## 1 Introduction  
The Fukang Fault Zone in the Junggar Basin, located in front of the Bogda Mountains [1; 2], has undergone complex structural deformations and oil and gas reservoir formation processes due to the superimposition of multiple tectonic movements, like the Himalayas, Yanshan, and Haisi [3]. Within the Fukang Depression, vertical sedimentary sequences are characterized by multiple intricate layers [4; 5; 6], representing a typical low porosity and ultra-low permeability reservoir [7]. In deep formations, where deep formations demonstrate a low ROP [8], with an average drilling rate of only 1.56 m per hour in the Permian strata [9]. The mechanical drilling rate is a crucial indicator for assessing drilling efficiency, making the development of efficient and accurate mechanical drilling rate prediction models of great significance. This is essential for optimizing drilling parameters and reducing drilling costs in the Fukang Depression, ultimately promoting efficient exploration and development [10; 11]. Experts and scholars worldwide have conducted extensive research on mechanical drilling rate prediction methods. Commonly employed methods include prediction based on field experience, prediction based on drilling rate equations, and numerical simulation-based predictions [12]. [PERSON] et al. [13] introduced a mechanical drilling rate prediction method based on multivariate regression, but this method involves several empirical parameters in its calculations. [PERSON] et al. [14] enhanced the prediction model for ROP by taking into account factors like bit wear, hydraulic parameters, and formation characteristics. [PERSON] et al. [15] developed a drilling rate prediction model related to bit weight through the analysis of laboratory test data. [PERSON] et al. and [PERSON] et al. [16; 17] derived drilling rate equations based on rock strength criteria and mechanical-specific energy theory. However, due to the complex and variable subsurface conditions, accurately depicting the relationship between ROP and variables, like formation properties and engineering parameters, poses a challenge: ROP cannot be predicted by a simple mapping relationship. [PERSON] et al. [18] highlighted the limitations of traditional mechanical drilling rate prediction methods based on analytical equations. These equations, as well as laboratory tests, struggle to comprehensively consider the influence of various drilling parameters, engineering factors, and geological conditions on ROP. Additionally, these parameters can interact with each other, making it difficult to predict ROP accurately using a standard equation. Existing equations for mechanical drilling rate predictions are often one-sided and exhibit significant deviations. With the rapid advancement of artificial intelligence, an increasing number of researchers are applying machine learning methods to the petroleum industry. [PERSON] et al. [19] used artificial neural networks (ANNs) to establish a mechanical drilling rate prediction model based on drilling and bit parameters, although the considered influencing parameters are not comprehensive. [PERSON] et al. and [PERSON] et al. [20; 21] employed extreme learning machines (ELMs) for the prediction of ROP in offshore wells. However, ELMs struggle to provide highly transparent and interpretable predictive results and are susceptible to overfitting. [PERSON] et al. [22] explored several machine learning approaches for predicting ROP, including neural network (ANN), extreme learning machine, support vector regression, and least-square support vector regression (LS-SVR), all demonstrating commendable performance. Nevertheless, these methods face challenges in handling high-dimensional data, sensitivity to noise, and capturing nonlinear relationships. Nevertheless, most of these studies focus primarily on data mapping relationships and overlook mechanistic models or provide explanations for the causes of mechanical drilling rate anomalies.