Enhanced Antenna Design through Hyper parameter Optimization of Diverse Machine Learning Models Using Bayesian Optimization

Enhanced Antenna Design through Hyper parameter Optimization of Diverse Machine Learning Models Using Bayesian Optimization | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Enhanced Antenna Design through Hyper parameter Optimization of Diverse Machine Learning Models Using Bayesian Optimization Chung-Hao Huang, Amir Ali, Chang-Chen Hsu, Han-Hsing Tsao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5453365/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This work investigates the use of machine learning (ML) models for microstrip patch antenna design optimization with Bayesian optimization. Based on datasets produced by CST Microwave Studio 2023 simulations, key antenna parameters, including resonance frequency, bandwidth, and return loss, were first predicted using Support Vector Regressor (SVR), k-Nearest Neighbor (KNN), and Gradient Boosting Regressor (GBR) models. With slot distance, patch length, and patch width as target parameters, pre-processing was used to transform CST output into structured input-output pairs in order to get the dataset ready for machine learning training. Extending this first method, we assessed ten machine learning models, each optimized with Bayesian hyperparameter tuning: SVR, KNN, GBR, Random Forest, XGBoost, Decision Tree, Stochastic Gradient Descent, Artificial Neural Network, Gaussian Process Regressor, and Linear Regression. By fine-tuning parameters like max_depth, n_estimator, Bayesian optimization greatly improved complicated models, lowering Mean Squared Error (MSE) and Root Mean Squared Error (RMSE) while raising R2 scores. After optimization, the Random Forest and XGBoost models produced the best predicted accuracy, according to comparative data. To further enable real-time model training, testing, and performance visualization, a unique graphical user interface (GUI) was created, offering a useful tool for interactive antenna optimization. This system provides a solid basis for data-driven improvements in advanced engineering applications by showcasing how ML models combined with Bayesian tuning can successfully handle challenging antenna design problems. Ai Based Antenna Optimization Bayesian Optimization Hyperparameter Tuning Ml Models Antenna Design Gui Interface Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1. Introduction Antennae design process is a complex problem when it comes to design it by using a simulation software which takes a long time while doing the simulation and running again and again to get the desired results. In the wireless business, strong mobile networks are crucial, but networks of the future will be even more difficult. For long-distance communications, these networks need antennas with a large bandwidth and high gain. These communication techniques are suitable for patch antenna arrays. Therefore, designing a high-performance antenna becomes a significant problem that needs to be resolved [ 1 ]. It is anticipated that sixth-generation (6G) mobile communication networks will feature a wide bandwidth, dense infrastructure, huge antennas, affordable technology, a variety of positioning techniques, and improved intelligence. These developments present 6G's practical design with both fresh opportunities and challenges. However, with 6G, it becomes very difficult to obtain channel state information (CSI) in real time for every wireless link. The estimated channels or beams between base station (BS) and user equipment (UE), for example, would be among the many data sources in 6G that would provide high-quality location-tagged channel data, allowing for a better understanding of the local wireless environment. A prospective paradigm shift from the traditional environment-unaware communications to the CSI acquisition challenge can be achieved by taking use of this new possibility. The microstrip patch antennas are essentially considered in the advancement of the latest communication mechanisms in contrast to the conventional type because they offer the advantage of being low profile along with simple or inexpensive manufacturing procedures. Microstrip is probably the most successful and revolutionary antenna technology ever. Its success comes from very well-known advantages. And it also has some limitations, the most well-known being the inherent narrow bandwidth, narrow impedance, low axial ratio (AR), small gain, lower power handling capacity and low efficiency [ 3 ]. One of the most widely used antennas in radar applications is the microstrip Ultra-Wideband radar (UWB) antenna. It has garnered a lot of interest due to its benefits, which include simplicity in construction, ease of manufacture, and ease of integration with microwave integrated circuits. A microstrip antenna's geometric shape consists of a ground plane on one side and a radiating element on the dielectric substrate. The most popular type of microstrip patch antenna is the rectangular element, while there are other types as well, such as the triangular, semicircular, circular, and square radiating elements [ 4 ]. This paper use machine learning models to predict the required parameters of the rectangular microstrip patch antenna and use the Bayesian optimizer for the optimization of the hyperparameters of each of the ML model used. We are using 10 ML models, Support Vector Regressor (SVR), Random Forest (RF), XGBoost Regressor (XGB), K-Nearest Neighbors (KNN), Decision Tree Regressor (DT), Gradient Boosting Regressor (GBR), Stochastic Gradient Descent (SGD), Artificial Neural Network (ANN/MLP), Gaussian Process Regressor (GPR), Linear Regressor (Ridge Regressor). ML models predict future inputs based on probability aspects and learn nonlinear qualities from the datasets [ 5 ]. Bayesian optimization is used for the tuning of the hyperparameters of all three ML models according to our datasets we created, to make the performance of the models better. Hyperparameter tuning is a type of optimization in which the black-box or optimization's objective function is unknown. It is not possible to use conventional optimization methods like gradient descent or the Newton method. An excellent approach for resolving this type of optimization issue is Bayesian optimization. Using the Bayesian formula, it obtains posterior information on the function distribution by combining sample data with previous knowledge about the unknown function [ 6 ]. The factors that control the learning process and establish the final parameters of the models are known as hyperparameters of a learning algorithm. The goal of hyperparameter optimization is to quickly determine optimal hyperparameter settings to obtain good results from data [ 7 ]. ADS, HFSS, CST, and IE3D are the most popular commercial CEM programs for antenna design and simulation. Additionally, these software products are devoid of a number of crucial capabilities. For example, IE3D cannot simulate structures with finite features, ADS cannot model 3D structures, and the execution time of HFSS and CST is significant and grows with the size of the antenna structure. As will be covered in more detail later in this work, ML has been extensively examined as a complementary technique to CEM in the design and optimization of different kinds of antennas for a number of benefits because of their intrinsic nonlinearities. Because machine learning (ML) is a broad field within artificial intelligence (AI) that focuses on extracting valuable information from data, it is commonly linked to statistics and data science. In fact, ML's data-driven methodology has made it possible for us to create systems like never before, bringing us one step closer to creating fully autonomous systems that can rival, equal, and occasionally surpass human intelligence and skills. However, the quality, quantity, and availability of data—all of which might be difficult to come by in some situations—are critical to the success of machine learning techniques. Since there is currently no standardized dataset for antennas, like those for computer vision, this data must be obtained, if it isn't already accessible, from the standpoint of antenna design. This can be accomplished by using CEM simulation software to simulate the required antenna on a broad range of parameters [ 8 ]. Our work is divided into five sections: part I is an introduction; part II explains the dataset and machine learning models utilized; part III discusses Bayesian Optimization; part IV is a methodology section; and part V is the study’s results, GUI and conclusions. 2. Literature Review The need for effective and high-performance antenna designs that can satisfy the demands of contemporary networks has increased due to recent developments in wireless communication. Antenna design and performance optimization can be achieved by machine learning. Nowadays, the most common option for worldwide search is bio-inspired population-based approaches. This class includes popular methods like invasive weed optimization64, firefly algorithm, particle swarm optimizers (PSO), harmony search, evolutionary algorithms (EAs), evolutionary strategies, genetic algorithms (GAs), differential evolution (DE), and ant systems. The use of these algorithms has increased significantly in recent years, but the differences between them in practice seem to be negligible. The ability to perform global search is usually ascribed to the algorithm processing the information exchanged between members of a population, which is aided by recombination and mutation operators (GAs, EAs), or by imitating social behavior (or hunting/preying habits). For example, randomized biasing of design relocation toward the best solution found so far, either locally or globally. The lower computational efficiency of bio-inspired approaches is a drawback. Thousands of objective function calls are usually required for these algorithms to yield a satisfying result. When it comes to direct EM-driven antenna design, these expenses are frequently unaffordable unless each simulation can be finished quickly (within a few seconds, or if there are enough resources available for parallelization. Surrogate modelling techniques have been proposed as a solution to the previously noted cost difficulties. The fast replacement model (kriging, neural networks, Gaussian process regression, etc.) is created using EM analysis results obtained during the optimization process and used to produce additional approximations of the optimal design [ 9 ]. Surrogate-assisted frameworks are typically implemented in practice as iterative procedures. ML-assisted optimization (MLAO) techniques are covered in another paper. In this study, ANN, Gaussian process regression (GPR), and support vector machines (SVM) are used to develop a surrogate model for effective antenna design and sensitivity analysis. Designing antennas can benefit from the usage of ML algorithms. Through a process of trial and error, the antenna dimensions are modified after researchers use EM simulation software to build the antennas. Because so many simulations are needed, this is an extremely time-consuming task, and the projected degree of accuracy may not always be reached. To address the aforementioned bottleneck, antenna designers employ a variety of practical machine learning techniques, including the multistage collaborative machine learning approach (MS CoML), single output GPR (SOGPR), multi-output GPR (MOGPR), SVR, SVM, ANN, KNN, DTR, DFR, and others. Thus, while retaining high accuracy, reducing errors, and saving time, machine learning (ML) can predict antenna behavior, boost computational efficiency, reduce the number of simulations required, and expedite the antenna design process. ML improves evolutionary computation methods like PSO and differential evolution (DE) and optimizes the antenna parameter. Multiband patch and E-shaped antennas are designed using the PSO and DE algorithms, respectively. Both techniques eliminate unnecessary, time-consuming EM simulations to guarantee a quick design process [ 10 ]. This article uses a variety of machine learning methods, including ANN, KNN, random forest, and decision tree, to optimize the microstrip line fed dielectric resonator antenna. This is the first time that radiators based on dielectric resonators have been optimized using machine learning algorithms. The HFSS EM simulator is used to build the dataset for the same [ 11 ]. The design of stacked patch antennas has been treated as an optimization issue in this study. The simulator has been replaced by a trained artificial neural network (ANN) and integrated into a particle swarm optimization algorithm (PSOA) to provide a faster CAD module for the stacked-antenna design problem. The "function mapping black-box," which can relate the antenna's frequencies and related bandwidths with its dimensional parameters, is built with the aid of the ANN [ 12 ]. This paper proposes a sophisticated meta-heuristic optimization solution for the antenna architectural design optimization problem. The approach is intended to train neural network-based Multilayer Perceptrons (MLPs) by utilizing a mix of the Sine Cosine approach (SCA) and the Grey Wolf Optimizer (GWO). The suggested optimization approach is a useful, adaptable, and reliable platform for identifying the design parameters for a double T-shaped monopole antenna array in the best possible way [ 13 ]. This study presents a neural network-based elliptical printed dipole antenna design for current WiMAX, Bluetooth, WLAN, LTE, and upcoming 5G applications. The substrate on which the dipole patch is printed has a relative permittivity of 2.2 and a thickness of 0.787 mm. The main and minor axes of the ellipse regulate the operating frequency of the single band elliptical dipole antenna. A simulated dataset of 24 samples obtained using the electromagnetic simulator CST Microwave Studio is used to create a neural network consisting of one input layer, one hidden layer, and one output layer [ 14 ]. In order to forecast the microstrip antenna dimension, this study applies machine learning. Rectangular patch microstrip antennas with resonance frequencies between 1 and 8 GHz were the subject of the investigation. The simulation dataset used to produce the forecast has antenna widths ranging from 19 to 63 mm and lengths ranging from 10 to 54 mm. Decision trees, random forests, Support Vector Regression (SVR), and artificial neural networks (ANN) are the four techniques used [ 15 ]. In this research, we present a machine learning based antenna design strategy that combines patch antenna and log-periodic dual-dipole antenna (LPDA) to accomplish directional communication from the relay tag to the receiving reader, hence ensuring the security of the IoT communication system. In order to minimize the amount of big side lobes and lower the side lobe level (SLL), a multiobjective evolutionary algorithm optimizes the antenna's side lobe, gain, standing wave ratio, and return loss [ 16 ]. A multiband rectangular microstrip antenna with spiral-shaped configurations is presented in this study. Machine learning algorithms have also been used to increase accuracy and efficiency. According to the performance requirements, machine learning has been investigated to model the suggested antenna; nevertheless, in order to increase accuracy, there must be enough training data. The accuracy and generalization performance are enhanced by applying three distinct machine learning models, which are then contrasted with simulation and measurement outcomes [ 17 ]. In order to soft compute the dual-band circularly polarized bone-shaped patch antenna (BSPA) at 28 GHz and 38 GHz for 5G applications, a deep neural network (DNN) is used in this study. An adaptive learning rate approach is used to build a DNN model on a 5-layer system via a simulated database of 150 BSPAs. During the training phase of a hybrid method that combines the advantages of particle swarm optimization (PSO) with a modified version of the gravitational search algorithm (MGSA-PSO), the framework and hyper-parameters of the DNN model are tuned. Using a precise electromagnetic analysis platform, 150 BSPAs with various geometrical configurations are simulated in terms of the resonant frequency in order to provide the database needed for training and testing the model [ 18 ]. Large datasets are typically used to train effective machine learning techniques in order to ensure accuracy and prevent overfitting. However, when data collecting is difficult, the popularity of machine learning techniques is limited by the size of the dataset. In order to address this issue, this research proposes a novel machine learning approach based on the modified K-Nearest Neighbors (KNN) algorithm, which can extract more features from datasets using sophisticated simulation and processing methodologies [ 19 ]. 3. Dataset and Machine Learning Models This study uses simulation in CST Microwave Studio 2023 to investigate the effects of various configurations on the performance of a microstrip patch antenna. Figure 1 shows the antenna’s essential design, while Table 1 lists their symbols and numerical values used during simulation. The antenna’s substrate is FR-4, which has a thickness of 1.6 mm and a dielectric constant of 4.3. The research focuses on rectangular patch size, with resonance frequencies ranging from 2 to 5 GHz. Patch width and length are varied from 20 to 24 mm in 0.5 mm increments, while slot aperture intervals are varied from 0 to 5 mm in 0.2 increments. After running the simulation on CST, the datasets are exported in a txt file. Where the txt files are further processed using python code to find three important metrics —bandwidth, return loss and resonance frequency. The resonance frequency, when the capacitance and inductance are matched for optimal performance, at this frequency point antenna gain its high radiation efficiency. Signal reflection due to impedance mismatch is the return loss that is measured in decibels (dB). Better match between antenna and feed system will always have higher return loss. The bandwidth of an antenna refers to the frequency range over which it can perform properly. This range is calculated at the difference between the lowest and highest frequencies for which the return loss is less than − 10dB. The CST simulation generated 2106 data points in total, which included the following six parameters, slot spacing, antenna patch length, and patch width are considered as output parameters, whereas resonance frequency, return loss, and bandwidth are considered as input parameters for the ML models. These metrics are critical for evaluating the antenna’s efficiency, matching, and operational range. K-Nearest Neighbors (KNN), Decision Tree Regressor (DT), Gradient Boosting Regressor (GBR), Stochastic Gradient Descent (SGD), Artificial Neural Network (ANN/MLP), Gaussian Process Regressor (GPR), Support Vector Regressor (SVR), Random Forest (RF), XGBoost Regressor (XGB), and K-Nearest Neighbors (KNN) are the ten machine learning models that are used for training on this dataset. Support Vector Regression is a sort of regression that is based on Vapnik's Support Vector Machines (SVMs). Several publications have claimed that SVMs are superior to ANNs because of their generalization capabilities. In the literature, SVR has also been used to build microwave devices and antennas [ 20 ]. Finding a predetermined number of training samples that are closest to the new point is the basic idea behind the KNN method, a supervised neighbor-based learning regression algorithm discussed in this article. In order to forecast new data points, the algorithm employs "feature similarity," which assigns a value to the new point according to how closely it resembles the training set. The input vector is represented by x, the output vector by y, and the number of neighbors employed to make the prediction by k is indicated when utilizing the KNN regressor [ 21 ]. One machine learning method for resolving regression and classification issues is the gradient boosting algorithm. Every phase creates a weak prediction model (like the decision tree), which is then added to the overall model to form a strong prediction model. Gradient boosting is the process of generating a weak prediction model for each step based on the gradient direction of the loss function. By repeatedly choosing a weak model in the direction of the negative gradient, GB gradually approximates the minimal value of the loss function after first defining a target loss function whose domain consists of all weak prediction models [ 22 ]. In order to construct a microstrip patch antenna for wireless WiMAX/WLAN applications at the 5G-n78 sub-band frequency (3.3GHz), a careful endeavor is made in this article to introduce the decision tree machine learning algorithm. The suggested antenna is a straightforward 0.304λ x 0.238λ rectangular patch that was created using the line feeding technique on a FR-4 substrate (ʛr = 4.4). With an S11 of -37.4dB, a VSWR of 0.233, and a gain of 4.06dB, the antenna is radiating at a frequency of 3.3GHz. The decision tree was constructed using the R-language platform, and the data points were gathered via the High Frequency Structural Simulator (HFSS), a full wave electromagnetic solver [ 23 ]. This study proposes an online data-driven E-XGBoost method for antenna optimization that integrates IVFM and AOM. The E-XGBoost model uses IVFM as a variable sensitivity analyzer to reduce the dimension of design variables [ 24 ]. The neural network is used in this work as a technique for designing microstrip antennas. The forward side of the problem in this design process is synthesis, and the reverse side is analysis. As a result, by entering the resonant frequency, height, and dielectric constants of the selected substrate, one may receive the geometric dimensions—that is, the length and width of the patch in our geometry—at the output of the synthesis network with great precision [ 25 ]. The side length of a monopole antenna intended for usage in a wireless local area network has been optimized in this paper using the linear regression algorithm. The purpose of this study is to determine the ideal antenna dimension for the lowest return loss using machine learning. A one-to-one approach—one label for one feature—was used to train the simulation dataset, and this process was repeated to cover the full dataset. The data was examined using a variety of machine learning algorithms, including lasso and linear regression, although the linear regression algorithm performed the best because of processing constraints and data size limitations. The simulated result is consistent with the approach, which is implemented in Python [ 26 ]. Figure1: CST Simulation of Antenna Structure Table 1 Important Parameters Parameters Symbols Values dielectric constant ε r 4.2 substrate width Wa 68.5mm substrate length La 68.5mm patch width Wb 20-24mm patch length Lb 17-21mm feedline width Wc 3.1mm feedline length Lc 13mm slot width Wd 1.5mm slot length Ld 6mm substrate thickness h 1.6mm distance to feedline d 0-5mm 4. Hyperparameter Tuning with Bayesian Optimization In order to solve an issue, a machine learning algorithm typically converts it into an optimization problem and applies several optimization techniques. The optimization function affects how the machine learning algorithm fits the model to the data and is made up of several hyperparameters that are selected before the learning process begins. The internal model parameters, like the weights of the neural network, which can be determined from the data during the model training phase, are distinct from hyperparameters. We want to identify a set of hyperparameter values that archive the greatest performance on the data in a fair period of time before to the training phase. We refer to this procedure as hyperparameter tuning or optimization. With just a few samples, Bayesian optimization could determine the ideal value. In contrast to conventional optimization techniques, it does not require the function to be expressed explicitly. Therefore, three popular machine learning models' hyperparameters are optimized using the Bayesian optimization technique [ 27 ]. This study proposes an optimization algorithm known as multi-objectives pre-screening parallel Bayesian optimization (MPPBO). This new technique, which differs from the parallel Bayesian optimization (PBO) algorithm, considers several acquisition functions in order to achieve potentially better update points in terms of fitness functions, hence decreasing the total simulation time. The side lobe level (SLL) of a dielectric loading monopole antenna is optimized using the suggested MPPBO method in order to verify the idea [ 28 ]. For many years, optimization and parameter estimation approaches have been used to explore and improve designs in a variety of fields. The complexity of antenna and antenna array designs has increased the need for optimization methods like Bayesian estimates and evolutionary algorithms in the design process [ 29 ]. The Bayesian optimization method used in this paper supports machine learning for hyperparameter extraction. Additionally, it has been thoroughly validated using the task of classifying news as either true or fake. This study examines the fundamentals of the Bayesian optimization technique and its use to the selection of machine learning model parameters. Gradient Boosted Decision Trees (GBDT), Random Forest, and K-Nearest Neighbor (KNN) are the machine learning models that will be utilized in this work [ 30 ]. This paper examines the automatic tuning problem in the context of Bayesian optimization, where the generalization performance of a learning algorithm is represented as a sample from a Gaussian process (GP) [ 31 ]. 5. Methodology A comprehensive methodology was followed to design, simulate, and optimize a microstrip patch antenna using machine learning models. This section outlines the process, from data acquisition through CST Microwave Studio to model training, hyperparameter tuning, evaluation, and the development of a GUI for interactive model deployment(Fig. 2). Figure2: Methodology Workflow Flowchart 5.1. Antenna Design and Data Acquisition CST Microwave Studio 2023 was used to design and simulate a microstrip patch antenna. To capture a broad range of antenna performance metrics, key parameters were periodically adjusted within CST. This process generated a substantial dataset, including essential performance indicators, which was then exported as text files. 5.2. Data Pre-processing The dataset initially contained raw data in an irregular format. Pre-processing was conducted to standardize and structure the data, which involved identifying and selecting necessary parameters. This stage ensured data consistency, making it suitable for training machine learning models. The pre-processed dataset was divided into training and testing subsets, with 80% of the data allocated for model training and 20% for testing. 5.3. Machine Learning Models Ten machine learning models were selected to explore a diverse range of predictive capabilities for antenna parameter optimization. The models included: Support Vector Regressor (SVR), Random Forest (RF), XGBoost Regressor (XGB), K-Nearest Neighbors (KNN), Decision Tree Regressor (DT), Gradient Boosting Regressor (GBR), Stochastic Gradient Descent (SGD), Artificial Neural Network (ANN/MLP), Gaussian Process Regressor (GPR), Linear Regressor (Ridge Regressor). Each model was implemented in both default and optimized configurations, providing a baseline comparison and allowing for insights into the effects of hyperparameter tuning. 5.4. Hyperparameter Tuning with Bayesian Optimization To enhance model performance, Bayesian Optimization was employed for hyperparameter tuning. This optimization method was particularly effective for the complex models in the set, such as Random Forest, XGBoost, and ANN, where tuning parameters like the learning rate, tree depth, and hidden layer configurations were crucial for improving predictive accuracy. Bayesian optimization proved effective in refining these parameters by balancing exploration and exploitation, leading to more precise predictions. 5.5. Evaluation Metrics Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and R2 Score were the three main metrics used to assess the model's performance. These measurements made it easier to evaluate each model's capacity for generalization and prediction accuracy in-depth. Both default and optimized results were recorded, providing a clear comparison of the impact of Bayesian tuning on each model’s performance. 5.6. GUI Development for Model Deployment To streamline model deployment and evaluation, a custom GUI was developed. This user-friendly interface allows researchers to interact with each of the 10 machine learning models, offering functionalities for: Dataset Pre-processing: Users can prepare data through the GUI, ensuring it meets model requirements. Model Training and Testing: Each model can be trained and tested through interactive buttons, enabling real-time exploration of default and optimized configurations. Results Visualization: The GUI provides visual representations of model performance, displaying plots for trained models and comparing MSE, RMSE, and R² metrics for each configuration. This standalone GUI allows for efficient experimentation and quick comparisons, providing a valuable tool for practical antenna optimization research. 5.7. Workflow Overview The complete workflow, from CST simulation to model evaluation and GUI deployment, is illustrated in the flowchart (see Fig. 7 ). This figure outlines the stages, including data acquisition, pre-processing, model training, Bayesian optimization, evaluation, and the GUI interface, reflecting the systematic approach used in this study. 6. Results and Discussion 6.1 Overview of Model Performance This study evaluates the performance of 10 machine learning models for antenna design optimization, comparing default and Bayesian-optimized configurations. Each model was assessed using Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and R² score. Figures labelled MSE comparison, RMSE comparison, and R 2 score comparison visually summarize these metrics across all models, while Figures (a) through (j) depict individual model performance with default and optimized curves. 6.2 Individual Model Results 6.2.1 Support Vector Regressor (SVR) SVR (Fig. 3 a) demonstrated substantial gains post-optimization, with MSE dropping from 0.6213 to 0.2355, RMSE from 0.7882 to 0.4853, and R² increasing from 0.6614 to 0.8738. Bayesian optimization enabled SVR to capture more nuanced patterns within the dataset by optimizing the kernel parameters, making it highly effective for antenna data with complex structures. 6.2.2 Random Forest Regressor (RF) RF (Fig. 3 b) achieved robust results both before and after optimization, with MSE improving from 0.1052 to 0.1038, RMSE from 0.3244 to 0.3221, and a consistent high R² of 0.9458. The optimized RF model outperformed many others, underscoring the strong predictive capability of ensemble methods when applied to antenna optimization tasks. 6.2.3 XGBoost Regressor (XGB) XGB (Fig. 3 c) benefited notably from Bayesian optimization, with MSE reducing from 0.1257 to 0.1183, RMSE from 0.3545 to 0.3440, and R² increasing from 0.9328 to 0.9378. Optimization of the learning rate and max depth proved effective in enhancing XGB’s performance, allowing it to model complex relationships accurately within the data. 6.2.4 K-Nearest Neighbors (KNN) KNN (Fig. 3 d) showed moderate improvements, with MSE dropping from 0.2997 to 0.2424, RMSE from 0.5474 to 0.4923, and R² increasing from 0.8382 to 0.8694. Bayesian tuning optimized the number of neighbours, improving KNN’s sensitivity to data patterns while maintaining simplicity in its computations. 6.2.5 Decision Tree Regressor (DT) Decision Tree Regressor (DT): DT (Fig. 3 e) experienced minimal improvements from Bayesian tuning, with MSE shifting from 0.1921 to 0.2044, RMSE from 0.4383 to 0.4521, and R² decreasing from 0.8999 to 0.8941. These results suggest that DT’s high variance susceptibility limited its benefits from tuning, emphasizing its tendency to overfit. 6.2.6 Gradient Boosting Regressor (GBR) GBR (Fig. 3 f) showed significant improvement, with MSE reducing from 0.3153 to 0.1439, RMSE from 0.5615 to 0.3794, and R² increasing from 0.8293 to 0.9222. Bayesian tuning enhanced GBR’s learning rate and boosting stages, indicating that GBR is well-suited for capturing complex, layered patterns in antenna data. 6.2.7 Stochastic Gradient Descent (SGD) The SGD model (Fig. 3 g) displayed minor improvements, with MSE holding around 0.9975, RMSE close to 0.9987, and R² at 0.4911. While Bayesian optimization had limited impact, SGD’s linear nature aligns well with simple data structures, but struggled with the dataset's complexity. 6.2.8 Artificial Neural Network (ANN) / Multi-Layer Perceptron (MLP) ANN (Fig. 3 h) benefitted from tuning, reducing MSE from 0.6113 to 0.6118, RMSE from 0.7819 to 0.7822, and slightly increasing R² from 0.6665 to 0.6676. Bayesian optimization effectively tuned learning rates and hidden layer configurations, improving ANN’s capacity to model non-linear data patterns. 6.2.9 Gaussian Process Regressor (GPR) GPR (Figure i) had stable performance, with MSE and RMSE consistently at 0.9026 and 0.9500, and an R² score of 0.5329. Bayesian tuning had limited impact, as GPR’s kernel parameters required extensive customization to adapt to the dataset’s intricacies. 6.2.10 Linear Regression (Ridge) Ridge Regression (Figure j) exhibited minimal change after optimization, with MSE around 0.9985, RMSE at 0.9992, and R² near 0.4906. Linear Regression’s limited complexity was reflected in its modest performance on data with non-linear characteristics. 6.3 Comparative Analysis of Optimized Models 6.3.1 MSE and RMSE Comparison: The Random Forest and XGBoost models showed the lowest MSE and RMSE values post-optimization, demonstrating superior performance in antenna optimization tasks (see Figs. 4 and 5 ). This was followed by Gradient Boosting and SVR, indicating these models are particularly adept at capturing complex patterns in the dataset. In contrast, simpler models like SGD and Linear Regression exhibited higher MSE and RMSE values, as their linear structures were less suited for modelling intricate relationships. 6.3.2 R² Score Analysis: Random Forest and XGBoost achieved the highest R² scores, reflecting strong explanatory power and variance capture (see Fig. 6 ). Models such as Decision Tree and SGD had relatively lower R² scores, likely due to overfitting tendencies in DT and the linear assumptions in SGD, which limit their adaptability to complex data. 6.4 Impact of Bayesian Optimization Bayesian hyperparameter tuning significantly improved the performance of ensemble models like Random Forest and XGBoost by fine-tuning parameters such as the number of estimators and maximum depth. These optimizations resulted in considerable reductions in MSE and RMSE and increased R² values, enhancing the models' predictive power for complex data. For models like ANN, Bayesian tuning allowed refinement of learning rates and hidden layers, leading to improved error metrics and better alignment with non-linear data structures. In contrast, simpler models like Linear Regression and Decision Tree showed minimal gains, highlighting the limited impact of Bayesian optimization on models that inherently lack flexibility for complex datasets. 7. Implementation of the GUI for Model Deployment and Evaluation 7.1. Purpose and Functionality The GUI was designed to streamline the antenna optimization process by enabling users to interact with the machine learning models developed in this study. The GUI allows users to pre-process datasets, train and test different machine learning models, and visualize performance metrics in real-time. This tool offers a practical approach to deploying machine learning models, allowing for interactive exploration and analysis of model performance. 7.2. Key Features of the GUI Dataset Pre-processing: The GUI includes buttons labelled for pre-processing functions, which allow users to prepare the data before training. This includes options for data cleaning, feature selection, and scaling, ensuring that the data is correctly formatted and optimized for model input. Model Training and Testing: The GUI provides buttons for selecting any of the 10 machine learning models, initiating the training process, and then testing the models on new data. Users can choose either the default or Bayesian-optimized version of each model, enabling them to compare the effect of optimization directly within the interface. Results Visualization: Once the models are trained, the GUI has buttons for visualizing model performance, such as plotting trained model curves and displaying MSE, RMSE, and R² metrics. Users can view side-by-side comparisons of default and optimized curves (as seen in Figures a-j in the main document), helping them understand the model improvements achieved through Bayesian optimization. 7.3. User Interface and Practical Application The GUI’s design (Figure is user-friendly, with clearly labelled buttons and an intuitive layout that guides users through each step, from data pre-processing to visualization. The layout simplifies the complex process of model selection, training, testing, and evaluation, making it accessible for users with varying levels of technical expertise. The GUI also includes tooltips or labels to provide further guidance on each button’s function, enhancing usability. Standalone Deployment: The GUI operates as a standalone application, meaning it can be deployed independently, outside of development environments. This allows for broad application in real-world settings where antenna design researchers or engineers can quickly test different models and evaluate performance. 7.4. Significance of the GUI in Antenna Design This GUI represents a practical application of machine learning in antenna optimization, bridging the gap between research and implementation. It allows researchers and engineers to experiment with different models and observe the direct impact of Bayesian hyperparameter tuning, which is particularly useful in complex, data-intensive fields like antenna design. The GUI enables real-time exploration and rapid analysis, making it a valuable tool for both research and industry applications in engineering. 8. Conclusion This study presents an effective approach to antenna optimization by employing a diverse array of machine learning models and refining their predictive performance through Bayesian hyperparameter tuning. Using a carefully curated dataset generated from CST Microwave Studio simulations, we explored ten machine learning models, including SVR, KNN, GBR, RF, XGB, DT, SGD, ANN, GPR, and LR, to predict critical antenna design parameters. The use of Bayesian optimization significantly enhanced the performance of complex models, such as Random Forest and XGBoost, by fine-tuning parameters like the number of estimators and maximum depth, thereby achieving lower Mean Squared Error (MSE) and Root Mean Squared Error (RMSE) values, as well as higher R² scores. Ensemble methods (RF, XGB) and neural networks (ANN) proved particularly capable of capturing intricate, nonlinear patterns within the dataset, underlining their suitability for antenna design tasks that involve complex parameter interactions. The comparative analysis of models before and after optimization revealed that ensemble and gradient-based models yielded the best predictive accuracy, with Random Forest and XGBoost achieving the highest performance in terms of error minimization and explanatory power. In contrast, simpler models like SGD and Linear Regression showed minimal improvement post-optimization, likely due to their linear structures, which limit their adaptability to complex datasets. These findings underscore the importance of selecting appropriate machine learning models for antenna design and optimizing them to capture nuanced relationships within the data. In addition to model selection and optimization, a user-friendly GUI was developed to facilitate real-time interaction with the machine learning models, enabling streamlined data pre-processing, model training, testing, and performance visualization. This interface allows researchers and engineers to experiment with default and optimized models efficiently, making it a valuable tool for practical antenna design optimization. In conclusion, this work demonstrates that leveraging advanced machine learning models alongside Bayesian hyperparameter tuning performance in antenna design, providing a robust framework for data-driven optimization in engineering applications. Future research could explore the integration of additional optimization techniques and the application of this framework to other types of antennas or real-time deployment in adaptive communication systems, further enhancing the utility and adaptability of machine learning in complex engineering domains. Table 2 Details for Tuned Hyperparameters of 10 ML Models ML Model Tuned Hyperparameters R 2 Score MSE Score RMSE Score SVM(SVR) estimator_C = 105.0375 estimator__gamma = 10.0 estimator__kernel = 'rbf' 0.8738 0.2355 0.4853 RF max_depth = 22 n_estimators = 300 0.9458 0.1037 0.3221 XGBoost learning_rate = 0.03286 max_depth = 49 n_estimators = 277 0.9377 0.1183 0.3440 KNN n_neighbors = 4 'p'=1(1 is for Manhattan distance) weights', 'distance' 0.8694 0.2424 0.4923 DT max_depth = 29 min_samples_leaf = 1 min_samples_split = 2 0.8974 0.1986 0.4457 GBR estimator_learning_rate = 0.1117 estimator__max_depth = 9 estimator__n_estimators = 72 0.9249 0.1414 0.3761 SGD estimator__alpha' = 0.0001 estimator__l1_ratio = 0 estimator__loss = squared_error estimator__penalty' = l2 0.4911 0.9975 0.9987 ANN(MLP) estimator__activation = relu estimator__alpha = 0.0001 estimator__hidden_layer_sizes = 150 estimator__learning_rate_init = 0.001323367 0.6676 0.6118 0.7822 GPR Bayesian optimization is typically less suited for directly tuning the hyperparameters of Gaussian Process Regression due to the complex, continuous nature of GPR's kernel parameters, which require optimization methods that can effectively handle their intricate dependencies and continuous domain. 0.5329 0.9025 0.9500 Linear Regression alpha = 0.0428 0.4906 0.9985 0.9992 Declarations Author Contribution Chung-Hao Huang and Amir Ali wrote the main manuscript text. Chang-Chen Hsu and Han-Hsing Tsao prepared figures 1-7. All authors reviewed the manuscript. References Kurniawati, N., Arif, F., & Alam, S. (2021). Predicting rectangular patch microstrip antenna dimension using machine learning. J Commun , 16 (9), 394–399. NIYATO, D. (2024). ‘Editorial: Third Quarter 2024 IEEE Communications Surveys and Tutorials’, IEEE Commun. Surv. Tutor., Vol. 26, No. 3, Third Quart., Available: https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=10643728 MOHAMMED, A. S. B., KAMAL, S., AIN, M. F., & AHMAD, Z. A. (2019). ‘Microstrip Patch Antenna: A Review and the Current State of the Art’, J. Adv. Res. Dyn. Control Syst. , 11, (07-Special Issue), pp. 510–524. Available: https://www.researchgate.net/publication/336922045_Microstrip_Patch_Antenna_A_Review_and_the_Current_State_of_the_Art Li, X., Ma, R., Cai, H., et al. (2023). High-gain dual-band aperture-shared CP patch antenna with wide AR beamwidth for satellite navigation system. Ieee Antennas And Wireless Propagation Letters , 22 (8), 1888–1891. Haque, M. A., et al. (2022). Dual band antenna design and prediction of resonance frequency using machine learning approaches. Appl Sci , 12 (20), 10505. Shakya, S. R., Kube, M., & Zhou, Z. (2023). 'A comparative analysis of machine learning approach for optimizing antenna design'. International Journal Of Microwave And Wireless Technologies , pp. 1–11. ALI, Y. A., AWWAD, E. M., AL-RAZGAN, M., & MAAROUF, A. (2023). ‘Hyperparameter Search for Machine Learning Algorithms for Optimizing the Computational Complexity’, Processes , 11, (2), p. 349. Available: https://doi.org/10.3390/pr11020349 EL MISILMANI, H., NAOUS, T., and, & AL KHATIB, S. (2020). ‘A Review on the Design and Optimization of Antennas Using Machine Learning Algorithms and Techniques’, Int. J. RF Microw. Comput. Aided Eng. , 30, (7), p. e22356.Available:https://doi.org/10.1002/mmce.2236 KOZIEL, S., PIETRENKO-DABROWSKA, A., & LEIFSSON, L. (2024). ‘Antenna optimization using machine learning with reduced-dimensionality surrogates’, Sci. Rep. , 14, Article 21567. Available: https://doi.org/10.1038/s41598-024-21567 Sarker, N., Podder, P., Mondal, M. R. H., Shafin, S. S., & Kamruzzaman, J. (2023). ‘Applications of Machine Learning and Deep Learning in Antenna Design, Optimization, and Selection: A Review’, IEEE Access , Vol. 11, p. 10256193. Available: https://doi.org/10.1109/ACCESS.2023.3317371 Singh, O., Bharamagoudra, M. R., Gupta, H., Dwivedi, A. K., Ranjan, P., & Sharma, A. (2022). ‘Microstrip line fed dielectric resonator antenna optimization using machine learning algorithms’. Sādhanā , 47, Article 226. Jain, S. K. (2015). Bandwidth enhancement of patch antennas using neural network dependent modified optimizer. Int J Microwave Wireless Technol , 8 (7), 1–9. 10.1017/S1759078715000616 El-Kenawy, E. M., Abutarboush, H. F., Mohamed, A. W., & Ibrahim, A. (2021). Advance artificial intelligence technique for designing double T-shaped monopole antenna. Comput Mater Continua , 69 (3), 2983–2995. 10.32604/cmc.2021.019114 Hammoodi, A. I., & Milanova, M. (2018). Elliptical printed dipole antenna design using ANN based on Levenberg–Marquardt algorithm. Adv Sci Technol Eng Syst J , 3 (5). 10.25046/aj030545 Kurniawati, N. (2021). Predicting rectangular patch microstrip antenna dimension using machine learning. J Commun , 16 (9), 394–399. 10.12720/jcm.16.9.394-399 Hong, T., Liu, C., & Kadoch, M. (2019). Machine learning based antenna design for physical layer security in ambient backscatter communications. Wirel Commun Mobile Comput , 1–8. 10.1155/2019/4870656 Aoad, A. (2021). Design and manufacture of a multiband rectangular spiral-shaped microstrip antenna using EM-driven and machine learning. Elektronika ir Elektrotechnika , 27 (1), 29–40. 10.5755/j02.eie.27583 Montaser, A. M., & Mahmoud, K. R. (2021). Deep learning based antenna design and beam-steering capabilities for millimeter-wave applications. Ieee Access : Practical Innovations, Open Solutions , (99), 1–1. 10.1109/ACCESS.2021.3123219 Cui, L., Zhang, Y., Zhang, R., & Liu, Q. H. (2020). A modified efficient KNN method for antenna optimization and design. Ieee Transactions On Antennas And Propagation , (99), 1–1. 10.1109/TAP.2020.3001743 Yiğit, M. E., Günel, G. Ö., & Günel, T. (2021). 'SVR based design of triple band rectangular microstrip antenna for WLAN and 5G applications', in Proc. 4th Int. Symp. Adv. Electrical and Communication Technol. (ISAECT), Alkhobar, Saudi Arabia, pp. 1–5. Cui, L., Zhang, Y., Zhang, R., et al. (2020). A modified efficient KNN method for antenna optimization and design. Ieee Transactions On Antennas And Propagation , 68 (10), 6858–6866. Tiwari, R., Sharma, R., & Dubey, R. (2022). 'Microstrip patch antenna parameter optimization prediction model using machine learning techniques'. IJRITCC , 10, (9). Pusuluri, V. B., Prasad, A. M., & Darimireddy, N. K. (2023). 'Decision-tree based machine learning approach for the design and optimization of 5G n78 sub-band antenna for WiMAX/WLAN applications'. Proc. 2023 IEEE Wireless Antenna and Microwave Symp. (WAMS), June 10.1109/WAMS57261.2023.10242820 Li, W. T., Tang, H. S., Cui, C., Hei, Y. Q., & Shi, X. W. 'Efficient online data-driven enhanced-XGBoost method for antenna optimization', IEEE, [Online]. Available: https://ieeexplore.ieee.org Türker, N., Güneş, F., & Yildirim, T. (2006). Artificial neural design of microstrip antennas. Turk J Electr Eng Comput Sci , 14 (3), 445–453. Shobana, M., Aggarwal, S., & Pandeeswari, R. 'Machine Learning Hexagonal Monopole Antenna using Linear Regression Algorithm', IEEE. Xue, M., Shi, D., He, Y. (2019). 'A novel intelligent antenna synthesis system using hybrid machine learning algorithms', in Proc. Int. Symp. Electromagnetic Compatibility - EMC EUROPE, Barcelona, Spain, pp. 902–907, 10.1109/EMCEurope.2019.8871996 Bai, H., Yang, N., Zheng, S., Lu, K., & Hu, P. (2023). 'Multi-Objectives Prescreening Parallel Bayesian Optimization for Antenna Synthesis'. Proc. 2023 Int. Conf. Microwave and Millimeter Wave Technol. (ICMMT) , Guangzhou, China. Inman, M. J., Earwood, J. M., Elsherbeni, A., & Smith, C. E. (2004). Bayesian optimization techniques for antenna design. Prog Electromagn Res , 49 , 71–86. 10.2528/PIER04021302 Zhao, G., Song, S., Lin, H., & Jiang, W. 'Bayesian Optimization Machine Learning Models for True and Fake News Classification', IEEE . Snoek, J., Larochelle, H., & Adams, R. P. (2012). Practical Bayesian Optimization of Machine Learning Algorithms. Advances in Neural Information Processing Systems , 4 , arXiv. Additional Declarations No competing interests reported. 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Flowchart\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5453365/v1/0968ef2bdafc3ab50c15e34c.png"},{"id":70386703,"identity":"17779306-779b-4263-9ead-c0bc2e9fc939","added_by":"auto","created_at":"2024-12-02 17:22:47","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":340121,"visible":true,"origin":"","legend":"\u003cp\u003eScattered plots of 10 ML Models\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5453365/v1/148ea16b57e925d9c386a364.png"},{"id":70386655,"identity":"4e36e504-3a4a-40df-a982-e253b184a024","added_by":"auto","created_at":"2024-12-02 17:22:37","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":77352,"visible":true,"origin":"","legend":"\u003cp\u003eMSE Comparison of 10 ML Models\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5453365/v1/66d5151647516401d3649e1b.png"},{"id":70386645,"identity":"bf9df4f0-caf0-4d71-bc84-a9521286d2f1","added_by":"auto","created_at":"2024-12-02 17:22:28","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":71867,"visible":true,"origin":"","legend":"\u003cp\u003eRMSE Comparison of 10 ML Models\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5453365/v1/405fc4efd83dce4f2953b333.png"},{"id":70386756,"identity":"a7b592b5-448b-41a3-906c-3c7d8b7edfd8","added_by":"auto","created_at":"2024-12-02 17:22:54","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":68252,"visible":true,"origin":"","legend":"\u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e Score Comparison of 10 ML Models\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5453365/v1/8cc8d1c238c241089eed297d.png"},{"id":70386705,"identity":"29368987-9a48-4dd6-a266-3938d5192fb3","added_by":"auto","created_at":"2024-12-02 17:22:48","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":187965,"visible":true,"origin":"","legend":"\u003cp\u003eGUI Interface for Antenna Optimization Using ML\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-5453365/v1/b0979bb63162d4f93f5354d1.png"},{"id":71049638,"identity":"073fda0b-de06-4075-9b73-8929e85f7481","added_by":"auto","created_at":"2024-12-10 15:23:41","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1633817,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5453365/v1/d90ef9d7-2f85-4a7d-86d3-d7d8eba71c77.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Enhanced Antenna Design through Hyper parameter Optimization of Diverse Machine Learning Models Using Bayesian Optimization","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eAntennae design process is a complex problem when it comes to design it by using a simulation software which takes a long time while doing the simulation and running again and again to get the desired results. In the wireless business, strong mobile networks are crucial, but networks of the future will be even more difficult. For long-distance communications, these networks need antennas with a large bandwidth and high gain. These communication techniques are suitable for patch antenna arrays. Therefore, designing a high-performance antenna becomes a significant problem that needs to be resolved [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIt is anticipated that sixth-generation (6G) mobile communication networks will feature a wide bandwidth, dense infrastructure, huge antennas, affordable technology, a variety of positioning techniques, and improved intelligence. These developments present 6G's practical design with both fresh opportunities and challenges. However, with 6G, it becomes very difficult to obtain channel state information (CSI) in real time for every wireless link. The estimated channels or beams between base station (BS) and user equipment (UE), for example, would be among the many data sources in 6G that would provide high-quality location-tagged channel data, allowing for a better understanding of the local wireless environment. A prospective paradigm shift from the traditional environment-unaware communications to the CSI acquisition challenge can be achieved by taking use of this new possibility.\u003c/p\u003e \u003cp\u003eThe microstrip patch antennas are essentially considered in the advancement of the latest communication mechanisms in contrast to the conventional type because they offer the advantage of being low profile along with simple or inexpensive manufacturing procedures. Microstrip is probably the most successful and revolutionary antenna technology ever. Its success comes from very well-known advantages. And it also has some limitations, the most well-known being the inherent narrow bandwidth, narrow impedance, low axial ratio (AR), small gain, lower power handling capacity and low efficiency [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eOne of the most widely used antennas in radar applications is the microstrip Ultra-Wideband radar (UWB) antenna. It has garnered a lot of interest due to its benefits, which include simplicity in construction, ease of manufacture, and ease of integration with microwave integrated circuits. A microstrip antenna's geometric shape consists of a ground plane on one side and a radiating element on the dielectric substrate. The most popular type of microstrip patch antenna is the rectangular element, while there are other types as well, such as the triangular, semicircular, circular, and square radiating elements [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThis paper use machine learning models to predict the required parameters of the rectangular microstrip patch antenna and use the Bayesian optimizer for the optimization of the hyperparameters of each of the ML model used. We are using 10 ML models, Support Vector Regressor (SVR), Random Forest (RF), XGBoost Regressor (XGB), K-Nearest Neighbors (KNN), Decision Tree Regressor (DT), Gradient Boosting Regressor (GBR), Stochastic Gradient Descent (SGD), Artificial Neural Network (ANN/MLP), Gaussian Process Regressor (GPR), Linear Regressor (Ridge Regressor). ML models predict future inputs based on probability aspects and learn nonlinear qualities from the datasets [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Bayesian optimization is used for the tuning of the hyperparameters of all three ML models according to our datasets we created, to make the performance of the models better. Hyperparameter tuning is a type of optimization in which the black-box or optimization's objective function is unknown. It is not possible to use conventional optimization methods like gradient descent or the Newton method. An excellent approach for resolving this type of optimization issue is Bayesian optimization. Using the Bayesian formula, it obtains posterior information on the function distribution by combining sample data with previous knowledge about the unknown function [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe factors that control the learning process and establish the final parameters of the models are known as hyperparameters of a learning algorithm. The goal of hyperparameter optimization is to quickly determine optimal hyperparameter settings to obtain good results from data [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eADS, HFSS, CST, and IE3D are the most popular commercial CEM programs for antenna design and simulation. Additionally, these software products are devoid of a number of crucial capabilities. For example, IE3D cannot simulate structures with finite features, ADS cannot model 3D structures, and the execution time of HFSS and CST is significant and grows with the size of the antenna structure. As will be covered in more detail later in this work, ML has been extensively examined as a complementary technique to CEM in the design and optimization of different kinds of antennas for a number of benefits because of their intrinsic nonlinearities.\u003c/p\u003e \u003cp\u003eBecause machine learning (ML) is a broad field within artificial intelligence (AI) that focuses on extracting valuable information from data, it is commonly linked to statistics and data science. In fact, ML's data-driven methodology has made it possible for us to create systems like never before, bringing us one step closer to creating fully autonomous systems that can rival, equal, and occasionally surpass human intelligence and skills. However, the quality, quantity, and availability of data\u0026mdash;all of which might be difficult to come by in some situations\u0026mdash;are critical to the success of machine learning techniques. Since there is currently no standardized dataset for antennas, like those for computer vision, this data must be obtained, if it isn't already accessible, from the standpoint of antenna design. This can be accomplished by using CEM simulation software to simulate the required antenna on a broad range of parameters [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Our work is divided into five sections: part I is an introduction; part II explains the dataset and machine learning models utilized; part III discusses Bayesian Optimization; part IV is a \u003cspan refid=\"Sec5\" class=\"InternalRef\"\u003emethodology\u003c/span\u003e section; and part V is the study\u0026rsquo;s results, GUI and conclusions.\u003c/p\u003e"},{"header":"2. Literature Review","content":"\u003cp\u003eThe need for effective and high-performance antenna designs that can satisfy the demands of contemporary networks has increased due to recent developments in wireless communication. Antenna design and performance optimization can be achieved by machine learning. Nowadays, the most common option for worldwide search is bio-inspired population-based approaches. This class includes popular methods like invasive weed optimization64, firefly algorithm, particle swarm optimizers (PSO), harmony search, evolutionary algorithms (EAs), evolutionary strategies, genetic algorithms (GAs), differential evolution (DE), and ant systems. The use of these algorithms has increased significantly in recent years, but the differences between them in practice seem to be negligible. The ability to perform global search is usually ascribed to the algorithm processing the information exchanged between members of a population, which is aided by recombination and mutation operators (GAs, EAs), or by imitating social behavior (or hunting/preying habits). For example, randomized biasing of design relocation toward the best solution found so far, either locally or globally. The lower computational efficiency of bio-inspired approaches is a drawback. Thousands of objective function calls are usually required for these algorithms to yield a satisfying result. When it comes to direct EM-driven antenna design, these expenses are frequently unaffordable unless each simulation can be finished quickly (within a few seconds, or if there are enough resources available for parallelization. Surrogate modelling techniques have been proposed as a solution to the previously noted cost difficulties. The fast replacement model (kriging, neural networks, Gaussian process regression, etc.) is created using EM analysis results obtained during the optimization process and used to produce additional approximations of the optimal design [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Surrogate-assisted frameworks are typically implemented in practice as iterative procedures. ML-assisted optimization (MLAO) techniques are covered in another paper. In this study, ANN, Gaussian process regression (GPR), and support vector machines (SVM) are used to develop a surrogate model for effective antenna design and sensitivity analysis. Designing antennas can benefit from the usage of ML algorithms. Through a process of trial and error, the antenna dimensions are modified after researchers use EM simulation software to build the antennas. Because so many simulations are needed, this is an extremely time-consuming task, and the projected degree of accuracy may not always be reached. To address the aforementioned bottleneck, antenna designers employ a variety of practical machine learning techniques, including the multistage collaborative machine learning approach (MS CoML), single output GPR (SOGPR), multi-output GPR (MOGPR), SVR, SVM, ANN, KNN, DTR, DFR, and others. Thus, while retaining high accuracy, reducing errors, and saving time, machine learning (ML) can predict antenna behavior, boost computational efficiency, reduce the number of simulations required, and expedite the antenna design process. ML improves evolutionary computation methods like PSO and differential evolution (DE) and optimizes the antenna parameter. Multiband patch and E-shaped antennas are designed using the PSO and DE algorithms, respectively. Both techniques eliminate unnecessary, time-consuming EM simulations to guarantee a quick design process [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. This article uses a variety of machine learning methods, including ANN, KNN, random forest, and decision tree, to optimize the microstrip line fed dielectric resonator antenna. This is the first time that radiators based on dielectric resonators have been optimized using machine learning algorithms. The HFSS EM simulator is used to build the dataset for the same [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. The design of stacked patch antennas has been treated as an optimization issue in this study. The simulator has been replaced by a trained artificial neural network (ANN) and integrated into a particle swarm optimization algorithm (PSOA) to provide a faster CAD module for the stacked-antenna design problem. The \"function mapping black-box,\" which can relate the antenna's frequencies and related bandwidths with its dimensional parameters, is built with the aid of the ANN [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. This paper proposes a sophisticated meta-heuristic optimization solution for the antenna architectural design optimization problem. The approach is intended to train neural network-based Multilayer Perceptrons (MLPs) by utilizing a mix of the Sine Cosine approach (SCA) and the Grey Wolf Optimizer (GWO). The suggested optimization approach is a useful, adaptable, and reliable platform for identifying the design parameters for a double T-shaped monopole antenna array in the best possible way [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. This study presents a neural network-based elliptical printed dipole antenna design for current WiMAX, Bluetooth, WLAN, LTE, and upcoming 5G applications. The substrate on which the dipole patch is printed has a relative permittivity of 2.2 and a thickness of 0.787 mm. The main and minor axes of the ellipse regulate the operating frequency of the single band elliptical dipole antenna. A simulated dataset of 24 samples obtained using the electromagnetic simulator CST Microwave Studio is used to create a neural network consisting of one input layer, one hidden layer, and one output layer [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. In order to forecast the microstrip antenna dimension, this study applies machine learning. Rectangular patch microstrip antennas with resonance frequencies between 1 and 8 GHz were the subject of the investigation. The simulation dataset used to produce the forecast has antenna widths ranging from 19 to 63 mm and lengths ranging from 10 to 54 mm. Decision trees, random forests, Support Vector Regression (SVR), and artificial neural networks (ANN) are the four techniques used [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn this research, we present a machine learning based antenna design strategy that combines patch antenna and log-periodic dual-dipole antenna (LPDA) to accomplish directional communication from the relay tag to the receiving reader, hence ensuring the security of the IoT communication system. In order to minimize the amount of big side lobes and lower the side lobe level (SLL), a multiobjective evolutionary algorithm optimizes the antenna's side lobe, gain, standing wave ratio, and return loss [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. A multiband rectangular microstrip antenna with spiral-shaped configurations is presented in this study. Machine learning algorithms have also been used to increase accuracy and efficiency. According to the performance requirements, machine learning has been investigated to model the suggested antenna; nevertheless, in order to increase accuracy, there must be enough training data. The accuracy and generalization performance are enhanced by applying three distinct machine learning models, which are then contrasted with simulation and measurement outcomes [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. In order to soft compute the dual-band circularly polarized bone-shaped patch antenna (BSPA) at 28 GHz and 38 GHz for 5G applications, a deep neural network (DNN) is used in this study. An adaptive learning rate approach is used to build a DNN model on a 5-layer system via a simulated database of 150 BSPAs. During the training phase of a hybrid method that combines the advantages of particle swarm optimization (PSO) with a modified version of the gravitational search algorithm (MGSA-PSO), the framework and hyper-parameters of the DNN model are tuned. Using a precise electromagnetic analysis platform, 150 BSPAs with various geometrical configurations are simulated in terms of the resonant frequency in order to provide the database needed for training and testing the model [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Large datasets are typically used to train effective machine learning techniques in order to ensure accuracy and prevent overfitting. However, when data collecting is difficult, the popularity of machine learning techniques is limited by the size of the dataset. In order to address this issue, this research proposes a novel machine learning approach based on the modified K-Nearest Neighbors (KNN) algorithm, which can extract more features from datasets using sophisticated simulation and processing methodologies [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e"},{"header":"3. Dataset and Machine Learning Models","content":"\u003cp\u003eThis study uses simulation in CST Microwave Studio 2023 to investigate the effects of various configurations on the performance of a microstrip patch antenna. Figure\u0026nbsp;1 shows the antenna\u0026rsquo;s essential design, while Table \u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e lists their symbols and numerical values used during simulation.\u003c/p\u003e \u003cp\u003eThe antenna\u0026rsquo;s substrate is FR-4, which has a thickness of 1.6 mm and a dielectric constant of 4.3. The research focuses on rectangular patch size, with resonance frequencies ranging from 2 to 5 GHz. Patch width and length are varied from 20 to 24 mm in 0.5 mm increments, while slot aperture intervals are varied from 0 to 5 mm in 0.2 increments.\u003c/p\u003e \u003cp\u003eAfter running the simulation on CST, the datasets are exported in a txt file. Where the txt files are further processed using python code to find three important metrics \u0026mdash;bandwidth, return loss and resonance frequency. The resonance frequency, when the capacitance and inductance are matched for optimal performance, at this frequency point antenna gain its high radiation efficiency. Signal reflection due to impedance mismatch is the return loss that is measured in decibels (dB). Better match between antenna and feed system will always have higher return loss. The bandwidth of an antenna refers to the frequency range over which it can perform properly. This range is calculated at the difference between the lowest and highest frequencies for which the return loss is less than \u0026minus;\u0026thinsp;10dB.\u003c/p\u003e \u003cp\u003eThe CST simulation generated 2106 data points in total, which included the following six parameters, slot spacing, antenna patch length, and patch width are considered as output parameters, whereas resonance frequency, return loss, and bandwidth are considered as input parameters for the ML models. These metrics are critical for evaluating the antenna\u0026rsquo;s efficiency, matching, and operational range.\u003c/p\u003e \u003cp\u003e K-Nearest Neighbors (KNN), Decision Tree Regressor (DT), Gradient Boosting Regressor (GBR), Stochastic Gradient Descent (SGD), Artificial Neural Network (ANN/MLP), Gaussian Process Regressor (GPR), Support Vector Regressor (SVR), Random Forest (RF), XGBoost Regressor (XGB), and K-Nearest Neighbors (KNN) are the ten machine learning models that are used for training on this dataset. Support Vector Regression is a sort of regression that is based on Vapnik's Support Vector Machines (SVMs). Several publications have claimed that SVMs are superior to ANNs because of their generalization capabilities. In the literature, SVR has also been used to build microwave devices and antennas [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFinding a predetermined number of training samples that are closest to the new point is the basic idea behind the KNN method, a supervised neighbor-based learning regression algorithm discussed in this article. In order to forecast new data points, the algorithm employs \"feature similarity,\" which assigns a value to the new point according to how closely it resembles the training set. The input vector is represented by x, the output vector by y, and the number of neighbors employed to make the prediction by k is indicated when utilizing the KNN regressor [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. One machine learning method for resolving regression and classification issues is the gradient boosting algorithm. Every phase creates a weak prediction model (like the decision tree), which is then added to the overall model to form a strong prediction model. Gradient boosting is the process of generating a weak prediction model for each step based on the gradient direction of the loss function. By repeatedly choosing a weak model in the direction of the negative gradient, GB gradually approximates the minimal value of the loss function after first defining a target loss function whose domain consists of all weak prediction models [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. In order to construct a microstrip patch antenna for wireless WiMAX/WLAN applications at the 5G-n78 sub-band frequency (3.3GHz), a careful endeavor is made in this article to introduce the decision tree machine learning algorithm. The suggested antenna is a straightforward 0.304λ x 0.238λ rectangular patch that was created using the line feeding technique on a FR-4 substrate (ʛr\u0026thinsp;=\u0026thinsp;4.4). With an S11 of -37.4dB, a VSWR of 0.233, and a gain of 4.06dB, the antenna is radiating at a frequency of 3.3GHz. The decision tree was constructed using the R-language platform, and the data points were gathered via the High Frequency Structural Simulator (HFSS), a full wave electromagnetic solver [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. This study proposes an online data-driven E-XGBoost method for antenna optimization that integrates IVFM and AOM. The E-XGBoost model uses IVFM as a variable sensitivity analyzer to reduce the dimension of design variables [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. The neural network is used in this work as a technique for designing microstrip antennas. The forward side of the problem in this design process is synthesis, and the reverse side is analysis. As a result, by entering the resonant frequency, height, and dielectric constants of the selected substrate, one may receive the geometric dimensions\u0026mdash;that is, the length and width of the patch in our geometry\u0026mdash;at the output of the synthesis network with great precision [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. The side length of a monopole antenna intended for usage in a wireless local area network has been optimized in this paper using the linear regression algorithm. The purpose of this study is to determine the ideal antenna dimension for the lowest return loss using machine learning. A one-to-one approach\u0026mdash;one label for one feature\u0026mdash;was used to train the simulation dataset, and this process was repeated to cover the full dataset. The data was examined using a variety of machine learning algorithms, including lasso and linear regression, although the linear regression algorithm performed the best because of processing constraints and data size limitations. The simulated result is consistent with the approach, which is implemented in Python [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFigure1: CST Simulation of Antenna Structure\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eImportant Parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSymbols\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eValues\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003edielectric constant\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eε\u003csub\u003er\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003esubstrate width\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWa\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e68.5mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003esubstrate length\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLa\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e68.5mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003epatch width\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWb\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e20-24mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003epatch length\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLb\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e17-21mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003efeedline width\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWc\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.1mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003efeedline length\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLc\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e13mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eslot width\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWd\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.5mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eslot length\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLd\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003esubstrate thickness\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eh\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.6mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003edistance to feedline\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ed\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0-5mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"4. Hyperparameter Tuning with Bayesian Optimization","content":"\u003cp\u003eIn order to solve an issue, a machine learning algorithm typically converts it into an optimization problem and applies several optimization techniques. The optimization function affects how the machine learning algorithm fits the model to the data and is made up of several hyperparameters that are selected before the learning process begins. The internal model parameters, like the weights of the neural network, which can be determined from the data during the model training phase, are distinct from hyperparameters. We want to identify a set of hyperparameter values that archive the greatest performance on the data in a fair period of time before to the training phase. We refer to this procedure as hyperparameter tuning or optimization. With just a few samples, Bayesian optimization could determine the ideal value. In contrast to conventional optimization techniques, it does not require the function to be expressed explicitly. Therefore, three popular machine learning models' hyperparameters are optimized using the Bayesian optimization technique [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. This study proposes an optimization algorithm known as multi-objectives pre-screening parallel Bayesian optimization (MPPBO). This new technique, which differs from the parallel Bayesian optimization (PBO) algorithm, considers several acquisition functions in order to achieve potentially better update points in terms of fitness functions, hence decreasing the total simulation time. The side lobe level (SLL) of a dielectric loading monopole antenna is optimized using the suggested MPPBO method in order to verify the idea [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. For many years, optimization and parameter estimation approaches have been used to explore and improve designs in a variety of fields. The complexity of antenna and antenna array designs has increased the need for optimization methods like Bayesian estimates and evolutionary algorithms in the design process [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. The Bayesian optimization method used in this paper supports machine learning for hyperparameter extraction. Additionally, it has been thoroughly validated using the task of classifying news as either true or fake. This study examines the fundamentals of the Bayesian optimization technique and its use to the selection of machine learning model parameters. Gradient Boosted Decision Trees (GBDT), Random Forest, and K-Nearest Neighbor (KNN) are the machine learning models that will be utilized in this work [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. This paper examines the automatic tuning problem in the context of Bayesian optimization, where the generalization performance of a learning algorithm is represented as a sample from a Gaussian process (GP) [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e].\u003c/p\u003e"},{"header":"5. Methodology","content":"\u003cp\u003e \u003c/p\u003e \u003cp\u003eA comprehensive methodology was followed to design, simulate, and optimize a microstrip patch antenna using machine learning models. This section outlines the process, from data acquisition through CST Microwave Studio to model training, hyperparameter tuning, evaluation, and the development of a GUI for interactive model deployment(Fig.\u0026nbsp;2).\u003c/p\u003e \u003cp\u003eFigure2: Methodology Workflow Flowchart\u003c/p\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e5.1. Antenna Design and Data Acquisition\u003c/h2\u003e \u003cp\u003eCST Microwave Studio 2023 was used to design and simulate a microstrip patch antenna. To capture a broad range of antenna performance metrics, key parameters were periodically adjusted within CST. This process generated a substantial dataset, including essential performance indicators, which was then exported as text files.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e5.2. Data Pre-processing\u003c/h2\u003e \u003cp\u003eThe dataset initially contained raw data in an irregular format. Pre-processing was conducted to standardize and structure the data, which involved identifying and selecting necessary parameters. This stage ensured data consistency, making it suitable for training machine learning models. The pre-processed dataset was divided into training and testing subsets, with 80% of the data allocated for model training and 20% for testing.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e5.3. Machine Learning Models\u003c/h2\u003e \u003cp\u003eTen machine learning models were selected to explore a diverse range of predictive capabilities for antenna parameter optimization. The models included: Support Vector Regressor (SVR), Random Forest (RF), XGBoost Regressor (XGB), K-Nearest Neighbors (KNN), Decision Tree Regressor (DT), Gradient Boosting Regressor (GBR), Stochastic Gradient Descent (SGD), Artificial Neural Network (ANN/MLP), Gaussian Process Regressor (GPR), Linear Regressor (Ridge Regressor).\u003c/p\u003e \u003cp\u003eEach model was implemented in both default and optimized configurations, providing a baseline comparison and allowing for insights into the effects of hyperparameter tuning.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e5.4. Hyperparameter Tuning with Bayesian Optimization\u003c/h2\u003e \u003cp\u003eTo enhance model performance, Bayesian Optimization was employed for hyperparameter tuning. This optimization method was particularly effective for the complex models in the set, such as Random Forest, XGBoost, and ANN, where tuning parameters like the learning rate, tree depth, and hidden layer configurations were crucial for improving predictive accuracy. Bayesian optimization proved effective in refining these parameters by balancing exploration and exploitation, leading to more precise predictions.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e5.5. Evaluation Metrics\u003c/h2\u003e \u003cp\u003eMean Squared Error (MSE), Root Mean Squared Error (RMSE), and R2 Score were the three main metrics used to assess the model's performance. These measurements made it easier to evaluate each model's capacity for generalization and prediction accuracy in-depth. Both default and optimized results were recorded, providing a clear comparison of the impact of Bayesian tuning on each model\u0026rsquo;s performance.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e5.6. GUI Development for Model Deployment\u003c/h2\u003e \u003cp\u003eTo streamline model deployment and evaluation, a custom GUI was developed. This user-friendly interface allows researchers to interact with each of the 10 machine learning models, offering functionalities for:\u003c/p\u003e \u003cp\u003eDataset Pre-processing: Users can prepare data through the GUI, ensuring it meets model requirements.\u003c/p\u003e \u003cp\u003eModel Training and Testing: Each model can be trained and tested through interactive buttons, enabling real-time exploration of default and optimized configurations.\u003c/p\u003e \u003cp\u003eResults Visualization: The GUI provides visual representations of model performance, displaying plots for trained models and comparing MSE, RMSE, and R\u0026sup2; metrics for each configuration.\u003c/p\u003e \u003cp\u003eThis standalone GUI allows for efficient experimentation and quick comparisons, providing a valuable tool for practical antenna optimization research.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e5.7. Workflow Overview\u003c/h2\u003e \u003cp\u003eThe complete workflow, from CST simulation to model evaluation and GUI deployment, is illustrated in the flowchart (see Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e7\u003c/span\u003e). This figure outlines the stages, including data acquisition, pre-processing, model training, Bayesian optimization, evaluation, and the GUI interface, reflecting the systematic approach used in this study.\u003c/p\u003e \u003c/div\u003e"},{"header":"6. Results and Discussion","content":"\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e6.1 Overview of Model Performance\u003c/h2\u003e \u003cp\u003eThis study evaluates the performance of 10 machine learning models for antenna design optimization, comparing default and Bayesian-optimized configurations. Each model was assessed using Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and R\u0026sup2; score. Figures labelled MSE comparison, RMSE comparison, and R\u003csup\u003e2\u003c/sup\u003e score comparison visually summarize these metrics across all models, while Figures (a) through (j) depict individual model performance with default and optimized curves.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e6.2 Individual Model Results\u003c/h2\u003e \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e \u003ch2\u003e6.2.1 Support Vector Regressor (SVR)\u003c/h2\u003e \u003cp\u003eSVR (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e3\u003c/span\u003ea) demonstrated substantial gains post-optimization, with MSE dropping from 0.6213 to 0.2355, RMSE from 0.7882 to 0.4853, and R\u0026sup2; increasing from 0.6614 to 0.8738. Bayesian optimization enabled SVR to capture more nuanced patterns within the dataset by optimizing the kernel parameters, making it highly effective for antenna data with complex structures.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e \u003ch2\u003e6.2.2 Random Forest Regressor (RF)\u003c/h2\u003e \u003cp\u003eRF (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e3\u003c/span\u003eb) achieved robust results both before and after optimization, with MSE improving from 0.1052 to 0.1038, RMSE from 0.3244 to 0.3221, and a consistent high R\u0026sup2; of 0.9458. The optimized RF model outperformed many others, underscoring the strong predictive capability of ensemble methods when applied to antenna optimization tasks.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e \u003ch2\u003e6.2.3 XGBoost Regressor (XGB)\u003c/h2\u003e \u003cp\u003eXGB (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e3\u003c/span\u003ec) benefited notably from Bayesian optimization, with MSE reducing from 0.1257 to 0.1183, RMSE from 0.3545 to 0.3440, and R\u0026sup2; increasing from 0.9328 to 0.9378. Optimization of the learning rate and max depth proved effective in enhancing XGB\u0026rsquo;s performance, allowing it to model complex relationships accurately within the data.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section3\"\u003e \u003ch2\u003e6.2.4 K-Nearest Neighbors (KNN)\u003c/h2\u003e \u003cp\u003eKNN (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e3\u003c/span\u003ed) showed moderate improvements, with MSE dropping from 0.2997 to 0.2424, RMSE from 0.5474 to 0.4923, and R\u0026sup2; increasing from 0.8382 to 0.8694. Bayesian tuning optimized the number of neighbours, improving KNN\u0026rsquo;s sensitivity to data patterns while maintaining simplicity in its computations.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section3\"\u003e \u003ch2\u003e6.2.5 Decision Tree Regressor (DT)\u003c/h2\u003e \u003cp\u003eDecision Tree Regressor (DT): DT (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e3\u003c/span\u003ee) experienced minimal improvements from Bayesian tuning, with MSE shifting from 0.1921 to 0.2044, RMSE from 0.4383 to 0.4521, and R\u0026sup2; decreasing from 0.8999 to 0.8941. These results suggest that DT\u0026rsquo;s high variance susceptibility limited its benefits from tuning, emphasizing its tendency to overfit.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec21\" class=\"Section3\"\u003e \u003ch2\u003e6.2.6 Gradient Boosting Regressor (GBR)\u003c/h2\u003e \u003cp\u003eGBR (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e3\u003c/span\u003ef) showed significant improvement, with MSE reducing from 0.3153 to 0.1439, RMSE from 0.5615 to 0.3794, and R\u0026sup2; increasing from 0.8293 to 0.9222. Bayesian tuning enhanced GBR\u0026rsquo;s learning rate and boosting stages, indicating that GBR is well-suited for capturing complex, layered patterns in antenna data.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec22\" class=\"Section3\"\u003e \u003ch2\u003e6.2.7 Stochastic Gradient Descent (SGD)\u003c/h2\u003e \u003cp\u003eThe SGD model (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e3\u003c/span\u003eg) displayed minor improvements, with MSE holding around 0.9975, RMSE close to 0.9987, and R\u0026sup2; at 0.4911. While Bayesian optimization had limited impact, SGD\u0026rsquo;s linear nature aligns well with simple data structures, but struggled with the dataset's complexity.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec23\" class=\"Section3\"\u003e \u003ch2\u003e6.2.8 Artificial Neural Network (ANN) / Multi-Layer Perceptron (MLP)\u003c/h2\u003e \u003cp\u003eANN (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e3\u003c/span\u003eh) benefitted from tuning, reducing MSE from 0.6113 to 0.6118, RMSE from 0.7819 to 0.7822, and slightly increasing R\u0026sup2; from 0.6665 to 0.6676. Bayesian optimization effectively tuned learning rates and hidden layer configurations, improving ANN\u0026rsquo;s capacity to model non-linear data patterns.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec24\" class=\"Section3\"\u003e \u003ch2\u003e6.2.9 Gaussian Process Regressor (GPR)\u003c/h2\u003e \u003cp\u003eGPR (Figure i) had stable performance, with MSE and RMSE consistently at 0.9026 and 0.9500, and an R\u0026sup2; score of 0.5329. Bayesian tuning had limited impact, as GPR\u0026rsquo;s kernel parameters required extensive customization to adapt to the dataset\u0026rsquo;s intricacies.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec25\" class=\"Section3\"\u003e \u003ch2\u003e6.2.10 Linear Regression (Ridge)\u003c/h2\u003e \u003cp\u003eRidge Regression (Figure j) exhibited minimal change after optimization, with MSE around 0.9985, RMSE at 0.9992, and R\u0026sup2; near 0.4906. Linear Regression\u0026rsquo;s limited complexity was reflected in its modest performance on data with non-linear characteristics.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec26\" class=\"Section2\"\u003e \u003ch2\u003e6.3 Comparative Analysis of Optimized Models\u003c/h2\u003e \u003cdiv id=\"Sec27\" class=\"Section3\"\u003e \u003ch2\u003e6.3.1 MSE and RMSE Comparison:\u003c/h2\u003e \u003cp\u003eThe Random Forest and XGBoost models showed the lowest MSE and RMSE values post-optimization, demonstrating superior performance in antenna optimization tasks (see Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e5\u003c/span\u003e). This was followed by Gradient Boosting and SVR, indicating these models are particularly adept at capturing complex patterns in the dataset. In contrast, simpler models like SGD and Linear Regression exhibited higher MSE and RMSE values, as their linear structures were less suited for modelling intricate relationships.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec28\" class=\"Section3\"\u003e \u003ch2\u003e6.3.2 R\u0026sup2; Score Analysis:\u003c/h2\u003e \u003cp\u003eRandom Forest and XGBoost achieved the highest R\u0026sup2; scores, reflecting strong explanatory power and variance capture (see Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e6\u003c/span\u003e). Models such as Decision Tree and SGD had relatively lower R\u0026sup2; scores, likely due to overfitting tendencies in DT and the linear assumptions in SGD, which limit their adaptability to complex data.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec29\" class=\"Section2\"\u003e \u003ch2\u003e6.4 Impact of Bayesian Optimization\u003c/h2\u003e \u003cp\u003eBayesian hyperparameter tuning significantly improved the performance of ensemble models like Random Forest and XGBoost by fine-tuning parameters such as the number of estimators and maximum depth. These optimizations resulted in considerable reductions in MSE and RMSE and increased R\u0026sup2; values, enhancing the models' predictive power for complex data. For models like ANN, Bayesian tuning allowed refinement of learning rates and hidden layers, leading to improved error metrics and better alignment with non-linear data structures. In contrast, simpler models like Linear Regression and Decision Tree showed minimal gains, highlighting the limited impact of Bayesian optimization on models that inherently lack flexibility for complex datasets.\u003c/p\u003e \u003c/div\u003e"},{"header":"7. Implementation of the GUI for Model Deployment and Evaluation","content":"\u003cdiv id=\"Sec31\" class=\"Section2\"\u003e \u003ch2\u003e7.1. Purpose and Functionality\u003c/h2\u003e \u003cp\u003eThe GUI was designed to streamline the antenna optimization process by enabling users to interact with the machine learning models developed in this study. The GUI allows users to pre-process datasets, train and test different machine learning models, and visualize performance metrics in real-time. This tool offers a practical approach to deploying machine learning models, allowing for interactive exploration and analysis of model performance.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec32\" class=\"Section2\"\u003e \u003ch2\u003e7.2. Key Features of the GUI\u003c/h2\u003e \u003cp\u003eDataset Pre-processing: The GUI includes buttons labelled for pre-processing functions, which allow users to prepare the data before training. This includes options for data cleaning, feature selection, and scaling, ensuring that the data is correctly formatted and optimized for model input.\u003c/p\u003e \u003cp\u003eModel Training and Testing: The GUI provides buttons for selecting any of the 10 machine learning models, initiating the training process, and then testing the models on new data. Users can choose either the default or Bayesian-optimized version of each model, enabling them to compare the effect of optimization directly within the interface.\u003c/p\u003e \u003cp\u003eResults Visualization: Once the models are trained, the GUI has buttons for visualizing model performance, such as plotting trained model curves and displaying MSE, RMSE, and R\u0026sup2; metrics. Users can view side-by-side comparisons of default and optimized curves (as seen in Figures a-j in the main document), helping them understand the model improvements achieved through Bayesian optimization.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec33\" class=\"Section2\"\u003e \u003ch2\u003e7.3. User Interface and Practical Application\u003c/h2\u003e \u003cp\u003eThe GUI\u0026rsquo;s design (Figure is user-friendly, with clearly labelled buttons and an intuitive layout that guides users through each step, from data pre-processing to visualization. The layout simplifies the complex process of model selection, training, testing, and evaluation, making it accessible for users with varying levels of technical expertise. The GUI also includes tooltips or labels to provide further guidance on each button\u0026rsquo;s function, enhancing usability.\u003c/p\u003e \u003cp\u003eStandalone Deployment: The GUI operates as a standalone application, meaning it can be deployed independently, outside of development environments. This allows for broad application in real-world settings where antenna design researchers or engineers can quickly test different models and evaluate performance.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec34\" class=\"Section2\"\u003e \u003ch2\u003e7.4. Significance of the GUI in Antenna Design\u003c/h2\u003e \u003cp\u003eThis GUI represents a practical application of machine learning in antenna optimization, bridging the gap between research and implementation. It allows researchers and engineers to experiment with different models and observe the direct impact of Bayesian hyperparameter tuning, which is particularly useful in complex, data-intensive fields like antenna design. The GUI enables real-time exploration and rapid analysis, making it a valuable tool for both research and industry applications in engineering.\u003c/p\u003e \u003c/div\u003e"},{"header":"8. Conclusion","content":"\u003cp\u003eThis study presents an effective approach to antenna optimization by employing a diverse array of machine learning models and refining their predictive performance through Bayesian hyperparameter tuning. Using a carefully curated dataset generated from CST Microwave Studio simulations, we explored ten machine learning models, including SVR, KNN, GBR, RF, XGB, DT, SGD, ANN, GPR, and LR, to predict critical antenna design parameters. The use of Bayesian optimization significantly enhanced the performance of complex models, such as Random Forest and XGBoost, by fine-tuning parameters like the number of estimators and maximum depth, thereby achieving lower Mean Squared Error (MSE) and Root Mean Squared Error (RMSE) values, as well as higher R\u0026sup2; scores. Ensemble methods (RF, XGB) and neural networks (ANN) proved particularly capable of capturing intricate, nonlinear patterns within the dataset, underlining their suitability for antenna design tasks that involve complex parameter interactions. The comparative analysis of models before and after optimization revealed that ensemble and gradient-based models yielded the best predictive accuracy, with Random Forest and XGBoost achieving the highest performance in terms of error minimization and explanatory power. In contrast, simpler models like SGD and Linear Regression showed minimal improvement post-optimization, likely due to their linear structures, which limit their adaptability to complex datasets. These findings underscore the importance of selecting appropriate machine learning models for antenna design and optimizing them to capture nuanced relationships within the data. In addition to model selection and optimization, a user-friendly GUI was developed to facilitate real-time interaction with the machine learning models, enabling streamlined data pre-processing, model training, testing, and performance visualization. This interface allows researchers and engineers to experiment with default and optimized models efficiently, making it a valuable tool for practical antenna design optimization. In conclusion, this work demonstrates that leveraging advanced machine learning models alongside Bayesian hyperparameter tuning performance in antenna design, providing a robust framework for data-driven optimization in engineering applications. Future research could explore the integration of additional optimization techniques and the application of this framework to other types of antennas or real-time deployment in adaptive communication systems, further enhancing the utility and adaptability of machine learning in complex engineering domains.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDetails for Tuned Hyperparameters of 10 ML Models\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eML Model\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTuned Hyperparameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e Score\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMSE Score\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRMSE Score\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSVM(SVR)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eestimator_C\u0026thinsp;=\u0026thinsp;105.0375\u003c/p\u003e \u003cp\u003eestimator__gamma\u0026thinsp;=\u0026thinsp;10.0\u003c/p\u003e \u003cp\u003eestimator__kernel = 'rbf'\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.8738\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.2355\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.4853\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eRF\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003emax_depth\u0026thinsp;=\u0026thinsp;22\u003c/p\u003e \u003cp\u003en_estimators\u0026thinsp;=\u0026thinsp;300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9458\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1037\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.3221\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eXGBoost\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003elearning_rate\u0026thinsp;=\u0026thinsp;0.03286\u003c/p\u003e \u003cp\u003emax_depth\u0026thinsp;=\u0026thinsp;49\u003c/p\u003e \u003cp\u003en_estimators\u0026thinsp;=\u0026thinsp;277\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9377\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1183\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.3440\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eKNN\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003en_neighbors\u0026thinsp;=\u0026thinsp;4\u003c/p\u003e \u003cp\u003e'p'=1(1 is for Manhattan distance)\u003c/p\u003e \u003cp\u003eweights', 'distance'\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.8694\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.2424\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.4923\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eDT\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003emax_depth\u0026thinsp;=\u0026thinsp;29\u003c/p\u003e \u003cp\u003emin_samples_leaf\u0026thinsp;=\u0026thinsp;1\u003c/p\u003e \u003cp\u003emin_samples_split\u0026thinsp;=\u0026thinsp;2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.8974\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1986\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.4457\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eGBR\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eestimator_learning_rate\u0026thinsp;=\u0026thinsp;0.1117\u003c/p\u003e \u003cp\u003eestimator__max_depth\u0026thinsp;=\u0026thinsp;9\u003c/p\u003e \u003cp\u003eestimator__n_estimators\u0026thinsp;=\u0026thinsp;72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9249\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1414\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.3761\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSGD\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eestimator__alpha' = 0.0001\u003c/p\u003e \u003cp\u003eestimator__l1_ratio\u0026thinsp;=\u0026thinsp;0\u003c/p\u003e \u003cp\u003eestimator__loss\u0026thinsp;=\u0026thinsp;squared_error\u003c/p\u003e \u003cp\u003eestimator__penalty' = l2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.4911\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9975\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9987\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eANN(MLP)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eestimator__activation\u0026thinsp;=\u0026thinsp;relu\u003c/p\u003e \u003cp\u003eestimator__alpha\u0026thinsp;=\u0026thinsp;0.0001\u003c/p\u003e \u003cp\u003eestimator__hidden_layer_sizes\u0026thinsp;=\u0026thinsp;150\u003c/p\u003e \u003cp\u003eestimator__learning_rate_init\u0026thinsp;=\u0026thinsp;0.001323367\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6676\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.6118\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.7822\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eGPR\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBayesian optimization is typically less suited for directly tuning the hyperparameters of Gaussian Process Regression due to the complex, continuous nature of GPR's kernel parameters, which require optimization methods that can effectively handle their intricate dependencies and continuous domain.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5329\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9025\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9500\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eLinear Regression\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ealpha\u0026thinsp;=\u0026thinsp;0.0428\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.4906\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9985\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9992\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eChung-Hao Huang and Amir Ali wrote the main manuscript text. Chang-Chen Hsu and Han-Hsing Tsao prepared figures 1-7. All authors reviewed the manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003e\u003cspan\u003eKurniawati, N., Arif, F., \u0026amp; Alam, S. (2021). Predicting rectangular patch microstrip antenna dimension using machine learning. \u003cem\u003eJ Commun\u003c/em\u003e, \u003cem\u003e16\u003c/em\u003e(9), 394\u0026ndash;399.\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eNIYATO, D. (2024). \u0026lsquo;Editorial: Third Quarter 2024 IEEE Communications Surveys and Tutorials\u0026rsquo;, IEEE Commun. Surv. Tutor., Vol. 26, No. 3, Third Quart., Available:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=10643728\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eMOHAMMED, A. S. B., KAMAL, S., AIN, M. F., \u0026amp; AHMAD, Z. A. 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Practical Bayesian Optimization of Machine Learning Algorithms. \u003cem\u003eAdvances in Neural Information Processing Systems\u003c/em\u003e, \u003cem\u003e4\u003c/em\u003e, arXiv.\u003c/span\u003e\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Ai Based Antenna Optimization, Bayesian Optimization, Hyperparameter Tuning, Ml Models, Antenna Design Gui Interface","lastPublishedDoi":"10.21203/rs.3.rs-5453365/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5453365/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis work investigates the use of machine learning (ML) models for microstrip patch antenna design optimization with Bayesian optimization. Based on datasets produced by CST Microwave Studio 2023 simulations, key antenna parameters, including resonance frequency, bandwidth, and return loss, were first predicted using Support Vector Regressor (SVR), k-Nearest Neighbor (KNN), and Gradient Boosting Regressor (GBR) models. With slot distance, patch length, and patch width as target parameters, pre-processing was used to transform CST output into structured input-output pairs in order to get the dataset ready for machine learning training. Extending this first method, we assessed ten machine learning models, each optimized with Bayesian hyperparameter tuning: SVR, KNN, GBR, Random Forest, XGBoost, Decision Tree, Stochastic Gradient Descent, Artificial Neural Network, Gaussian Process Regressor, and Linear Regression. By fine-tuning parameters like max_depth, n_estimator, Bayesian optimization greatly improved complicated models, lowering Mean Squared Error (MSE) and Root Mean Squared Error (RMSE) while raising R2 scores. After optimization, the Random Forest and XGBoost models produced the best predicted accuracy, according to comparative data. To further enable real-time model training, testing, and performance visualization, a unique graphical user interface (GUI) was created, offering a useful tool for interactive antenna optimization. This system provides a solid basis for data-driven improvements in advanced engineering applications by showcasing how ML models combined with Bayesian tuning can successfully handle challenging antenna design problems.\u003c/p\u003e","manuscriptTitle":"Enhanced Antenna Design through Hyper parameter Optimization of Diverse Machine Learning Models Using Bayesian Optimization","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-12-02 16:35:21","doi":"10.21203/rs.3.rs-5453365/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"a0a599ea-bafa-42c7-8635-7678ecb91467","owner":[],"postedDate":"December 2nd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-12-10T15:23:14+00:00","versionOfRecord":[],"versionCreatedAt":"2024-12-02 16:35:21","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5453365","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5453365","identity":"rs-5453365","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}