Physically Consistent Machine Learning Prediction of Hydrogen Adsorption in Coal Seams: Implications for Underground Hydrogen Storage

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The growing deployment of renewable energy sources has intensified the need for large-scale energy storage solutions capable of managing the supply–demand variability. Underground hydrogen storage (UHS) in coal seams has emerged as a promising option, where adsorption governs the storage capacity and efficiency. However, accurately predicting hydrogen adsorption in coal remains challenging due to the complex, multivariable interactions among thermodynamic conditions and coal’s compositional properties. Experimental approaches are time-consuming and difficult to replicate under subsurface conditions, while molecular dynamics (MD) simulations are computationally demanding and sensitive to force field assumptions. To address these limitations, this work develops a hybrid machine learning model, GMDH-DDE, which couples the group method of data handling with discrete differential evolution, to predict hydrogen adsorption across six coal types. Using a data set of 300 points spanning temperature, pressure, moisture content, volatile matter, and carbon content, the model’s performance was rigorously assessed through 10-fold cross-validation and an independent external data set and compared against three established methods: standalone GMDH, support vector regression (SVR), and a multilayer perceptron (MLP). The proposed GMDH-DDE model achieved superior predictive performance compared with GMDH, SVR, and MLP, with coefficients of determination (R2) of 0.9994 and 0.9984 for the training and testing data sets, respectively, together with the lowest prediction errors, including root-mean-square errors (RMSE) of 0.0112 and 0.0215 and mean absolute errors (MAE) of 0.0014 and 0.0016, respectively. External validation further confirmed excellent generalization, achieving an R2 of 0.9982, an RMSE of 0.0075, and an MAE of 0.0048. Sensitivity analysis identified pressure as the dominant controlling variable, followed by the temperature and carbon content. Moreover, trend analysis confirmed that model predictions are physically consistent with the Langmuir isotherm and Henry’s law across all coal types. These findings establish GMDH-DDE as a reliable, computationally efficient, and physically consistent alternative to experimental and simulation-based methods for estimating hydrogen adsorption with significant potential for the design and optimization of coal-based UHS systems.