Metamaterial Design with Nested-CNN and Prediction Improvement with Imputation

Abstract

Metamaterials, which are not found in nature, are used to increase the performance of antennas with their extraordinary electromagnetic properties. Since metamaterials provide unique advantages, performance improvements have been made with many optimization algorithms. Objective: The article aimed to develop a deep learning model that, unlike traditional optimization algorithms, takes the desired reflection coefficients' parameter as an input and gives the image of the corresponding metamaterial. Method: An amount of 29,722 metamaterial images and reflection coefficients corresponding to the metamaterials were collected. Nested-CNN, designed for this task, consisted of Model-1 and Model-2. Model-1 was designed to generate the shape of metamaterial with a reflection coefficient as the input. Model-2 was designed to detect the reflection coefficient of a given image of metamaterial input. Created by using Model-2 in Model-1's loss function, the nested-CNN was updated by comparing the reflection coefficient of the produced image with the desired reflection coefficient. Secondly, imputation, which is usually the complete missing data before the process of training in machine learning algorithms, was proposed to use in the prediction side to improve the performance of the nested-CNN. The imputation for prediction was used for the non-interested part of the reflection coefficient to decrease the error of the interested region of the reflection coefficient. In the experiment, 27,222 data were used for the KNN-imputer, half of the reflection coefficient was considered as the non-interested region. Additionally, 40 neighbors and 50 neighbors were given the best mean absolute errors (MAE) for specified conditions. Result: The given results are based on test data. For Model-2, the MAE was 0.27, the R2 score was 0.96, and the mean correlation coefficient was 0.93. The R2 score for the nested-CNN was 0.9, the MAE of nested-CNN was 0.42, and the MAE of nested-CNN with 50 neighbors was 0.17.