## 1 Introduction  
Loess, a material extensively employed in engineering applications, finds wide usage in various projects such as the construction of cement-soil waterproof curtains, artificial water-impermeable layers, and landfills. Among the crucial engineering properties of loess, permeability holds particular significance, directly influencing the practical implementation of engineering projects [1]. While research on improved loess has primarily focused on its mechanical properties, the exploration of its permeability necessitates further development. The permeability coefficient, a key indicator assessing loess permeability, predominantly signifies the soil's capacity to permit water passage and transmission, constituting a vital parameter in hydrogeology. This coefficient is notably affected by initial water content [2], dry density [3], void ratio [4], compaction [5], pressure [6], and the temperature [7] of the soil. An analysis of these elements' impact on the permeability coefficient of loess can significantly enhance its suitability for engineering purposes. Loess, categorized as a distinctive type of porous medium and water-sensitive soil, exhibits noteworthy mechanical characteristics, including a rapid decline in strength and increased deformation under infiltration or humidification [8]. Consequently, the mechanical and permeability properties of loess are commonly improved through compaction techniques and the incorporation of additives such as cement, fly ash, and lime [9], utilizing compaction methods and physicochemical reactions induced by the additives [10]. In a comprehensive study by [PERSON] [11], it was established that the permeability coefficient of loess exhibited a nonlinear relationship with the void ratio. This relationship, intricately tied to soil properties, was elucidated through saturated permeability tests on both intact and remolded loess subjected to varying conditions. [PERSON] [12] et al. studied the influencing factors of the permeability coefficient of unsaturated loess by adjusting the dry density of compacted loess samples, and the test results showed that the permeability coefficient increased monotonically and accelerated with the increase in volumetric water content, so the dry density is an important factor affecting the permeability coefficient of compacted loess. [PERSON]'s research [13] introduced cement, lime, and fly ash as improvement materials to typical loess soils, analyzing their effects on soil grading and permeability. The findings highlighted a gradual reduction in permeability for the improved soils as the hydration reaction of cement, lime, and fly ash progressed. However, their study did not consider the influence of dry density and loess grading properties on permeability. [PERSON] [14] took the losses of Xi'an, Yan'an, and Mili as research objects and found that the coarse grain mass ratio gradually increased and the grain size distribution curve transitioned from \"double peak\" to \"single peak\" through indoor tests. As the mass percentage of clay particles increased, the permeability coefficient decreased, resulting in a more significant disparity in permeability between the longitudinal and transverse directions. The equation for predicting the permeability coefficient was developed using test results and took into account grading parameters, grain size parameters, and porosity. However, it was found that this equation was not able to accurately forecast the permeability of loess material that had been affected with admixtures. The soil permeability coefficient (\(k\)) is a critical parameter in the design of civil engineering structures. Estimating \"\(K\)\" using empirical formulas related to other soil engineering parameters may not be accurate [15; 16]. Recently, machine learning (ML) algorithms have been widely applied in scientific research and engineering practices across various fields of civil engineering [17; 18].