# Machine Learning Aided Metamaterial Based Reconfigurable Antenna for Low Cost Portable Electronic Devices

This section briefly describes the need to use regression models during the simulation process and explains how regression models can be used to reduce time and resource requirements by 80% while simulating design efficiency. the antenna.

### Need for regression methods

Researchers use regression analysis to find the value of the dependent parameter(s) using the value(s) of the independent parameter(s)38,39,40,41. When simulating an antenna design, frequency is an independent parameter, while reflectance value is a dependent parameter. Simulating the experimental design requires a significant amount of time and resources. Increasing the complexity of experimental design requires more time and resources. When simulating the efficiency of an antenna, it must be evaluated for a wide variety of frequency values. As the range of tests expands, the demand for simulation resources also increases. As a result, the cost of modeling and experimentation increases. ML-based regression analysis methodologies can be used to solve this problem by following the following three steps.

Step 1: Simulate the antenna design using a higher step value for the frequency.

2nd step: Train the machine learning-based regression model using simulated data.

Step 3: Predict intermediate frequency reflectance values ​​using the trained regression model.

With an increase in the frequency step size value, simulation time and resource requirements are reduced. R Square score (R2S), Mean Absolute Percentage Error (MAPE), Mean Squared Error (MSE), and Adjusted R-Score Squared (AR2S) are commonly used criteria to quantify the prediction accuracy of the trained regression model. The formulas for calculating these metrics are shown in the equations. (5–8).

$$MSE= frac{1}{N}sum_{i=1}^{N}{({Actual,Target,Value}_{i}-{Predicted,Target,Value}_{ i})}^{2}$$

(5)

$$MAPE=frac{1}{n}sum_{i=1}^{n}leftlfloorfrac{{Actual,Target,Value}_{i}-{Expected,Target ,Value}_{i})}{{Actual,Target,Value}_{i}}rightrfloor *100$$

(6)

$${R}^{2}S= 1- frac{sum_{i=1}^{N}{({Predicted,Target,Value}_{i}-{Actual,Target, Value}_{i})}^{2}}{sum_{i=1}^{N}{({Actual,Target}_{i}- Average, Target,Value )}^{2 }}$$

(seven)

$$A{R}^{2}S= 1-left[frac{left(1-{R}^{2}right)*(N-1)}{N-K-1}right]$$

(8)

Here, “N” is a number of data points used to test the regression model and “K” is a number of independent parameters used to predict the value of the target parameter.

### Regression analysis using Supplemental Tree Regression Model (ExTRM)

A binary recursive partitioning algorithm is used to build the regression tree. Each recursive step is used to find a data point in the independent parameter, where dividing the data set into two halves minimizes the root mean square error in the regression analysis. To improve the accuracy of its predictions, the regression tree may need to be pruned or adjusted.

### Extremely random tree regression (additional tree)

This algorithm creates a collection of ‘M’ number of unpruned regression trees RT1…RTM. Unlike the regression tree, this technique picks the cutpoint at random and grows all the regression trees using the training dataset. As indicated in Eq. (9), the output of all regression trees is blended using an arithmetic mean.

$$Forecast,Value= sum_{j=1}^{M}{RT}_{j}(x)$$

(9)

Here x is the value of an independent parameter.

### Design of Experiment for Reflectance Value Prediction Using ExTRM

The experiments are performed using data obtained by simulating the antenna design presented in Sect. 2. TS-60, TS-70, TS-80 and TS-90 are four test cases (TS) which are used to verify how much simulation time and resource requirements can be reduced using an analysis approach of regression. In the TS-P test case, (100-P)% simulated data points are selected using a uniform random selection strategy to train the ExTRM, while the P % simulated data points remaining are used to quantify the prediction accuracy of the formed ExTRM. The number of data points used to train and quantify the ExTRM during various test scenarios is detailed in Supplementary Table ST2.

### Experimental results for prediction using ExTRM

100 regression trees are used to create ExTRMs for experimentation. AR2The S of the ExTRMs obtained for various inner square length values ​​during the TS-80 test case is shown in Fig. 6a.

The MAPE of the ExTRMs for various inner square length values ​​during the TS-80 test case is shown using a comparative bar graph in Figure 6b. When ExTRMs are trained using first-degree polynomial (PF) features, an AR2S greater than 0.95 is obtained for all values ​​of interior square length, as shown in Figure 6a. Additionally, the MAPE of the ExTRMs is less than 0.5% for all inner square length values ​​when the model is trained using first-degree PFs, except for the inner square length of 11 mm, as shown in Fig. 6b. It’s about 1.0% in this situation.

Figure 7a–d shows scatterplots of predicted vs. simulated reflectance values ​​for 15 mm inner square length during test scenarios TS-60, TS-70, TS-80, and TS- 90, respectively. Even though only 20% of the simulated data is used to predict the reflectance value for the remaining 80% of frequencies, the ExTRM can predict these values ​​with high accuracy, as shown in Figure 7c. The same cannot be said for the TS-90 test case. Fig. additional. (S3 to S7) show scatter plots for inner square lengths of 10 to 14 mm in uniform 1 nm increments, respectively. As a result, we can conclude that using ExTRM during antenna design simulation for various interior square length values ​​can reduce simulation requirements by 80%.

AR2The S of the ExTRMs obtained for various inner square length values ​​during the TS-90 test case is shown in Fig. 6c. The MAPE of the ExTRMs for various inner square length values ​​during the TS-90 test case is shown using a comparative bar graph in Figure 6d. When ExTRMs are trained using first/second/third degree PFs, an AR2An S value greater than 0.9 cannot be obtained for all values ​​of inner square length, as shown in Figure 6c. Moreover, the MAPE of the ExTRM is significantly greater than 1.0% for some values ​​of the length of the inner square, as shown in Fig. 6d. As a result, we can conclude that using ExTRM during antenna design simulation for different inner square length values ​​cannot reduce the simulation requirements by 90%.

AR2The S of the ExTRMs obtained for various outer square length values ​​during the TS-80 test case is shown in Fig. 8a. The MAPE of the ExTRMs for various outer square length values ​​during the TS-80 test case is shown using a comparative bar graph in Figure 8b. When ExTRMs are formed using first-degree PFs, an AR2S greater than 0.99 is obtained for all values ​​of the length of the outer square, as shown in Figure 8a. Moreover, the MAPE of the ExTRM is less than 0.47% for all values ​​of the length of the outer square, as shown in Figure 8b.

Figure 7e–h shows scatter plots of predicted vs. simulated reflectance values ​​for 24 mm outer square length during test scenarios TS-60, TS-70, TS-80, and TS- 90, respectively. Even though only 20% of the simulated data is used to predict the reflectance value for the remaining 80% frequencies, the ExTRM can predict these values ​​with high accuracy, as shown in Figure 7g. The same cannot be said for the TS-90 test case. Fig. additional. (S8–S16) show scatter plots for the remaining lengths of the outer square. As a result, we can conclude that using ExTRM during antenna design simulation for various values ​​of outer square length can reduce simulation requirements by 80%.

AR2The S of the ExTRMs obtained for various outer square length values ​​during the TS-90 test case is shown in Fig. 8c. The MAPE of the ExTRMs for various outer square length values ​​during the TS-90 test case is shown using a comparative bar graph in Figure 8d. When ExTRMs are formed using second-degree PFs, an AR2S greater than 0.94 can be obtained for all values ​​of interior square length, as shown in Fig. 8c. However, the MAPE of the ExTRM is greater than 1.0% for some values ​​of the outer square length, as shown in Fig. 8d. Therefore, we can conclude that using ExTRM during antenna design simulation for different values ​​of outer square length cannot reduce the simulation requirements by 90%.