## 1 Introduction  
Machine learning represented by deep learning has achieved great success in multiple fields [1], such as natural language processing [2], computer vision, quantitative transactions [3], and autonomous driving. These successful cases have attracted widespread attention in academia and industry, which has also promoted the advancement of machine learning technology. With the continuous development of basic theory, algorithm platforms, and computing power, the application of machine learning in the industry also has a good foundation. In the field of the petroleum industry, machine learning technology has also begun to be widely used [4], including formation parameter prediction, drilling equipment fault detection, the diagnosis of complex situations under the well, drilling parameter optimization, drilling fluid design, and hydraulic calculation [5; 6]. These applications have provided important technical support and are a guarantee for the development and optimization of the oil industry. The rate of penetration (ROP) is an important indicator affecting the drilling cost and drilling performance. Accurate prediction of the ROP has important guiding significance for increasing the drilling speed and reducing costs. However, drilling engineering operations are complex processes, and the formation, tools, and operating parameters are all important factors affecting the rock breaking by the drill bit [7], such as the formation drillability, drill-bit wear, revolutions per minute, mud performance, weight on bit, etc. [8]. Therefore, it is difficult to accurately predict the ROP. Over the years, technologists around the world have proposed a variety of methods for ROP prediction using logging data, drilling data, and engineering records, mainly including empirical methods and machine learning methods. Compared with empirical methods, machine learning algorithms have obvious technical advantages, especially in high-dimensional nonlinear regression and prediction. In 1974, [PERSON] et al. [9] established a classic ROP prediction model, known as the B-Y model, based on previous experience, combined with field construction data, and considering factors such as the weight on bit, compaction effect, pressure difference, and rotary speed. In 1994, [PERSON] et al. [10] proposed an ROP prediction model considering various drill-bit feature parameters. In 2010, [PERSON] et al. [11] proposed an ROP prediction method suitable for any PDC bit on the basis of [PERSON]'s research, and they achieved good application results. In 2019, [PERSON] et al. [12] and [PERSON] et al. [13] used integrated algorithms to establish ROP prediction models, and they used the goodness of fit as the evaluation indicator of the ROP prediction performance. [PERSON] et al. [14] and [PERSON] et al. [15] used the artificial neural network (ANN) algorithm to establish an ROP prediction model for directional wells. Assuming that the amount of data is sufficient, the ROP prediction accuracy can meet the requirements of the field. In 2021, [PERSON] et al. [16] and [PERSON] et al. [17] used a variety of genetic algorithms to optimize the neural network algorithm, and compared and analyzed the effect of the algorithm from multiple aspects, such as the relative error, R square (R\({}^{2}\)), and mean square error (MSE). [PERSON] et al. [18] used the circular neural network algorithm to predict the rate of penetration based on well logging data and mud logging data, with an accuracy of up to 85%. In 2022, [PERSON] et al. [19] established a prediction model of the ROP based on support vector regression (SVR), and they proposed an improved algorithm to solve the nonconvex problem of determining the optimal values of the model hyperparameters. In 2023, [PERSON] et al. [20] proposed an ROP prediction model based on stacking ensemble learning, and the prediction accuracy rate in specific oilfields reached 92.5%. There are two main types of existing ROP prediction models: empirical models and machine learning models.