Interpretable rate-of-penetration prediction using a Bayesian-optimized MAML-LSTM-Transformer under small-sample conditions

Well drilling relies on the rate of penetration (ROP) as a core indicator of efficiency. Accurate ROP prediction is vital for enhancing the extraction efficiency, optimizing the drilling process and reducing the production costs. However, drilling in deep and ultra-deep reservoirs faces three major challenges: (1) the available data are sparse, (2) the dynamic drilling characteristics exhibit complicated nonlinear behavior and strong coupling among drilling variables, and (3) existing models often show limited generalization ability and lack interpretability. To overcome these limitations, we propose a Bayesian-optimized meta-learning framework that couples an LSTM-Transformer base learner with Model-Agnostic Meta-Learning (MAML) and Bayesian Optimization (BO). First, the time series data from multiple drilling wells are organized as related tasks, and an LSTM-Transformer hybrid network is constructed to capture short-term temporal variations together with global sequence-level interactions among drilling parameters. Subsequently, MAML is employed to learn a task-agnostic initialization across wells, enabling rapid adaptation of the base learner to a previously unseen well through several gradient steps. Then, BO is integrated to systematically tune key hyperparameters of both the base learner (e.g., LSTM units, Transformer heads) and the meta-learning process (e.g., inner/out-loop learning rate). Finally, Shapley Additive exPlanations (SHAP) are used to quantify the contributions of operational and geological/logging variables to the predicted ROP, providing both global and local interpretability. The proposed framework is experimentally validated on field drilling datasets from multiple oil wells, including experiments with noisy data and an out-of-domain dataset to assess cross-well generalization. The findings show that the Bayesian-optimized MAML-LSTM-Transformer consistently outperforms conventional learning baselines, achieving on the test set an R 2 of 0.876, an RMSE of 1.687 m/h, an MAE of 1.324 m/h, and a MAPE of 9.056%. Overall, the results support the proposed framework as an effective and practically deployable solution for small-sample, cross-well ROP prediction. • A Bayesian-optimized MAML-LSTM-Transformer is developed for data-scarce, cross-well ROP prediction. • BO is integrated to automatically optimize key architectural and meta-learning hyperparameters. • Field validation on noisy data and unseen wells is conducted, and, besides the SHAP-based explanations, this validation demonstrates improved accuracy and interpretability.