Computer implementation method of heterogeneous graph convolutional network for antenna design

Abstract

There is provided a computer-implemented training method of a heterogeneous graph convolutional network (Het-GCN) for antenna design, the method comprising modeling an antenna as graph data, the graph data comprising heterogeneous graphs representing different components of the antenna, generating a radiation pattern and reflection coefficients of the antenna based on the graph data, and training the Het-GCN using the data set. The invention also provides a computer-implemented method for designing a cylindrical dielectric resonator antenna (DRA) by using the Het-GCN trained by the method.

Description

Technical Field

[0001] This invention relates to a deep learning-based antenna design method and system. Specifically, this invention provides a method and system for training a heterogeneous graph convolutional network (Het-GCN) for antenna design, and a method and system for antenna design based on Het-GCN. Background Technology

[0002] As a crucial component of wireless communication systems, antennas have been extensively studied to meet diverse and challenging requirements. Sometimes, simple antenna structures fail to meet specifications, necessitating the use of non-traditional antenna structures with numerous sensitive parameters. Directly simulating non-traditional antenna structures can be extremely time-consuming, especially when it relies on trial-and-error methods based on human experience. Therefore, developing new methods to address this issue is crucial.

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[0046] Exemplary embodiments of the present invention apply deep learning to the design or synthesis of directional dielectric resonator antennas (DRAs). Some embodiments of the invention explore a bi-branch heterogeneous graph convolutional network (Het-GCN) to assist in the design of complex and computationally intensive antennas. This model can directly generate the radiation pattern and reflection coefficient for a given antenna structure, with each prediction taking only milliseconds. Antenna configurations are modeled as graph structures and optimized via gradient descent. Some embodiments of the invention utilize Het-GCN to synthesize four cylindrical dielectric resonator antennas with different dielectric constant distributions. These antennas successfully achieved the expected main beam directions at 0°, 30°, 60°, and 90°. Comparison with existing machine learning methods shows that the method of this embodiment improves design flexibility and accuracy.

[0047] According to one aspect of the present invention, a computer implementation method for Het-GCN for antenna design is provided, the method comprising modeling the antenna as graph data, wherein the graph data includes heterogeneous graphs representing different components of the antenna; generating a dataset of radiation patterns and reflection coefficients of the antenna based on the graph data; and training Het-GCN using the dataset.

[0048] Preferably, the antenna may include a cylindrical DRA. The cylindrical DRA may include a ground plane, a dielectric resonator element operatively coupled to the ground plane, and a feed probe operatively coupled to the dielectric resonator element.

[0049] More preferably, the ground plane may include an aluminum ground. In some embodiments, the dielectric resonator element may include N layers with different dielectric constants arranged starting from the feed probe and divided into an Mth portion by an angle, such that the dielectric resonator element consists of N×M dielectric resonator blocks.

[0050] Most preferably, the cylindrical DRA can be centrally fed by a feed probe, the height of which is h. p .

[0051] In some variations of the preferred embodiment, the dielectric constant distribution within the dielectric resonator block and the height (h) of the feed probe can be adjusted. p ), and the width of the layers in the dielectric resonator element (w) d This is used to adjust the antenna characteristics of the cylindrical DRA.

[0052] In other variations of the preferred embodiment, modeling the antenna as graphical data may further include randomly generated antenna parameters. These antenna parameters include the dielectric constant distribution, the height of the feed probe (h... p ) and the width of the layers of the dielectric resonator element (w) d ).

[0053] In some variations of the preferred embodiment, the graph data may include node attributes of cylindrical DRA components (each component as a node) and edge attributes of interactions between nodes.

[0054] Preferably, the components of the cylindrical DRA may include a dielectric resonator block and a feed probe.

[0055] More preferably, node attributes can be constructed based on the geometric parameters and material properties of the cylindrical DRA component.

[0056] In some variations of the preferred embodiments, the interaction between nodes may include electromagnetic wave propagation between adjacent nodes.

[0057] In some variations of the preferred embodiment, Het-GCN can be designed to perform convolution functions on graph data.

[0058] Preferably, in Het-GCN, different types of relations are assigned through a specified convolution function, and the weights of different types of relations are not shared.

[0059] More preferably, in Het-GCN, a readout function is run on all node features in the convolutional graph to obtain a graph-level representation (GLR).

[0060] Most preferably, Het-GCN can predict radiation patterns and reflection coefficients by running two independent multilayer perceptron branches (MLPs) on the graph-level representation.

[0061] According to a second aspect of the invention, a computer implementation method for designing a cylindrical DRA using a Het-GCN trained by the method of the first aspect is provided, the method comprising obtaining a desired antenna structure of a cylindrical DRA having a specific radiation direction using the trained Het-GCN.

[0062] Preferably, obtaining the desired antenna structure includes providing the radiation pattern and reflection coefficient of a reference antenna structure to the trained Het-GCN, randomly initializing it in the neighborhood of the reference antenna structure, and iteratively obtaining the optimal antenna structure using mini-batch gradient descent.

[0063] More preferably, obtaining the optimal antenna structure through iteration may include adjusting the dielectric constant distribution within the dielectric resonator block to control the radiation pattern variation, and adjusting the height of the feed probe to achieve impedance matching.

[0064] Most preferably, the optimal antenna structure is obtained through iteration, and may also include adjusting the width of the layers of the dielectric resonator element.

[0065] In some variations of the preferred embodiment, the specific radiation direction can be one of four different elevation angles, namely 0°, 30°, 60° and 90°.

[0066] According to a third aspect of the invention, a system for training heterogeneous graph convolutional networks for antenna design is provided, the system comprising one or more processors and a memory storing one or more programs configured to be executed by the one or more processors, the one or more programs including instructions for performing or facilitating the execution of the methods of the first aspect described above.

[0067] According to a fourth aspect of the invention, a system for designing cylindrical DRAs using Het-GCN is provided. The system includes one or more processors and a memory storing one or more programs. The one or more programs are configured to be executed by the one or more processors, and the one or more programs include instructions for performing or facilitating the performance of the methods described in the second aspect above.

[0068] According to a fifth aspect of the invention, a non-volatile computer-readable storage medium is provided, which stores one or more programs executed by one or more processors, the one or more programs including instructions for performing or facilitating the performance of the method of the first aspect or the method of the second aspect described above.

[0069] Other features and aspects of the invention will become apparent from the detailed description and accompanying drawings. Any feature described herein in connection with one aspect or embodiment may be used in combination with other features described herein in connection with any other aspect or embodiment, as appropriate and suitable. Attached Figure Description

[0070] Exemplary embodiments of the present invention will now be described with reference to the accompanying drawings, wherein:

[0071] Figure 1a and Figure 1b A top view of a cylindrical dielectric resonator antenna according to an embodiment of the present invention is shown.

[0072] Figure 1b It shows Figure 1a A cross-sectional view of a cylindrical dielectric resonator antenna.

[0073] Figure 2 Antenna pattern modeling according to an embodiment of the present invention is shown.

[0074] Figure 3 The structure of a Het-GCN model according to an embodiment of the present invention is shown.

[0075] Figure 4 A flowchart of a design method according to an embodiment of the present invention is shown.

[0076] Figure 5aThe comparison of NMSE values ​​for each model is shown for different dataset sizes.

[0077] Figure 5b This shows a comparison of the relevance values ​​of each model for different dataset sizes.

[0078] Figure 6 This shows an example of batch gradient descent with a batch size of k. In each iteration i, k particles {p} are updated. i1 ,p i2 ,…,p ik}

[0079] Figure 7 The calculation of the cost function for radiation pattern optimization is shown.

[0080] Figure 8 The number of iterations in the four optimization processes is shown.

[0081] Figures 9a to 9d The design variable h is displayed respectively. p Reflection coefficients at 0°, 30°, 60° and 90°.

[0082] Figure 10 An example single unit is shown for 3D printing to obtain an effective media material.

[0083] Figures 11a-11d The optimized results of dielectric constant distribution for the four antennas at four different elevation angles (0°, 30°, 60° and 90°) are presented respectively.

[0084] Figure 11e-11h The equivalent 3D printed model structure of the four antennas optimized at four different elevation angles (0°, 30°, 60° and 90°) is shown.

[0085] Figure 11i-11l The results show the optimized reflection coefficients of the four antennas at four different elevation angles (0°, 30°, 60° and 90°).

[0086] Figure 11m-11p The optimized results of the 5.8 GHz frequency plane radiation pattern of four antennas at four different elevation angles (0°, 30°, 60° and 90°) are shown, including simulation results and Het-GCN prediction results.

[0087] Figure 12 An example of a 3D-printed model of a 30° antenna is shown.

[0088] Figure 13a and 13b Examples of top-view and perspective views of an antenna at 30° are shown respectively.

[0089] Figure 13c and 13d Examples of top-view and perspective views of a 60° antenna are shown.

[0090] Figure 14a and 14b The reflection coefficients (Si) of the fabricated 30° and 60° antennas are shown respectively. 11 Measurement results.

[0091] Figure 14c and 14d The radiation pattern measurements of the fabricated 30° and 60° antennas in the xz plane at 5.8 GHz are shown.

[0092] Figure 14e and 14f The results of gain measurements of the fabricated 30° and 60° antennas in the direction of maximum radiation are shown.

[0093] Figure 14g and 14h The efficiency measurement results of the fabricated 30° antenna and 60° antenna are shown respectively.

[0094] Before explaining any embodiment of the invention in detail, it should be understood that the application of the invention is not limited to the details and arrangement of components of the embodiments described below or shown in the drawings. The invention can be practiced or performed in various other ways. Furthermore, it should be understood that the wording and terminology used herein are for descriptive purposes only and should not be considered limiting. Detailed Implementation

[0095] Artificial intelligence (AI) has had a significant impact on the engineering field as it continues to develop. Besides traditional deep learning methods, graph neural networks (GNNs) are also a powerful AI approach. A graph is a data structure capable of describing non-Euclidean data. Structural design problems often involve both Euclidean and non-Euclidean data. Therefore, GNNs have become a powerful tool for engineers to efficiently find better solutions. This disclosure proposes a dual-branch heterogeneous graph convolutional network (Het-GCN or HGCN) for handling complex and computationally intensive antenna designs. The model can directly output the radiation pattern and reflection coefficient of a given antenna structure. Each prediction takes only milliseconds. Optimization is achieved by leveraging the differentiability of neural networks. After modeling the antenna configuration as a graph, the antenna is optimized using gradient descent. Based on Het-GCN, four cylindrical dielectric resonator antennas with different dielectric constant distributions were synthesized. These four antennas achieved the expected radiation pattern performance in specific directions (0°, 30°, 60°, and 90°).

[0096] The following will describe some embodiments of the present invention in detail with reference to the accompanying drawings.

[0097] Deep Learning-Based Synthesis of Directional Cylindrical Dielectric Resonator Antennas

[0098] In recent years, AI has received increasing attention in antenna design. AI can use basic mathematical tools and parallel processing to handle complex problems, thereby reducing the computational burden of simulation and greatly simplifying antenna design. Machine learning (ML) is a branch of AI[6] and is a promising solution to high computational cost problems, and has attracted widespread attention in the field of electromagnetics[1][2]. Currently, many typical ML algorithms have been used for electromagnetic (EM) problems. For example, population-based metaheuristic optimization methods, such as genetic algorithms

[12] -

[14] , have been widely used in antenna optimization to replace manual adjustment. This method identifies the global optimum by evaluating previous solutions and generating new optimal solutions. However, this method is computationally expensive and therefore time-consuming. To solve this problem, researchers have proposed the surrogate-assisted evolutionary algorithm (SAEA) optimization method

[15] -

[17] as a trade-off between efficiency and accuracy. SAEA combines machine learning prediction models with evolutionary algorithms to achieve optimization goals. It uses a surrogate model with low accuracy but high computational efficiency to guide the optimization process. In contrast, Kriging interpolation

[22] and radial basis function (RBF)

[23] can be trained to obtain more accurate models, directly infer electromagnetic parameters, and improve efficiency in dealing with nonlinear problems. Other widely used machine learning algorithms include support vector machine (SVM)[3], artificial neural network (ANN)[5] and autoencoder[4]. In recent years, these high-precision models, combined with EM simulation, have been applied to antenna design to achieve more efficient and reliable optimization

[18] -

[21] .

[0099] Machine learning is fast to train, but not suitable for complex problems. To address this limitation, deep learning (DL) was subsequently developed to handle complex problems. It requires more datasets and training parameters to obtain a solution. Generative adversarial networks (GANs) [7], recurrent neural networks (RNNs) [8], convolutional neural networks (CNNs) [9], reinforcement learning

[11] , and transfer learning

[10] are popular learning methods in deep learning. Based on these deep learning algorithms, various methods have also been explored in the field of antenna design. For example, a DL-FDTD method combining RNN or CNN modules has been proposed as an enhanced version of the finite difference time domain (FDTD) technique to effectively solve forward scattering problems such as electromagnetic calculation and parameter prediction

[26] . In

[24] and

[25] , artificial neural networks (ANNs) have been extended to multi-branch structures to solve multi-objective optimization problems. With the help of deep learning, the number of simulations in complex optimization processes can be significantly reduced, thereby improving efficiency. Sometimes simulations are not even necessary. Once the AI ​​model learns the relationship between antenna geometry parameters and corresponding electromagnetic properties from the collected dataset, antenna performance can be predicted directly. Furthermore, the probability of finding a optimal solution increases as more trials can be conducted automatically.

[0100] Existing models may encounter limitations when handling non-Euclidean structural data, thus restricting their generalization ability. Most existing methods treat antenna data as sequential data (time domain) or Euclidean datasets (spatial domain). Whether the data is sequential or Euclidean depends on how the researchers construct the database. However, some antenna parameters are independent of each other, and treating them as sequential or Euclidean data can be controversial. Take a rectangular patch antenna as an example: its length and width are independent and time-independent. However, when they are sequentially grouped, temporal relationships are inevitably introduced. Length and width parameters are spatially independent, but grouping them in Euclidean data format introduces spatial relationships between them to some extent. Although existing methods can provide accurate predictions, their solutions are like "black boxes" due to limited interpretability. When the antenna configuration is slightly changed (e.g., adding components), the pre-trained model will fail and needs to be retrained.

[0101] By introducing graph neural networks (GNNs), interpretability and generalization ability can be improved. Early research on GNNs was inspired by Sperduti and Starita

[27] , who applied neural networks to directed acyclic graphs. The concept of GNNs was first systematically discussed in

[28] and further developed in

[29] and

[30] . Subsequently, convolutional graph neural networks (ConvGNNs)

[31] extended convolution operations from Euclidean data to non-Euclidean data. It uses multiple graph convolutional layers to extract high-level nodes and edge segmentation in the graph, thereby constructing complex GNN models. Integrating convolution operations into graph neural networks can improve interpretability and modeling ability, and help extract spatial features from non-Euclidean data.

[0102] In complex structure design, Het-GCN

[32] is an extension of ConvGNN. Unlike ConvGNN, which only handles simple homogeneous graphs, Het-GCN can handle heterogeneous graphs containing multiple node types. This method has been successfully applied to molecular structure prediction and generation

[33] ,

[34] and circuit layout design

[35] . Its important advantage is that it can incorporate prior knowledge into the input, and make the neural network learn more meaningful information through information transmission in the graph. Therefore, for structural optimization problems, the performance of Het-GCN is theoretically better than that of traditional neural networks. Although graph learning models are flexible in dealing with physical structure problems, they have not been applied to antenna design to date. In this disclosure, the Het-GCN method is deployed to design antennas.

[0103] The dielectric resonator antenna (DRA) proposed by SALong et al. in 1983

[36] generates radiation by resonating electromagnetic waves in a dielectric constant medium. It has the advantages of small size, light weight, low loss and easy excitation. Since the DRA is a three-dimensional structure, it has a higher degree of design freedom compared with wire and microstrip antennas. This provides greater design flexibility and adaptability to meet the specific needs of diverse applications of 5G communication systems. Some embodiments of the present invention will use the Het-GCN method to design directional DRAs. Directional DRAs can be obtained by placing a monopole inside the DRA

[13]

[38] . In some embodiments, alternative methods to achieve directivity by modifying the dielectric constant distribution through multilayer structure (ML) are studied.

[0104] The objective of certain embodiments of this invention is to design or synthesize a cylindrical DRA that radiates in a specific direction. In some embodiments of the invention, the DRA is divided into multiple unit blocks, and the objective is achieved by manipulating the dielectric constant distribution within the dielectric resonator blocks. The Het-GCN method can accelerate the design process of this complex structure with highly complex antenna parameters. A graph representation is constructed as the input to the Het-GCN. The output of the Het-GCN model contains two branches for predicting the reflection coefficient and radiation pattern. Experimental results show that by training the Het-GCN model with 3000 data samples, excellent prediction performance can be obtained on the validation set, with a normalized mean square error (NMSE) of only 0.06602 and a Pearson correlation coefficient (PCC or The efficiency is as high as 0.95308. In this disclosure, the Het-GCN model is compared with existing machine learning models to demonstrate its superiority. With the help of Het-GCN, four directional antennas radiating at different E-plane elevation angles (θ = 0°, 30°, 60°, 90°) can be efficiently synthesized.

[0105] I. Antenna Configuration

[0106] According to some embodiments of the invention, the design of a directional antenna begins with a broadband, low-profile omnidirectional multi-ring cylindrical DRA

[37] . Figure 1a and Figure 1b The initial configuration (top view and cross-sectional view) of a cylindrical DRA 100 according to an embodiment of the present invention is shown. The cylindrical DRA 100 includes a ground plane 10, a cylindrical dielectric resonator element 20 operatively coupled to the ground plane 10, and a feed probe 30 operatively coupled to the dielectric resonator element 20. The ground plane 10 may be an aluminum ground, and the feed probe 30 may be a centrally fed coaxial probe. The dielectric resonator element 20 may include a first number (N) of layers with different dielectric constants arranged outwards from the feed probe 30, and divided into a second number (M) segments along an angular direction, such that the dielectric resonator element 20 consists of N×M dielectric resonator blocks. For example, the dielectric resonator element 20 has 7 layers with different dielectric constants and a fixed height (h) of 9 mm. It is angularly divided into 16 sections. The antenna is centrally fed through the coaxial probe 30, with a probe height of h. p By changing the dielectric constant distribution and the probe height h p and ring width w d (d = 1, 2, ..., 7), allowing for corresponding adjustments to the antenna characteristics. For example, the cylindrical DRA 100 has dimensions h = 9 mm and 2R... p =1.27mm, R g =44mm, t=2mm. h p ∈[6.0mm, 7.0mm]. When d = 1, 2, 3, wd ∈[0mm,5mm], and when d=4,5,6,7, w d ∈[5mm,15mm].

[0107] II. Design Methodology of HET-GCN

[0108] Antenna structures can be modeled as graph data. Antennas are typically composed of different parts, which can be represented as a heterogeneous graph, with each component of the antenna acting as a node in the graph. Therefore, a heterogeneous graph convolutional neural network (Het-GCN) can be constructed to learn from the antenna graph and interpret it as the interactions between nodes corresponding to the propagation of electromagnetic waves between adjacent parts.

[0109] According to some embodiments of the present invention, the geometric parameters and dielectric constant of each antenna section are considered simultaneously to improve optimization flexibility. Het-GCN learns graph information and utilizes a message passing module to extract useful information from the graph.

[0110] A. Antenna diagram modeling

[0111] To input antenna data into the Het-GCN, each data sample is reconstructed as a graph representation. The graph consists of two main elements: vertices (or nodes) represented by V, and edges represented by E. Therefore, the graph can be represented as follows: An edge is a connection between nodes. Each node is defined by v. i ∈V represents. From v j Pointing to v i The edge can be represented as e ij =(v i ,v j If node v has an edge (v, u), then u is considered a neighbor of v, denoted as N(v). The graph may contain node attributes X ∈ R. n×d With edge attribute X e ∈R m×c Let n and m be the number of nodes and edges, respectively, and d and c be the dimension of node attributes and the dimension of edge attributes, respectively. The feature vector of node v is represented as x. v ∈R d The eigenvectors of edge e = (v, u) are represented as

[0112] Based on the physical relationships between different antenna components, an antenna can be modeled as an undirected heterogeneous graph, that is, a graph containing nodes of different categories with undirected edges.

[0113] like Figure 2 As shown, the antenna components (such as the previously divided dielectric resonator block (DR block) and coaxial probe) can be considered as independent nodes in the figure. v ,φ v ,h v and These represent the width, angle, height, and dielectric constant of the DR block of node v, respectively, and together constitute the node attributes. ΔR r,(v,u) ,Δφ r,(v,u) and Δh r,(v,u) The relative positions of two nodes v and u in three directions within the cylindrical coordinate system together constitute the edge properties. It is worth noting that the aluminum grounding is not included in the graphical representation because it is fixed and will not change during the automated design process. Based on the geometric parameters and material properties of the antenna assembly, the property x of node v in the Het-GCN model... v It can be constructed as follows:

[0114]

[0115] Among them, w v ,φ v h v and These represent the width, angle, height, and effective dielectric constant of node v, respectively. Nodes in the antenna diagram can be classified as DR blocks or probes. The node angle of a feed probe is zero, while the effective dielectric constant ε... eff Set it to 1.

[0116] In the antenna diagram representation, the connections between nodes follow a physical structure, meaning edges exist only between adjacent components. The edge attribute with relation r between nodes v and u is defined as...

[0117] In some embodiments, the DRA is divided into 7 × 16 = 112 DR blocks. Including the probes, the diagram contains a total of 112 + 1 = 113 nodes. Clearly, there are two types of nodes in the antenna diagram (x... v∈DR ,x v∈probe ) and two types of undirected edges (x r∈(DR,DR) ,x r∈(probe,DR) A set of node attributes X∈R 113×4 With a set of edge attributes X e ∈R 224×3 Together they form graph information. This modeling approach offers flexibility for antenna design because it supports a variety of geometries and properties, while allowing both Euclidean and non-Euclidean connections.

[0118] B.Het-GCN

[0119] Graph-level task. Predicting the electromagnetic characteristics of an antenna is a graph-level task. Let... A set of images, in which The label is defined as y p The goal of a graph-level task is to predict the properties of unseen graphs, specifically the electromagnetic response of antenna graphs.

[0120] Het-GCN model. Figure 3 A Het-GCN structure (hereinafter referred to as "the proposed model") according to an embodiment of the present invention is shown. Unlike conventional GCNs, Het-GCN can handle heterogeneous graph data. In Het-GCN, different types of relations are mapped by a specified convolution function. Weights are not shared between different relations. Het-GCN can handle different types of relations by specific convolution functions, such as graph convolution

[39] and SAGE convolution

[40] . In this model, all types of relations use the following graph convolution function

[41] :

[0121]

[0122] Where σ(·) is the activation function, where and W (l) Let e ​​represent the hidden state and weight matrix of the l-th layer, respectively. In equation (2), e ji These are predefined weights from node j to node i. (Using c) r,ji Normalization, in which and Let c be the node degree, which represents the number of neighbors of node i. r,ji Used to normalize the contributions of neighbor nodes. e for all edges ji Initialized to 1, ReLU(·) = max(0,·) is used as σ(·) in this model. Overall, this equation describes the hidden state of node i in layer l of the Het-GCN model. The calculation process.

[0123] After convolution of the graph using Equation (2), the attributes of each node are updated. To further obtain the graph-level representation (GLR), the features of all nodes in the convolved graph are processed. The readout function R(·) in Equation (4) is applied. This function summarizes the entire graph by integrating node features. After the readout function, two independent multilayer perceptron (MLP) branches are used. Each branch contains a hidden layer and operates on the same GLR. These MLP branches serve as predictors for two tasks: one predicts the radiation pattern and the other predicts the reflectance coefficient.

[0124]

[0125] C. Forward and Reverse Processes of Antenna Design

[0126] A flowchart of a design method according to an embodiment of the present invention is shown below. Figure 4As shown, the automatic antenna design process is divided into two parts: the forward problem and the inverse problem. In the forward problem, the goal is to obtain the electromagnetic characteristics of a given antenna structure. The inverse problem is to find the antenna configuration and numerical parameter set that satisfy specific criteria. Antenna parameters are randomly generated during the forward process. First, tools such as ANSYS HFSS are used to obtain the corresponding radiation pattern RP and reflection coefficient S. 11 The above data constitutes the training dataset D for training Het-GCN, and its weights are initialized to random values ​​ω. i The model's input is the antenna diagram. Including the dielectric constant ε of each node eff , ring width w d (or relative radius) and probe height h p Information such as...

[0127] In the reverse engineering process, a set of reference antenna parameters close to the ideal requirements is provided based on human experience. This reference antenna serves as the starting point for the optimization algorithm. After random initialization near the reference antenna, the optimal antenna structure is found iteratively through a mini-batch gradient descent algorithm.

[0128] III. Dataset Construction and Model Training

[0129] A. Data Acquisition

[0130] Dataset D was created in the frequency range of 3.5 GHz to 10.5 GHz through extensive simulations in ANSYS HFSS. Each simulation took approximately 8 minutes. After antenna pattern modeling, each sample in the dataset was... Let i = 1, 2, ..., N, where i represents the index of the sample and N is the size of the dataset D. In one example of model training, N equals 3000.

[0131] B. Model Training and Evaluation

[0132] As mentioned earlier, the Het-GCN model takes the constructed antenna pattern as input and generates the output through two branches. For example, the RP branch generates a 1×74 vector at a frequency of 5.8 GHz, containing 37 co-polarization values ​​and 37 cross-polarization values ​​in the xz plane. 11 The branches generate a total of 71 output values, each corresponding to a frequency point uniformly distributed within the frequency range of 3.5 GHz to 10.5 GHz. The model is trained under the guidance of the average loss of the two branches. The loss of each branch is calculated using a loss function. The calculated function is the Normalized Mean Squared Error (NMSE), as shown in Equation (6). This loss function quantifies the difference between the predicted and actual values ​​and ensures consistency across different scales through normalization. The performance of Het-GCN is assessed using an additional metric: the Pearson correlation coefficient. The evaluation is performed, and its calculation formula is shown in Equation (7). The Pearson correlation coefficient measures the linear relationship between the predicted and actual values, reflecting the model's ability to capture patterns and trends in the data.

[0133]

[0134] Where y and These represent the actual value and the predicted result, respectively.

[0135] The hyperparameters of the Het-GCN model are shown in Table 1. During model training, the number of Het-GCN layers was set to 2 to balance computational complexity and accuracy. The maximum number of training iterations was set to 50, and the batch size was 16.

[0136] Table 1. Parameters of Het-GCN

[0137]

[0138] The Het-GCN model was trained using 3000 data samples, with the remaining 1000 used for validation. Performance comparisons with other commonly used AI algorithms are shown in Table 2. The proposed Het-GCN method achieves the lowest NMSE value of 0.06602, indicating excellent performance. In terms of Pearson correlation coefficient, its value of 0.9508 outperforms other methods. However, it is worth noting that graph data requires more memory to accommodate additional information, such as node and edge features. Inter-node interactions also require more weights than traditional convolutional neural networks, leading to a training time of 15862.29 seconds. However, since the model only needs to be trained once for subsequent applications, the training time of the Het-GCN model is considered acceptable.

[0139] Table 2 Model performance on the validation set

[0140]

[0141] Comparison of model performance under different data sizes, such as Figure 5a and Figure 5b As shown, all models were evaluated on the same validation set. The accuracy of the Het-GCN model improves with increasing dataset size. However, the improvement becomes insignificant when the dataset size exceeds 3000. Compared to other algorithms, the Het-GCN model requires more training data because it has more trainable parameters. When the dataset size is greater than 1000, the Het-GCN method consistently outperforms all other methods in terms of accuracy. In short, the Het-GCN model requires relatively more data to work effectively and provide more reliable results.

[0142] IV. Synthesis of Directional Radiation Cylindrical Dielectric Resonator Antennas

[0143] A. Optimization process

[0144] The optimization process aims to synthesize four antennas with specific radiation directions, located at four different elevation angles: 0°, 30°, 60°, and 90°. To achieve this, adjustments to the effective dielectric constant distribution ε are considered. eff To control changes in the radiation pattern, and by adjusting the height h p Achieve impedance matching. ε eff This has a significant impact on the corresponding electromagnetic behavior. Here, the effective dielectric constant is set to seven discrete values, ε... eff ∈{1,2.5,4,5.5,7,8.5,10}. h p The height can be adjusted from 6.0mm to 7.0mm. Initially, for all d, ΔR d All are fixed at 5mm. When ε eff When the degrees of freedom are insufficient to find a solution, consider adjusting ΔR. d When d = 1, 2, 3, ΔR d The value range is [0mm, 5mm]. When d = 4, 5, 6, 7, ΔR d The value range is [5mm, 15mm].

[0145] A well-trained Het-GCN model can be used to optimize complex antenna structures. For this purpose, a batch gradient descent algorithm is employed. Figure 6 This demonstrates an example workflow for the batch gradient descent algorithm, where the batch size is k. Each iteration updates k samples simultaneously. The best k samples are then evaluated using simulation, and the optimal design is selected based on the simulation results. In this scenario, k is set to 10.

[0146] The goal of the design optimization is to enable the antenna to radiate in specified directions (0°, 30°, 60°, and 90°) at a frequency of 5.8 GHz, while simultaneously meeting the return loss requirements. In other words, to synthesize an antenna with satisfactory performance at 5.8 GHz, the return loss S... 11 It must be less than -10dB. 11 The -10dB band should cover the frequency range of 5.4GHz to 6.2GHz. During the optimization process, the L2 norm is used to measure the ideal S. 11 With the current S 11 The differences between them. The backwave stage is adjusted through the expected main beam angle, the backwave stage, and the cross-polarization stage. The cost function aimed at minimizing during optimization is shown below:

[0147]

[0148] in

[0149]

[0150] θ0 and θ0 represent the predicted and expected elevation directions of the main beam, respectively. and These represent the radiation patterns of co-polarized and cross-polarized systems, respectively. For the xz plane, And θ∈{-180°,180°}. Upper bound G upper and the lower bound G lower like Figure 7 As shown. The boundary defines the acceptable range of co-polarization angles. Co-polarization angles should lie between the upper and lower bounds. α1 and α2 are S 11 The cost value weights of the radiation pattern.

[0151] B. Optimization Results

[0152] Optimization iterative process such as Figure 8 As shown. Among all synthetic antennas, the 0-degree lateral antenna requires the longest computation time for convergence. This is due to physical limitations. The feed coaxial probe radiates omnidirectionally in a manner similar to a monopole antenna. However, the feed peak radiation direction changes from the xy plane to an elevation direction at a certain angle to that plane. Therefore, the optimization of the 0-degree lateral antenna is particularly difficult because it is hard to control the radiation direction in the lateral direction. The S of the four antennas... 11 The NMSE values ​​of the radiation pattern outputs are mostly below 0.1. Furthermore, the Pearson correlation coefficient is close to 1, indicating a strong correlation between the predicted and simulated values. These results demonstrate the effectiveness and promising future of the Het-GCN model. Although the NMSE is slightly higher for the 90-degree antenna, indicating a larger difference between the predicted and simulated values, the high correlation still suggests a reliable trend match.

[0153] The application of the Het-GCN model significantly improves the efficiency of the optimization process. With the Het-GCN model, each optimization round takes approximately 2 minutes, while the same optimization without an AI model would take thousands of minutes. The relevant results are shown in Table 3. This efficiency enables broader exploration and iterative experimentation, reduces the risk of getting trapped in local optima during optimization, and increases the probability of finding the global optimum.

[0154] Table 3 Comparison of Model Performance and Solid State Simulation Results

[0155]

[0156] Figures 11a-11p The optimization and simulation results for four antennas are presented. The dielectric constant distribution (ε) of the four antennas is also shown. eff )like Figure 11a–11d is shown. It is clear from these figures that the asymmetrical and irregular dielectric constant distribution pattern is quite difficult to adjust manually. The probe heights of the four antennas were optimized to 7mm, 6.7mm, 6.5mm, and 6.0mm, respectively. The ring width w d (Or the ring radius ΔR) is fixed at 5mm for all d values ​​for 0°, 30°, and 60° antennas. The total radius of these three antennas is 35mm. However, for the 90° antenna, the w of the 7 rings... d,90度 The values ​​were optimized to [0mm, 0mm, 0mm, 6mm, 6mm, 12mm, 13mm], with a total radius of 37mm. The change in loop radius indicates that graphical data has greater versatility compared to sequential or Euclidean data. Figures 9a-9d The design variable h was studied. p The S corresponding to the four types of antennas 11 Results: The proposed optimization method ensures the maximum value of the reflection coefficient bandwidth.

[0157] In the manufacturing process, an effective dielectric constant can be achieved through the cubic single cell proposed in

[37] , such as Figure 10 As shown. According to Figure 10 The effective 3D printing model shown can be optimized to model the antenna as a 3D printed structure. With increasing wall thickness t... c By varying the wall thickness t of each dielectric unit, the effective dielectric constant of each unit can be achieved within the range of 0-10. c The ratio of t to the side length 'a' adjusts the effective dielectric constant. When the side length is fixed at 4mm, t c With ε eff The relationship is described as follows:

[0158] ε eff =0.55t c ε r -0.04ε r +1.3 (10)

[0159] To achieve different effective dielectric constant values, ε values ​​were used in the 3D printed models. r =5 and ε r Two materials with a ε = 10. According to Table 4, the ε for each material was calculated. eff The wall thickness t of the lower cubic unit block c Subsequently, a 3D printed model was constructed based on the corresponding physical model, such as... Figure 11e –11h is shown. Using ε r A material with a thickness of 5 helps avoid the risk of excessively thin walls. As an example, the final 30-degree 3D-printed antenna structure to be manufactured would look like this... Figure 12 As shown.

[0160] Table 4

[0161] Effective dielectric constant and corresponding wall thickness

[0162]

[0163] Simulated S 11 (including solid models and 3D printed models) and predicted S 11 like Figure 11i As shown in –11l. The electromagnetic characteristics of the optimized antenna remain stable after conversion to a 3D printed model. The radiation pattern on the xz plane is shown below. Figure 11m-11p As shown in the visualization, the Het-GCN model predictions agree well with the simulation results. The main radiating beams of each antenna are clearly visible. The optimization results meet the predefined requirements. However, due to the physical limitations discussed earlier, the cross-polarization pattern of the 0° antenna is slightly inferior. The slight shift in the main beam direction is acceptable because the RP prediction accuracy of Het-GCN is 10°. However, due to the aluminum grounding effect, the maximum gain of the 90° antenna, which should appear at 90° in the simulation, now appears at 70°. Nevertheless, the overall simulation pattern agrees well with the prediction pattern. The simulated peak gains of the 0°, 30°, 60°, and 90° antennas are 5.88 dBi, 10.13 dBi, 7.49 dBi, and 5.58 dBi, respectively. These peak gains indicate the maximum radiation concentration of each antenna in a specific direction.

[0164] C. Manufacturing and Measurement

[0165] 30° and 60° antenna prototypes were manufactured as proof of concept. Figures 13a-13d Showing top and perspective views of the manufacturing prototype, i.e. Figure 13a and 13b Top and perspective views of a 30-degree antenna. Figure 13c and 13d Top view and perspective view of a 60-degree antenna.

[0166] The 3D-printed structures of both antennas are 9 mm high and 35 mm in radius. To ensure easy alignment and separation of the printed DRA from the printing platform, a thin dielectric layer with a thickness of 0.3 mm and a radius of 35 mm was printed beneath the DRA. The 3D printer used in this study has a manufacturing tolerance of 0.1 mm and a resolution of 0.05 mm. Printing a single antenna takes approximately 5 hours, with a total material cost of less than $50 USD.

[0167] Measurement results and simulation results Figures 14a-14h A comparison was made. The results of solid-state model simulation, 3D printing simulation, and measurements of 30° and 60° antennas are as follows: Figure 14a and 14b As shown in the figure. The measured S11 The simulation results agree well with the 3D printed antenna model. Minor differences are due to experimental tolerances.

[0168] Simulation and measurement of radiation patterns of 3D printed models, as shown in the figure. Figure 14c and 14d As shown. Figure 14d and 14d The measurement results of the xz-plane radiation patterns of the fabricated 30-degree and 60-degree antennas at 5.8 GHz are shown. The figures clearly show that the measured co-polarized field is more than 20 dB stronger than its cross-polarized field. Figure 14e and 14f The actual gain measurements of the fabricated 30° and 60° antennas in the direction of maximum radiation are shown. The measured gain of the 30° antenna at 5.8 GHz is 8.8 dBi, while the gain of the 60° antenna reaches 8.14 dBi. Figure 14g and 14h As shown, both antennas maintain an efficiency of approximately 90% within the expected 5.8 GHz band. Overall, although there are some differences between the simulation and measurement results, the overall consistency is reasonable.

[0169] V. Conclusion

[0170] This study explores the synthesis of four cylindrical antennas using a robust graph convolutional network (Het-GCN). Het-GCN can be used for both forward simulation and automated reverse design. It facilitates the synthesis of antennas with specific performance requirements, such as radiation in a desired direction. A key advantage of Het-GCN compared to other AI models is its ability to capture more interactive information within the antenna structure, thus demonstrating greater accuracy. Het-GCN achieves a minimum NMSE loss of 0.06022 and a highest Pearson correlation coefficient of 0.95308. The flexible topology of Het-GCN allows for more flexible antenna design, enabling further transfer learning on other similar antenna types. This AI model effectively reduces simulation time while maintaining reasonable accuracy, particularly when designing multiple similar antennas. Using the Het-GCN model, four sets of directional antennas radiating in a half-elevation plane are efficiently generated. These antennas are divided into 7×16 dielectric resonator blocks. Directional radiation is achieved by adjusting the effective dielectric constant distribution within these blocks. The complex-shaped DRAs are fabricated using 3D printing technology. Although there are some discrepancies between the simulation results and the measurement results, the overall performance is consistent.

[0171] Features and modifications of some embodiments

[0172] Some embodiments of this invention implement four antennas with different radiation directions based on a robust graph convolutional network (Het-GCN). This model can be used for both forward simulation and reverse automated design to synthesize antennas with the desired performance (i.e., radiation direction). A key advantage of this model compared to other machine learning models is its ability to capture more interaction information within the antenna structure.

[0173] In some embodiments, the cylindrical DRA configuration may include additional numbers of dielectric resonator blocks.

[0174] In some embodiments, the effective dielectric constant may be formulated using other formulas.

[0175] In some embodiments, the dielectric constant and thickness of the material used may be changed to other values.

[0176] In some embodiments, the radiation direction of the cylindrical DRA can be other values.

[0177] In some embodiments, the operating frequency can be changed to other frequency bands.

[0178] Example functions and applications of some embodiments

[0179] Some embodiments of the present invention can flexibly realize high-gain beams with specific radiation directions across almost the entire upper half of space, suitable for complex communication angles. Therefore, antennas designed according to some embodiments of the present invention can be used for radar and various wireless communications.

[0180] Exemplary advantages of certain embodiments of the present invention

[0181] Compared to existing designs, directional dielectric resonator antennas designed or synthesized using deep graph learning models according to certain embodiments of the present invention exhibit higher efficiency and gain within the desired frequency band.

[0182] According to some embodiments of the present invention, by means of graph learning technology, design flexibility is significantly improved, and radiation of the entire upper space can be achieved under the same basic configuration.

[0183] Compared with existing design methods based on artificial intelligence, some embodiments of the present invention employ design methods with higher accuracy and generalization ability.

[0184] Those skilled in the art will understand that various variations and / or modifications can be made to the embodiments described and / or illustrated in this invention to provide other embodiments of the invention. Therefore, the embodiments described and / or illustrated in this invention should be considered exemplary in all respects and not restrictive. Optional features of certain embodiments of the invention are provided in the abstract and description. Certain embodiments of the invention may include one or more of these optional features. Certain embodiments of the invention may lack one or more of these optional features.

Claims

1. A computer implementation method for heterogeneous graph convolutional networks for antenna design, comprising the following steps: The antenna is modeled as graph data, which includes a heterogeneous graph representing the different components of the antenna; A dataset of the antenna's radiation pattern and reflection coefficients is generated based on the graph data; as well as The heterogeneous graph convolutional network is trained using the dataset.

2. The computer implementation method according to claim 1, wherein the antenna is a cylindrical dielectric resonator antenna, the antenna comprising: Grounding plane; A dielectric resonator element operatively coupled to the ground plane; as well as A feed probe operatively coupled to the dielectric resonator element.

3. The computer implementation method according to claim 2, wherein the grounding plane includes aluminum grounding; the dielectric resonator element includes N layers with different dielectric constants arranged starting from the feed probe and angularly divided into M parts, such that the dielectric resonator element is composed of N×M dielectric resonator blocks.

4. The computer implementation method according to claim 3, wherein the dielectric resonator antenna is centrally fed by the feed probe, wherein the feed probe has a height h p .

5. The computer implementation method according to claim 4, wherein the dielectric constant distribution within the dielectric resonator block and the height h of the feed probe are adjusted. p and the width w of the layer in the dielectric resonant element. d This is used to adjust the antenna characteristics of the dielectric resonator antenna.

6. The computer implementation method according to claim 3, wherein the step of modeling the antenna as the graph data further includes randomly generating antenna parameters; the antenna parameters include dielectric constant distribution, the height h of the feed probe, etc. p and the width w of the layer of the dielectric resonator element. d .

7. The computer implementation method according to claim 1, wherein the graph data includes node attributes of the dielectric resonator antenna and edge attributes of interactions between nodes; each component is a node.

8. The computer implementation method according to claim 7, wherein the components of the dielectric resonant element include a dielectric resonator block and a feed probe.

9. The computer implementation method of claim 8, wherein the node attributes are constructed based on the geometric parameters and material properties of the components of the dielectric resonator antenna.

10. The computer implementation method of claim 7, wherein the interaction between the nodes includes the propagation of electromagnetic waves between adjacent nodes.

11. The computer implementation method of claim 1, wherein the heterogeneous graph convolutional network is designed to perform a convolution function on the graph data.

12. The computer implementation method of claim 11, wherein in the heterogeneous graph convolutional network, different types of relations are assigned by a specified convolution function, and the different types of relations do not share weights.

13. The computer implementation method according to claim 12, wherein in the heterogeneous graph convolutional network, a readout function is run on all node features in the convolutional graph to obtain a graph-level representation.

14. The computer implementation method of claim 13, wherein the heterogeneous graph convolutional network predicts the radiation pattern and the reflection coefficient by running two independent multilayer perceptron branches on the graph representation, respectively.

15. A computer implementation method for designing a cylindrical dielectric resonator antenna using a heterogeneous graph convolutional network trained according to claim 1, comprising the following steps: The desired antenna structure for the dielectric resonator antenna with a specific radiation direction is obtained using the trained heterogeneous graph convolutional network.

16. The computer implementation method according to claim 15, wherein the step of obtaining the desired antenna structure includes: Provide the trained heterogeneous graph convolutional network with the radiation pattern and reflection coefficient of a reference antenna structure; Random initialization is performed within the neighborhood of the reference antenna structure. as well as The optimal antenna structure is obtained by using mini-batch gradient descent iterations.

17. The computer implementation method according to claim 16, wherein, The iteration to obtain the optimal antenna structure includes adjusting the dielectric constant distribution within the dielectric resonator block to control the radiation pattern variation, and adjusting the height of the feed probe to achieve impedance matching.

18. The computer implementation method according to claim 17, wherein, The iteration to obtain the optimal antenna structure also includes adjusting the width of the layers of the dielectric resonator element.

19. The computer implementation method according to claim 15, wherein the specific radiation direction is one of four different elevation angles, namely 0°, 30°, 60° and 90°.

20. A system for training heterogeneous graph convolutional networks for antenna design, comprising: One or more processors; as well as Memory that stores one or more programs; The one or more programs are configured to be executed by the one or more processors, and the one or more programs include instructions to perform or facilitate the execution of the method according to claim 1.

21. A system for designing a cylindrical dielectric resonator antenna using heterogeneous graph convolutional networks, comprising: One or more processors; as well as Memory that stores one or more programs; The one or more programs are configured to be executed by the one or more processors, and the one or more programs include instructions for performing or facilitating the performance of the method according to claim 15.

22. A non-volatile computer-readable storage medium storing one or more programs; said one or more programs being configured to be executed by one or more processors, said one or more programs including instructions for performing or facilitating the performance of the method according to claim 1.

23. A non-volatile computer-readable storage medium storing one or more programs configured to be executed by one or more processors, the one or more programs including instructions for performing or facilitating the performance of the method of claim 15.

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