## 1 Introduction  
Perforation completion is a prominent technique utilized in the oil and gas industry for completing wells in oil and gas fields. It has gained significant popularity and widespread application in the global petroleum sector. The productivity ratio is a vital metric used to assess the efficiency of perforated completions and serves as a fundamental basis for optimizing the parameters associated with the perforation process. Extensive research has been conducted to investigate the productivity ratio or productivity of wells that have undergone perforation completion [1; 2; 3; 4; 5]. Currently, the commonly employed methods for predicting the productivity ratio or productivity of such wells include physical experimental methods, semi-analytical methods, and numerical simulation methods. Physical experimental methods involve artificial rock sample simulation experiments [6; 7] and electrical analog experiments [8]. However, these methods have drawbacks such as implementation difficulties, long cycles, and high costs. Semi-analytical methods [9; 10] derive formulas based on various assumptions, which often include empirical coefficients related to perforation parameters. These coefficients are challenging to obtain onsite or accurately predict, resulting in low prediction accuracy. On the other hand, numerical simulation methods [11; 12; 13; 14; 15] can replicate the physical processes of reservoir exploitation but require extensive data on oilfield geology and development, which are often difficult to obtain or have significant uncertainties. This limitation severely impacts the accuracy of a numerical simulation. Additionally, numerical simulation methods demand substantial computational resources, have long processing times, low efficiency, and necessitate prediction personnel with a solid foundation in numerical simulation, posing inconveniences for engineering applications. Some researchers [16; 17] have performed regression analysis on productivity ratio data obtained from numerical simulation and derived simple linear or nonlinear fitting formulas. However, due to the numerous influencing factors and complex relationships involved in the productivity ratio, these fitting formulas obtained through simple regression often exhibit high errors and limited applicability. Consequently, there is an urgent need to explore a simpler, more efficient, and data-driven method for predicting the productivity ratio of perforated wells. In recent years, machine learning techniques have rapidly developed in the field of petroleum engineering. Their applications involve reservoir characterization and evaluation [18; 19], lithology classification and geological modeling [20; 21], reservoir fluid property prediction [22; 23], production optimization and intelligent decision making [24; 25], and fault prediction and maintenance [26; 27], providing new approaches for the productivity ratio prediction of perforated wells. Commonly used machine learning regression algorithms include artificial neural networks (ANN) [28; 29; 30], support vector machines (SVM) [31; 32; 33], decision trees (DT) [34; 35; 36], and random forests (RF) [37; 38; 39]. However, these methods have certain issues. ANN often require long training times, especially when dealing with large-scale datasets. Moreover, they and algorithms like DT tend to have high model complexity, which makes them susceptible to overfitting the training set and, consequently, leads to decreased performance on the test set. Additionally, these algorithms have multiple hyperparameters that need to be adjusted, making model optimization a complex task. Although support vector machines can overcome some of these drawbacks, they also have limitations in practical applications, such as the presence of noise in training data and the inability to handle nonlinear problems. In contrast, least squares support vector machine (LSSVM) offers several advantages.