Predicting methane adsorption in coal and shale with white-box and black-box machine learning models

Accurate prediction of methane (CH4) adsorption in coal and shale formations is essential for optimizing gas extraction, enhancing storage efficiency, mitigating greenhouse gas emissions, and ensuring safe mining and unconventional reservoir development. In this study, the most comprehensive dataset reported to date was compiled to model CH4 adsorption in coal and shale systems, using pressure (P), moisture content (M), and total organic carbon (TOC) as inputs for coal, and temperature (T), moisture content (M), and TOC for shale. To simultaneously achieve high predictive accuracy and physical interpretability, three transparent white-box models gene expression programming (GEP), group method of data handling (GMDH), and genetic programming (GP) and three advanced black-box models Gaussian process regression (GPR), categorical boosting (CatBoost), and light gradient boosting machine (LightGBM) were developed and systematically evaluated. The white-box models successfully produced explicit, closed-form mathematical correlations that directly link CH4 adsorption to key controlling parameters, providing transparent, physically interpretable tools that can be readily applied without specialized software. In parallel, the black-box models were employed to benchmark predictive performance, with CatBoost achieving the best overall accuracy, yielding mean squared errors (MSE) of 0.008 and 0.004 and coefficients of determination (R2) of 0.924 and 0.997 for coal and shale, respectively. Model interpretability was further enhanced using SHapley Additive exPlanations (SHAP), which consistently identified TOC as the dominant factor governing CH4 adsorption in both systems, while leverage-based outlier analysis confirmed the robustness of the optimal models, with more than 99% of coal data and over 95% of shale data falling within the applicability domain. Notably, this work represents the first application of GEP, GMDH, and GP to derive transparent, user-friendly analytical expressions for CH4 adsorption in coal, offering a practical and interpretable alternative to purely black-box machine-learning approaches.