A synergistic framework for shale volume prediction combining physics and data-driven models

• Developed hybrid physics–machine learning models for shale volume estimation. • Achieved superior performance using ANN with residual learning correction. • Validated models using core XRD data and unseen well logs from Iranian field. • Identified neutron porosity and sonic logs as key predictive features. • Hybrid ANN model outperformed classical and standalone ML approaches. Accurate shale volume estimation plays a critical role in petrophysical analysis, influencing porosity, water saturation, and reservoir evaluation. This study presents a comparative and integrative framework that evaluates three classical methods, two machine learning (ML) models, and two hybrid physics–ML models to enhance shale volume prediction in a heterogeneous carbonate reservoir in southern Iran. Well-log and core-derived X-ray diffraction (XRD) data from two wells were utilized: Well #1 (2395 points) for model development and Well #4 (1738 unseen points) for evaluation. After preprocessing—including outlier removal, normalization, and correlation-based feature selection—four key logs (neutron, sonic, density, and resistivity) were retained. Three classical methods (neutron, neutron-density, and sonic-density) yielded moderate accuracy, with the best-performing model (neutron-density) achieving RMSE = 0.119 and R² = 0.85 on the evaluation data. Standalone ML models, particularly artificial neural networks (ANNs), significantly improved performance, achieving RMSE = 0.088, MAE = 0.065, and R² = 0.92. The random forest (RF) model had RMSE = 0.105 and R² = 0.89. The hybrid models, constructed by correcting physical model residuals with ML predictions, delivered the best results. The hybrid ANN achieved RMSE = 0.062, MAE = 0.046, and R² = 0.95, whereas the hybrid RF yielded RMSE = 0.082 and R² = 0.93. Sensitivity analysis identified neutron porosity (NPHI) and sonic transit time (DT) as the most influential features, with relevancy factors above 0.75, whereas bulk density (RHOB) and shallow resistivity (LLS) had weaker or negative correlations. This study demonstrates that hybrid physics–ML models outperform both classical and standalone ML approaches in shale volume estimation, particularly in geologically complex carbonate environments. The methodology’s accuracy, interpretability, and robustness highlight its potential for broader applications in reservoir characterization.