Abstract: Accurate prediction of the rate of penetration (ROP) is significant for drilling optimization. While the intelligent ROP prediction model based on fully connected neural networks (FNN) outperforms traditional ROP equations and machine learning algorithms, its lack of interpretability undermines its credibility. This study proposes a novel interpretation and characterization method for the FNN ROP prediction model using the Rectified Linear Unit (ReLU) activation function. By leveraging the derivative of the ReLU function, the FNN function calculation process is transformed into vector operations. The FNN model is linearly characterized through further simplification, enabling its interpretation and analysis. The proposed method is applied in ROP prediction scenarios using drilling data from three vertical wells in the Tarim Oilfield. The results demonstrate that the FNN ROP prediction model with ReLU as the activation function performs exceptionally well. The relative activation frequency curve of hidden layer neurons aids in analyzing the overfitting of the FNN ROP model and determining drilling data similarity. In the well sections with similar drilling data, averaging the weight parameters enables linear characterization of the FNN ROP prediction model, leading to the establishment of a corresponding linear representation equation. Furthermore, the quantitative analysis of each feature's influence on ROP facilitates the proposal of drilling parameter optimization schemes for the current well section. The established linear characterization equation exhibits high precision, strong stability, and adaptability through the application and validation across multiple well sections.