# Metamaterial Design with Nested-CNN and Prediction Improvement with Imputation
## 1 Introduction  
Metamaterials(MM) are special materials that are not found in nature and are used in many fields with their unusual properties [1]. Metamaterials have a wide range of uses, including optical filters, medical devices, remote aerospace applications, sensor detection and infrastructure monitoring, smart solar power management, crowd control, high-frequency battlefield communication, and lenses for high-gain antennas, improving ultrasonic sensors, anti-radar devices, and superlenses. The breadth of these usage areas has been the motivation for many studies on developing metamaterials. The studies are generally based on iteration-based studies of optimization algorithms. Optimization algorithms generally proceed iteratively until optimum and satisfactory results are found. The increase in big data and processing power demonstrates that the future of optimization algorithms will be even brighter. In the past few decades, electromagnetic (EM) designers have rapidly andaccurately developed models for rapid progress in technology. Moreover, these models have allowed for more variety and modeling complex problems than previously imagined. In recent decades, although many global optimization techniques have been developed, the most used technique is the genetic algorithm (GA) for designing metamaterials. (GA) [2]. GAs mimic natural selection and mutation to optimize constrained and unconstrained problems. The GA's basic operation chooses the best options from the previous generation to breed the next generation; it was popularized and widely used by the design of pixelized metallic structures [3], which is the basis of many metamaterial designs [4]. Optical nanoantenna array configurations [5] and shapes [6] have been optimized to maximum field enhancement at the selected location. In [7], the GA has a decreased field enhancement, which is a prohibitive factor for metamaterial usage in high power microwave implementations and thus, has a reflectarray unit cell design based on pixels. In recent applications, coding metasurfaces based on radar cross-section (RCS) reduction and best suitable metamaterials developed for polarization conversion, has been included by the GA in [8; 9; 10]. Many algorithms are created by nature [11; 12], such as artificial bee colonies (ABC) [13] and bat-inspired algorithms [14]. These algorithms are known as lower branches of swarm intelligence algorithms that try to optimize complex problems by mimicking the collective behavior of decentralized, self-organized systems, natural or artificial [15]. The optimization of an ant colony (ACO) [16] is counted as one of the swarm intelligence algorithms, and uses stigmergy to find the best suitable solution. Ant colony optimization is used for graph-based solutions, such as finding the route of the vehicle, job scheduling, and traveling seller issues [17]. The GA has achieved immense results in electromagnetics and optical materials, but disjointed pixels in solution are a drawback of GAs because these designs are limited to planar configurations. On the other hand, ACO maps the optimal \"trace\" found by artificial \"ants\" in the graph topology to an adjacent structure. For that reason, ACO has achieved enormous success in the design of the electromagnetic device, particularly in the meander-line antennas [18]. For the high performance of frequency selective surfaces (FSS), the ACO algorithm and lazy ants combined and improved the performance of FSS by ZHU [19; 20]. In the mid-1990s, another branch of swarm intelligence algorithms, particle swarm optimization (PSO), emerged [21], and has been used immensely for the optimization of electromagnetic devices [22; 23; 24; 25]. Compared to PSO and GA, PSO offers many more advantages: firstly, PSO uses real values as vectors instead of binary values, and real values were later used in GAs [26]. Secondly, in PSO, members of the population tend to work more independently and cooperatively.