Gated multilayer perceptron Bayesian fusion network: A geological uncertainty-aware network for rate of penetration prediction in the nonlinear dynamic system of drill string-formation

Accurate prediction of rate of penetration (ROP) under complex geological conditions is a critical task in geological drilling operations, yet it remains challenging due to the nonlinear relationship of drill string dynamics and uncertainty inherent in subsurface formations. This paper proposes a gated MLP (multilayer perceptron)–Bayesian fusion network (G-BFNet) model, which integrates gated MLP architecture with Bayesian probabilistic inference to enhance prediction accuracy and quantify geological uncertainty (GU) in ROP forecasting. First, a dual-channel structure is designed to decouple engineering parameters and geological inputs, where geological features are modeled independently via a Bayesian neural network to ensure uncertainty originates solely from formation variability. Then, a spatial gating unit is employed to capture depth-dependent lithological transitions, while a sliding window mechanism enables dynamic adaptation to drilling depth changes. Experimental results based on field data from four wells show that G-BFNet consistently outperforms state-of-the-art baseline models across multiple prediction horizons (5, 10, and 15 m), with improved generalization and robustness in areas with interbedded formations and fault zones. Compared to existing models, the mean squared error and mean absolute error of G-BFNet are reduced by 33.2% and 27.6%, respectively. Furthermore, the proposed model provides uncertainty intervals that accurately reflect subsurface structural complexity, offering valuable support for real-time drilling risk assessment and decision-making. This work demonstrates the potential of GU–aware models for reliable and interpretable ROP prediction in complex drilling environments.