A correlation-based modeling algorithm is proposed to address the prediction and optimization of the rate of penetration in the drilling process. By analyzing 21,912 data points from ten oil and gas wells, the data were preprocessed, including the removal of irrelevant parameters, filling missing values, handling outliers, data smoothing, and normalization to ensure data quality and reliability. Subsequently, four correlation calculation methods (Pearson/ Spearman/ Kendall/Chatterjee) were used to analyze the relationships between various drilling parameters and ROP, revealing that parameters such as drilling fluid density, solid-phase content, and pump rate significantly impact ROP. In the modeling approach, two regression models, Multi-Layer Perceptron (MLP) and Random Forest (RF), were employed, and different quantities of correlation parameters were used for training and validation. The results show that Pearson's method performs best in the MLP model, while the performance of all algorithms in the RF model remains stable with an R2 value reaching 0.96. Additionally, the RF model outperforms the MLP model. The findings indicate that correlation analysis not only effectively extracts key parameters affecting ROP but also optimizes the modeling process. By combining machine learning and feature selection techniques, this study provides an intelligent new approach for ROP prediction and optimization and offers theoretical support for practical drilling engineering.