer, and finally superimposed with the main path output through an Add operation and activated by ReLU.

6. The metasurface reverse design method based on residual enhancement neural network as described in claim 1, characterized in that, The training process of the deep fully connected neural network model also includes: The learning rate is dynamically adjusted until the model converges. Overfitting is prevented by using early stopping and dynamic adjustment of the learning rate.

7. The metasurface reverse design method based on residual enhancement neural network as described in claim 1, characterized in that, The metasurface includes a broadband polarization conversion metasurface, a microwave absorber, or a phase-modulated metasurface.

8. The metasurface reverse design method based on residual enhancement neural network as described in claim 1, characterized in that, The acquisition of the correlation dataset between metasurface unit structure parameters and electromagnetic response within the target frequency band specifically includes: The unit structure parameters of the metasurface within the target frequency band and the corresponding electromagnetic response are obtained through full-wave simulation; and the electromagnetic response is subjected to logarithmic transformation and standardization to obtain a dataset relating the metasurface unit structure parameters and the electromagnetic response.

9. The metasurface reverse design method based on residual enhancement neural network as described in claim 8, characterized in that, The logarithmic transformation is expressed as taking the logarithm of the S-parameters; The standardization process uses StandardScaler to make the feature mean 0 and variance 1.

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