## 1 Introduction  
Currently, with the advancement of materials research and manufacturing technology, sound-absorbing structures that can modulate the acoustic properties of the environment are utilized in a wide variety of applications [1]. Given the high operability and flexibility of acoustic simulations, they appear in numerous acoustics-related studies [2, 3]. In this regard, optimizing the initial sound absorption structure for further investigation has become the mainstream trend. Using the two commonly used optimization methods as examples, the literature on optimization by parametric scanning examines these two techniques. [PERSON] et al. [4] have developed a new light and thin sound absorption structure that is composed of melamine foam and hollow porous spheres, which significantly enhances the low-frequency sound absorption performance. [PERSON] et al. [5] have investigated the impact of the incident angle on locally-reactive acoustic metamaterials and the relationship between the ideal absorption peak, the incident angle, and the frequency. Using parameters, such as the total stiffness and damping, as independent variables, and the average sound absorption coefficient in a specific frequency band as the optimization objective, [PERSON] et al. [6] have created a type of loudspeaker with a good sound absorption performance. [PERSON] et al. [7] have constructed a labyrinthine Helmholtz phonon crystal and have concluded that increasing the tube length and preserving a small lattice constant could significantly enhance the structure's low-frequency sound insulation capacity. [PERSON] et al. [8] have constructed a resonant metamaterial plate with a front radial film and have concluded that increasing the plate thickness and decreasing the film thickness could effectively improve the broadband and low-frequency properties. In the literature concerning the application of genetic algorithms (GA, NSGA-II), [PERSON] et al. [9] have proposed a tunable low-frequency absorber, achieving 84% absorption of 500-800 Hz sound waves with an 82 mm thickness structure. By combining the gradient-based finite element difference method with the original method, [PERSON] et al. [10] have maximized the acoustic transmission loss of suspended glass panels. [PERSON] et al. [11] have modified the structural geometrical parameters, obtaining the optimal sound absorption performance of the structure when the thickness and the boundary are fixed. [PERSON] et al. [12] have designed compact high-performance silencers that can effectively reduce pipeline noise. [PERSON] et al. [13] have achieved the desired sound absorption performance by optimizing the supercell area, as well as the number and shape of the cellular structures. [PERSON] et al. [14] have utilized finite elements and hybrid regression in order to optimize the geometry to attenuate the broadband acoustic signals. [PERSON] et al. [15] have extended the absorption bandwidth in order to encompass the entire low-frequency spectrum by evaluating the various cost functions. [PERSON] et al. [16] have designed an efficient method for calculating the acoustic transmission losses by combining the analytical and numerical methods. [PERSON] et al. [17] have combined hypercubic sampling with constrained optimization in order to enhance the implied energy and sound transmission levels of the hybrid slab. [PERSON] et al. [18] have applied a gradient-based partial differential equation constrained optimization method that has realized the optimal continuous radial distribution of solid elastic materials, thereby constructing a gradual acoustic cloak with effective low-frequency sound absorption. However, parametric scanning and genetic algorithms both have limitations when they are applied to the optimization of acoustic structures. Parametric scanning is no longer effective in solving the hyperparameter problem, since the efficiency of parametric scanning by exhaustive traversal is severely affected by the proliferation of the parameters.