Hybrid-driven prediction method for wellbore stability integrating mechanistic models and multi-task learning

Accurate prediction of collapse and fracture pressures is crucial for well trajectory design, wellbore stability control, and efficient drilling operations. Traditional numerical and analytical methods are often computationally complex and inefficient, while purely data-driven models, although faster, suffer from pronounced black-box characteristics and lack interpretability, which limits their engineering applicability. To overcome these challenges, this study proposes a hybrid-driven prediction method that integrates wellbore stability mechanistic models with a multi-task learning framework (MW-MMoE). In this approach, stress coordinate transformation is embedded as physical prior knowledge at the input stage, while the output targets are reconstructed by first predicting key stress components and then converting them into equivalent densities of collapse and fracture pressures through physical formulations. The Mohr-Coulomb criterion is further incorporated into the loss function as a physical constraint. The model architecture leverages a multi-gated mixture-of-experts network combined with the GradNorm algorithm to dynamically adjust task weights and balance gradients during training. Ablation experiments demonstrate that the proposed MW-MMoE achieves mean absolute errors as low as 0.0019 g/cm³ and 0.0033 g/cm³ for collapse and fracture pressure equivalent densities, respectively, significantly outperforming both single-task and conventional multi-task models, while achieving over a hundredfold improvement in computational efficiency compared with analytical methods. Case studies further validate its engineering applicability: the model can rapidly generate collapse and fracture pressure equivalent density curves for individual wells, produce high-resolution contour maps under arbitrary well inclinations, azimuths, and stress conditions, and perform large-scale three-dimensional predictions across the entire study area. These results highlight that the MW-MMoE model combines high accuracy, efficiency, and interpretability, providing a novel and practical solution for intelligent wellbore stability prediction with broad application prospects.