A multi-layer gat-based wave-absorbing metasurface spectral data intelligent prediction method

Abstract

The application provides a wave-absorbing metasurface spectrum data intelligent prediction method based on a multilayer graph attention network (GAT). The method adopts 0 / 1 matrix coding of a multilayer metasurface unit structure, combines PyAEDT and HFSS to realize parameterized modeling, boundary configuration and 2-6GHz sweep simulation, and automatically obtains the absorption rate data of 81 frequency points. Data enhancement is carried out through matrix rotation, and the unit space coordinates, sizes and material properties are constructed as node features, and the graph structure data is generated based on the adjacent relationship in the layer and the cross-layer projection relationship. Further, a multilayer GAT model is designed, the multi-head attention mechanism and global pooling are used to extract cross-scale electromagnetic features, the fast prediction from a three-dimensional structure to a wideband absorption spectrum is realized, and the design efficiency of the wave-absorbing metasurface is improved.

Description

Technical Field

[0001] This invention relates to the field of metamaterials and metasurface design technology, and more specifically to an intelligent prediction method for spectral data of absorbing metasurfaces based on multilayer GAT. Background Technology

[0002] With the widespread application of 5G communication, smart radar, and electromagnetic compatibility technologies, the demand for high-performance absorbing materials is becoming increasingly urgent. Traditional absorbing metasurface design mainly relies on finite element simulation and experimental trial-and-error methods, which suffer from high computational costs, long optimization cycles, and difficulties in cross-scale parameter coupling modeling.

[0003] In recent years, data-driven machine learning methods have been introduced into the field of metamaterial design to accelerate metasurface structure optimization by establishing a mapping relationship between structure and performance. However, existing methods are mostly based on fully connected neural networks or convolutional neural networks, which cannot effectively characterize complex physical mechanisms such as nonlocal coupling and cross-scale electromagnetic interactions in multilayer metasurfaces, resulting in insufficient prediction accuracy for broadband absorption spectra.

[0004] In practical engineering, multilayer absorbing metasurfaces require the coordinated design of dielectric layers, resonant layers, and impedance matching layers to achieve broadband absorption. The topological relationships and electromagnetic energy transfer between these layers exhibit significant graphical structure characteristics. Therefore, how to construct nonlinear relationships between layers and realize an intelligent method for end-to-end positive prediction from microstructure parameters to absorption spectra has become a key challenge in the design of absorbing metasurfaces. Summary of the Invention

[0005] In view of this, the present invention provides a method for positive prediction of absorption spectrum data of multilayer structure absorbing metasurfaces based on graph attention network (GAT), aiming to achieve accurate mapping from the three-dimensional structure of metamaterials to broadband absorption spectra by combining automated modeling, data augmentation and deep learning techniques.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A method for positively predicting absorption spectral data of multilayer absorbing metasurfaces based on Graph Attention Network (GAT) includes: Multilayer metasurface structure design and data coding To achieve structured characterization of absorbing metasurfaces, this invention introduces a binary encoding mechanism. By establishing a 0 / 1 encoding matrix to mathematically represent the three-layer metal configuration ("1" represents a metal sheet, and "0" represents an air gap), this method can effectively compress the design parameter space and significantly improve the optimization efficiency of metasurface configurations. Compared with traditional modeling methods, this encoding system has higher parameter resolution and stronger design scalability.

[0007] The absorbing metasurface constructed in this invention employs a five-layer heterostructure of alternating metal-dielectric layers (see [link]). Figure 1 (As shown). To achieve omnidirectional absorption characteristics, the angular sensitivity limitation is overcome through the symmetrical design of the metal layers: the middle metal layer is generated through a single centrosymmetric transformation, while the top and bottom metal layers form the same configuration through a double centrosymmetric transformation. This hierarchical symmetrical architecture not only enhances structural stability but also achieves omnidirectional absorption through electromagnetic coupling control.

[0008] Automated modeling and electromagnetic simulation for dataset construction

[0009] Based on the deep integration of PyAEDT and High Frequency Structure Simulator (HFSS), this invention constructs a fully automated modeling and simulation system, realizing the mapping from structural encoding to electromagnetic absorption rate. The specific implementation steps are as follows: Parametric 3D Modeling The absorbing metasurface employs a hierarchical 3D modeling strategy. The top-layer unit matrix consists of 11×11 periodic metal-air units, each with a size of 0.2mm×0.2mm. The distribution of surface units is controlled by a 0 / 1 coding matrix ("1" represents a metal sheet, and "0" represents an air gap). The middle-layer unit matrix is ​​an 11×11 array with a unit size of 0.4mm×0.4mm, and the coding rule is consistent with the upper layer. The bottom layer structure is completely identical to the top layer structure.

[0010] Simulation data extraction and processing

[0011] The simulation environment improves computational efficiency through intelligent boundary configuration, and the Floquet port edge z The axis positive and negative directions can be set to support the simulation of plane wave perpendicular incidence and multi-angle scattering characteristics. A master-slave boundary is applied. xoy The planar design simplifies the computational domain to a single-cell structure, reducing simulation resource consumption by 80%. The simulation settings define a 2-6 GHz frequency band (0.05 GHz step size), covering 81 frequency points. After each simulation, the system employs an automated process for efficient data management, automatically acquiring data from metamaterial structural elements via the HFSS script interface. S parameter S 11 and S21 The amplitude is calculated using the following formula to determine the electromagnetic absorption rate of the absorbing metasurface in this simulation:

[0012] Data augmentation strategies and dataset organization based on spatial transformation

[0013] To enhance the model's generalization ability, this invention proposes a data augmentation strategy based on spatial transformation. The original 0 / 1 matrix is ​​rotated (90°, 180°, and 270° clockwise) to generate four topological configuration variants, expanding the training dataset to four times the size of the original data. This significantly reduces the model's sensitivity to local structures and addresses the underfitting problem caused by insufficient samples in traditional methods. The final dataset architecture stores the design samples in an Excel spreadsheet, with each row containing the top / middle layer encoding matrix, geometric parameters, material properties, and an 81-dimensional absorption spectrum vector.

[0014] Hybrid GAT Network Model Design, Training, and Prediction

[0015] This design constructs a multi-scale geometric feature extraction framework for microwave absorbing metamaterials. Through a three-level collaborative design involving heterogeneous spatial graph structure transformation, a multi-scale attention network architecture, and an adaptive attention optimization mechanism, it overcomes the dependence of traditional Graph Convolutional Networks (GCNs) on regular grid data, achieving accurate cross-scale mapping from microstructure to macroscopic electromagnetic response. The system transforms complex three-dimensional metamaterial structures into topological representations of graph neural networks, combined with a physics-inspired attention mechanism optimization strategy. The specific design steps are as follows: In the transformation of heterogeneous spatial graph structures, an innovative multi-dimensional feature encoding scheme is proposed to construct a physically meaningful topological graph representation. Targeting the multi-layer stacking characteristics of metamaterials, a six-dimensional node feature vector is designed: spatial coordinates ( x , y , z Accurately record the three-dimensional position information and geometric dimensions of the metal unit. weight , height The physical dimensions of the patch structure are represented by the material properties (0 / 1), which distinguish between metal units and air units.

[0016] To address the spatial transmission characteristics of electromagnetic coupling effects, a dual-edge connection strategy is adopted: bidirectional edge connections are established between adjacent units within a layer to reflect electromagnetic reciprocity; and unidirectional edge connections are established between different layers based on projection overlap (upper layer → middle layer → lower layer) to simulate three-dimensional electromagnetic field interference. A dynamic weight allocation algorithm is specifically introduced to automatically calculate edge weight coefficients based on unit spacing, where the weight of adjacent units is 1 / (1+ d² ()( dUsing Euclidean distance, this method effectively quantifies the physical law of electromagnetic coupling strength attenuation with distance. This graph structure transformation method can completely preserve the spatial symmetry, size sensitivity, and material heterogeneity of metamaterials.

[0017] In the multi-head attention network architecture design, the system constructs the network model as follows: The primary feature extraction layer adopts a four-head graph attention mechanism. Through multi-head parallel computation, the network can simultaneously extract multiple electromagnetic interaction modes. The intermediate feature fusion layer innovatively proposes a cross-head feature splicing strategy, which recombines feature vectors of different physical dimensions into tensors and uses 1×1 convolution to achieve nonlinear fusion of multi-physics information. Then, the extracted global features are subjected to spatial max pooling to extract the key structural features that have the greatest impact on the absorption rate from the hidden features. Its physical essence is equivalent to identifying the dominant distribution mode of the resonant unit. Finally, the output regression layer maps the high-dimensional features to 81 frequency points through a fully connected network, and a specially designed Sigmoid activation function is used (see the Sigmoid function image). Figure 2 As shown in the figure, the output value is constrained to the [0,1] interval to conform to the physical definition of assimilation rate. This architecture maintains the network depth while achieving adaptive feature selection through an attention mechanism, which greatly reduces the risk of overfitting compared to traditional GCN models.

[0018] Regarding the adaptive attention optimization mechanism, the system first introduces a distance decay coefficient and embeds an exponential decay term into the attention calculation. exp(-d) ,in d The first step is to use Euclidean distance to simulate the nonlinear law of electromagnetic coupling attenuation with distance; the second step is to use frequency domain attention gate design to enable the network to autonomously identify the influence weights of different structural features on the absorption rate of a specific frequency band.

[0019] Based on the above design scheme, a GAT-based absorption characteristic prediction model is constructed. The network model framework is described in [reference needed]. Figure 3 As shown, the dataset is divided into training, validation, and test sets in a 7:1.5:1.5 ratio to ensure a uniform distribution of spatial transformation configurations. The model uses mean squared error (MSE) as the loss function and is trained for 200 epochs using the Adam optimizer (initial learning rate 1e-3, batch size 32), combined with Dropout and early stopping mechanisms to suppress overfitting. Test results are as follows. Figure 4 As shown.

[0020] Overall, the system achieves intelligent prediction of the electromagnetic response of metamaterials through the aforementioned technological innovations. The heterogeneous graph conversion module transforms the 11×11 two-layer matrix into a topological graph with an average of 368 nodes, fully preserving the three-dimensional electromagnetic properties of the structure; the multi-scale network architecture establishes a nonlinear mapping relationship between the distribution pattern of metallic units and broadband absorption characteristics through local-global feature extraction; and the adaptive optimization mechanism endows the model with physical interpretability, making the attention weight distribution highly consistent with the electromagnetic simulation results. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0022] Figure 1 is a flowchart of the overall process of forward prediction intelligent design of multilayer structure absorbing metamaterial based on GAT according to the present invention. Figure 2 is a schematic diagram of the surface design structure of the microwave absorbing metamaterial of the present invention; Figure 3 shows the graph of the Sigmoid function; Figure 4 is a framework diagram of the absorption characteristic prediction model based on GAT of the present invention; Figure 5 shows the sample prediction results of the present invention. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] This invention discloses a method for intelligent fabrication of omnidirectional dual-frequency absorbing metasurfaces based on deep learning, comprising: Multilayer Metamaterial Structure Design and Data Coding To achieve efficient characterization and parameter compression of the absorbing metamaterial, this invention employs a binary coding mechanism for mathematical modeling of the three metal layers. Specifically, each metal structure is defined by an 11×11 0 / 1 coding matrix, where "1" represents a metal unit and "0" represents an air gap. The top and bottom metal layers use periodic units of 0.2mm×0.2mm, while the middle metal layer has units of 0.4mm×0.4mm. The topological configuration of the metal patch is controlled by adjusting the distribution of "1"s in the coding matrix. To enhance omnidirectional absorption performance, the metal layer design follows a strict symmetry principle: the middle metal pattern is generated from the initial configuration through a single centrosymmetric transformation, while the top and bottom metal layers form the same configuration through a double centrosymmetric transformation. This design not only reduces angular sensitivity but also broadens the absorption bandwidth through multi-layer electromagnetic coupling effects. The parameterized compression characteristics of the coding matrix significantly reduce the dimensionality of the design space, simplifying the optimization problem, which requires tens of thousands of simulations in traditional methods, into a search of thousands of coding combinations.

[0025] Automated modeling and electromagnetic simulation for dataset construction

[0026] Based on the deep integration of PyAEDT and HFSS, this invention realizes a fully automated simulation process from structure encoding to absorption spectroscopy. In the parametric modeling stage, the system automatically generates three-dimensional metamaterial units based on the encoding matrix: the top and bottom 11×11 metal-air periodic structures are stacked layer by layer through Boolean operations, and the electromagnetic response is controlled by scaling the unit size in the middle metal layer. In the simulation environment configuration, the Floquet port... z The axial direction is set to simulate a vertically incident electromagnetic wave, and master-slave boundary conditions are applied. xoy The planar design restricts the computational domain to a single-cell structure, reducing simulation resource consumption by 80%. The frequency sweep range is set to 2-6 GHz (0.05 GHz step), covering 81 frequency points to ensure complete capture of broadband absorption characteristics.

[0027] After the simulation is completed, the system automatically extracts data through the HFSS script interface. S parameter( S 11 , S 21 The absorption rate is calculated based on formula (2). All data is stored in Excel spreadsheet format, with each row containing the top / middle layer coding matrix and the corresponding 81-dimensional absorption rate. The simulation task queue management and data archiving are realized through batch processing scripts, reducing the time for a single simulation from 30 minutes in traditional manual operation to less than 5 minutes.

[0028]

[0029] Data Augmentation and Dataset Optimization Based on Spatial Transformation

[0030] To address the problem of insufficient sample size in deep learning model training, this invention proposes a data augmentation strategy based on rotation transformation. The original 0 / 1 encoding matrix is ​​rotated clockwise by 90°, 180°, and 270° sequentially, generating four topologically equivalent variant configurations. Due to the periodicity of metamaterials, the rotated configurations maintain a high degree of consistency in electromagnetic response, thereby expanding the dataset size to four times that of the original dataset without introducing additional simulations. The augmented dataset is divided into training, validation, and test sets in a 7:1.5:1.5 ratio, ensuring that the rotated variants are evenly distributed across the subsets to avoid overfitting the model to specific spatial orientations.

[0031] Hybrid GAT Network Model Design and Training

[0032] The core innovation of this invention lies in the construction of a hybrid graph attention network that integrates physical laws. Its design includes three parts: heterogeneous spatial graph transformation, multi-scale attention architecture, and adaptive optimization mechanism.

[0033] Heterogeneous spatial graph structure transformation

[0034] The key to mapping metamaterial 3D structures to graph neural network topology lies in defining the physical meaning of nodes and edges. Each metal or air unit is abstracted as a node in the graph, and the node feature vector contains six physical properties: three-dimensional coordinates ( x , y , z Positioning unit spatial location, geometric dimensions ( weight , height The patch's dimensions and material properties (0 / 1) distinguish between metal and air. The edge connection strategy employs a dual mechanism: bidirectional edges are established between adjacent cells within a layer to simulate near-field coupling; unidirectional edges (upper layer → middle layer → lower layer) are established between cross-layer cells through projection overlap, characterizing electromagnetic wave interference and energy dissipation in the vertical direction. Edge weights are determined using a dynamic attenuation formula. w=1 / (1+αd 2 ) Calculation, where α For learnable parameters, d Let be the Euclidean distance between nodes. This formula quantifies the nonlinear relationship between electromagnetic coupling strength and distance attenuation.

[0035] Multi-scale graph attention network architecture

[0036] The network adopts a four-layer cascaded structure: Primary feature extraction layer: A four-headed graph attention mechanism extracts local electromagnetic interaction patterns in parallel. Each attention head aggregates neighborhood node information through weighted aggregation to generate a 256-dimensional feature vector.

[0037] Intermediate feature fusion layer: Nonlinear fusion of cross-physical field features is achieved through regional pattern integration and global feature aggregation, and batch normalization (BatchNorm) is used to stabilize the training process.

[0038] Global Feature Pooling Layer: Performs spatial max pooling on hidden features to extract key structural patterns that significantly affect the absorption rate, which is equivalent to identifying the dominant distribution of resonant units.

[0039] Output regression layer: The fully connected network maps the pooled features to an 81-dimensional output. The sigmoid activation function constrains the predicted values ​​to the interval [0,1], which conforms to the physical definition of absorption rate.

[0040] Adaptive attention optimization mechanism

[0041] To enhance the physical interpretability of the model, two types of optimization strategies are embedded in the network: Distance-decayed attention: Introducing an exponential term into the calculation of the attention coefficient. exp(-d) The model is forced to prioritize the strong coupling effect of nearby units.

[0042] Frequency domain attention gate: Add a frequency domain attention module before the regression layer to dynamically allocate the importance of structural features in different frequency bands through a learnable weight matrix.

[0043] Model training and validation

[0044] Using mean squared error (MSE) as the loss function, the Adam optimizer was trained for 200 epochs with an initial learning rate of 1e-3 and a batch size of 32. To prevent overfitting, Dropout (scale 0.5) and an early stopping mechanism (terminating training when the validation set loss did not decrease for 10 consecutive epochs) were employed during training. Test set results showed that the model had an average prediction error of 2.7% across 81 frequency points, a peak error not exceeding 5%, and the predicted spectra showed a high degree of consistency with the simulated results at the resonant frequencies.

[0045] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0046] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those 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 invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for intelligent prediction of spectral data from absorbing metasurfaces based on multilayer GAT, characterized in that: The metal layer configuration of the multilayer absorbing metasurface is mathematically characterized by a binary coding mechanism, generating a structured coding matrix that includes geometric parameters and material properties. A dataset of microwave absorbing metasurface unit structures and their absorption spectra was constructed based on automated modeling and electromagnetic simulation. Spatial transformation data augmentation is performed on the dataset to generate topologically equivalent variant configurations to expand the training samples; A hybrid GAT network model is constructed to map the three-dimensional structure of the metasurface into graph topology data, and absorption spectrum prediction is achieved through a multi-scale attention mechanism and adaptive optimization strategy. The electromagnetic absorption rate of the metasurface unit structure is predicted and a wideband spectral response is output using the trained GAT network model.

2. The method according to claim 1, wherein the binary encoding mechanism is characterized in that: A five-layer heterogeneous structure with alternating stacks of metal-dielectric-metal-dielectric-metal was constructed. The top and bottom metal structures adopted an 11×11 metal patch array with a metal patch unit size of 0.2mm×0.2mm. The middle metal structure also adopted an 11×11 metal patch array with a metal patch unit size of 0.4mm×0.4mm. The distribution of each metal patch is defined by a 0 / 1 encoding matrix. The structure pattern of the middle metal layer is generated by a single centrosymmetric transformation. The top and bottom metal layers have the same structure and are formed by two centrosymmetric transformations to achieve omnidirectional absorption characteristics.

3. The method according to claim 1, wherein the automated modeling and electromagnetic simulation are characterized in that: Parametric 3D modeling was achieved by combining PyAEDT and HFSS, automatically generating metal-air periodic structures; along z The Floquet port is set along the axis and master-slave boundary conditions are applied. The simulation frequency band covers 2-6 GHz with a step size of 0.05 GHz. Extracted by automated scripts S The parameters are used to calculate the 81-dimensional absorbance based on the following formula. The dataset contains the top and middle layer 0 / 1 coding matrices and their corresponding absorbance in the 2-6 GHz range. 。 4. The method according to claim 1, wherein the spatial transformation data augmentation method is characterized in that: The original 0 / 1 encoding matrix is ​​transposed by 90°, 180° and 270° to generate four topologically equivalent variant configurations. The size of the training set is expanded to four times that of the original data, and the rotated samples are evenly distributed in the training set, validation set and test set.

5. The method according to claim 1, wherein the construction of the hybrid GAT network model is characterized by: The metasurface unit is abstracted as a graph node and a six-dimensional node feature vector is defined, which includes three-dimensional coordinates, geometric dimensions and material properties. A strategy of connecting bidirectional edges within a layer and unidirectional edges projected across layers is adopted. The edge weights are calculated using a dynamic attenuation formula, the expression of which is: exp(-d) , d The distance between nodes is the Euclidean distance. Cross-layer edge connections are established by determining the projection overlap to create unidirectional connections from the upper layer to the middle layer to the lower layer in order to simulate the three-dimensional electromagnetic field interference phenomenon. Local electromagnetic interaction features are extracted using a four-head graph attention mechanism, and key structural patterns are extracted by global max pooling after cross-head feature splicing and nonlinear fusion. The output layer is mapped to 81-dimensional absorbance predictions via a fully connected network and the output range is constrained by a Sigmoid function.

6. The method according to claim 5, wherein the adaptive optimization strategy is characterized in that: An exponential decay term is embedded in the attention coefficient calculation to quantify the decay law of electromagnetic coupling with distance; A frequency domain attention gate is added before the regression layer to dynamically allocate the importance weights of structural features in different frequency bands.

7. The method according to claim 1, wherein the model training is characterized in that: Mean squared error was used as the loss function, and the Adam optimizer was trained for 200 rounds with an initial learning rate of 1e-3. Dropout and early stopping mechanisms were combined to suppress overfitting, and the batch size was set to 32.

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