Zezhang Song

Mohammad Nooraiepour, Mohammad Masoudi, Zezhang Song et al.

Accurate prediction of hydrogen sorption in fine-grained geological materials is essential for evaluating underground hydrogen storage capacity, assessing caprock integrity, and characterizing hydrogen migration in subsurface energy systems. Classical isotherm models perform well at the individual-sample level but fail when generalized across heterogeneous populations, with the coefficient of determination collapsing from 0.80-0.90 for single-sample fits to 0.09-0.38 for aggregated multi-sample datasets. We present a multi-scale physics-informed neural network framework that addresses this limitation by embedding classical adsorption theory and thermodynamic constraints directly into the learning process. The framework utilizes 1,987 hydrogen sorption isotherm measurements across clays, shales, coals, supplemented by 224 characteristic uptake measurements. A seven-category physics-informed feature engineering scheme generates 62 thermodynamically meaningful descriptors from raw material characterization data. The loss function enforces saturation limits, a monotonic pressure response, and Van't Hoff temperature dependence via penalty weighting, while a three-phase curriculum-based training strategy ensures stable integration of competing physical constraints. An architecture-diverse ensemble of ten members provides calibrated uncertainty quantification, with post-hoc temperature scaling achieving target prediction interval coverage. The optimized PINN achieves R2 = 0.9544, RMSE = 0.0484 mmol/g, and MAE = 0.0231 mmol/g on the held-out test set, with 98.6% monotonicity satisfaction and zero non-physical negative predictions. Physics-informed regularization yields a 10-15% cross-lithology generalization advantage over a well-tuned random forest under leave-one-lithology-out validation, confirming that thermodynamic constraints transfer meaningfully across geological boundaries.

Mohammad Nooraiepour, Zezhang Song, Wei Li et al.

Accurate methane sorption prediction across heterogeneous coal ranks requires models that combine thermodynamic consistency, efficient knowledge transfer across data-scarce geological systems, and calibrated uncertainty estimates, capabilities that are rarely addressed together in existing frameworks. We present a physics-informed transfer learning framework that adapts a hydrogen sorption PINN to methane sorption prediction via Elastic Weight Consolidation, coal-specific feature engineering, and a three-phase curriculum that progressively balances transfer preservation with thermodynamic fine-tuning. Trained on 993 equilibrium measurements from 114 independent coal experiments spanning lignite to anthracite, the framework achieves R2 = 0.932 on held-out coal samples, a 227% improvement over pressure-only classical isotherms, while hydrogen pre-training delivers 18.9% lower RMSE and 19.4% faster convergence than random initialization. Five Bayesian uncertainty quantification approaches reveal a systematic divergence in performance across physics-constrained architectures. Monte Carlo Dropout achieves well-calibrated uncertainty at minimal overhead, while deep ensembles, regardless of architectural diversity or initialization strategy, exhibit performance degradation because shared physics constraints narrow the admissible solution manifold. SHAP and ALE analyses confirm that learned representations remain physically interpretable and aligned with established coal sorption mechanisms: moisture-volatile interactions are most influential, pressure-temperature coupling captures thermodynamic co-dependence, and features exhibit non-monotonic effects. These results identify Monte Carlo Dropout as the best-performing UQ method in this physics-constrained transfer learning framework, and demonstrate cross-gas transfer learning as a data-efficient strategy for geological material modeling.

Mohammad Nooraiepour, Mohammad Masoudi, Zezhang Song et al.

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.