## 1 Introduction  
In recent years, rapid advancements in radar detection technology have made the stealth capabilities of various weapons, equipment, aircraft, and ships a critical area of research. Common approaches to enhancing stealth include reshaping and using absorptive materials [1, 2, 3, 4, 5]. A key parameter for evaluating the stealth performance of an object under radar illumination is the RCS, which quantitatively characterizes the scattering properties of a target [6]. Metasurfaces, which are ultra-thin, two-dimensional structures composed of subwavelength unit elements arranged in quasi periodic configurations, are powerful tools for manipulating the polarization, amplitude, and phase of electromagnetic (EM) waves. Due to their unique electromagnetic properties, metasurfaces have been widely used in RCS reduction, such as polarization rotation metasurfaces (PVM) [7, 8, 9, 10], phase gradient metasurfaces (PGM) [11, 12, 13], and artificial magnetic conductor (AMC) metasurfaces [14, 15, 16, 17, 18]. AMC refers to a class of metasurfaces characterized by their ability to reflect electromagnetic waves with a phase matching the incident wave. This property makes them highly effective in reducing the RCS when arranged in a chessboard configuration with a Perfect Electric Conductor (PEC). In such configurations, adjacent units cancel each other out due to a 180\({}^{\circ}\) phase difference in the reflected electromagnetic waves (the PEC reflects with a 180\({}^{\circ}\) phase shift, while the AMC reflects with a 0\({}^{\circ}\) phase shift) [15]. However, achieving a high bandwidth in chessboard metasurfaces is still challenging. To address this, [PERSON] et al. arranged two types of AMC units with nearly a 180-degree phase difference in a chessboard layout, achieving a 10 dB reduction band from 14.9 to 16.3 GHz, with the peak value reaching -31.9 dB [16]. [PERSON] et al. further extended the bandwidth by using 16 different AMC units with varying sizes and dielectric layer thicknesses to achieve a 10 dB RCS reduction band from 5.5 to 32.3 GHz [17]. Similarly, [PERSON] et al. achieved a 10 dB RCS reduction band from 3.75 to 10 GHz by arranging four types of AMCs in a chessboard pattern with irregular areas [18]. While these advanced AMC metasurfaces, including PGM and PRM, significantly improve the bandwidth, they require complicated arrangements and involve a large number of AMC units with varying heights. This complexity increases both manufacturing and design costs compared to simpler chessboard patterns, making it challenging to integrate these designs with target objects. Traditionally, most metasurface design approaches focus on adjusting or scaling specific geometric shapes, such as Jerusalem crosses, split rings, and square patches. In recent years, deep learning methods have also been applied in the design of metasurfaces. For example, in [19; 20], neural networks were employed to map electromagnetic responses to pixel matrices, which represent metasurface geometries. These trained networks can directly derive geometric structures from electromagnetic responses. Generative adversarial networks (GANs) can, to some extent, enhance the diversity and flexibility of the designs. By training the generator and discriminator on a dataset with similar properties, new structures can be obtained, although this method still largely depends on the dataset [21; 22]. Variational autoencoders (VAEs) take a different approach by encoding two-dimensional discrete matrices into continuous latent variables, which can then be decoded back into two-dimensional structures. Additionally, a neural network is trained to map these latent variables to electromagnetic responses, enabling optimization within the latent space to satisfy the design criteria. The continuous nature of the latent variables somewhat enhances design flexibility but remains closely tied to the dataset.