Adaptive Physics-Informed Neural Networks with Multi-Category Feature Engineering for Hydrogen Sorption Prediction in Clays, Shales, and Coals

Abstract

Accurate prediction of hydrogen sorption in clays, shales, and coals is vital for advancing underground hydrogen storage, natural hydrogen exploration, and radioactive waste containment. Traditional experimental methods, while foundational, are time-consuming, error-prone, and limited in capturing geological heterogeneity. This study introduces an adaptive physics-informed neural network (PINN) framework with multi-category feature engineering to enhance hydrogen sorption prediction. The framework integrates classical isotherm models with thermodynamic constraints to ensure physical consistency while leveraging deep learning flexibility. A comprehensive dataset consisting of 155 samples, which includes 50 clays, 60 shales, and 45 coals, was employed, incorporating diverse compositional properties and experimental conditions. Multi-category feature engineering across seven categories captured complex sorption dynamics. The PINN employs deep residual networks with multi-head attention, optimized via adaptive loss functions and Monte Carlo dropout for uncertainty quantification. K-fold cross-validation and hyperparameter optimization achieve significant accuracy (R2 = 0.979, RMSE = 0.045 mol per kg) with 67% faster convergence despite 15-fold increased complexity. The framework demonstrates robust lithology-specific performance across clay minerals (R2 = 0.981), shales (R2 = 0.971), and coals (R2 = 0.978), maintaining 85-91% reliability scores. Interpretability analysis via SHAP, accumulated local effects, and Friedman's H-statistics reveal that hydrogen adsorption capacity dominates predictions, while 86.7% of feature pairs exhibit strong interactions, validating the necessity of non-linear modeling approaches. This adaptive physics-informed framework accelerates site screening and enables risk-informed decision-making through robust uncertainty quantification.