Thermodynamically Constrained Deep Learning for Hydrogen Sorption Prediction: Overcoming Classical Isotherm Generalization Failure through Physics-Informed Cross-Lithology Transferability

Abstract Accurate prediction of hydrogen sorption in fine-grained geological materials is essential for subsurface energy systems. While classical isotherm models describe individual samples effectively, they fail to generalize across heterogeneous populations, with R2 dropping from 0.80–0.90 for single-sample fits to 0.09–0.38 for aggregated data sets. This limitation demonstrates that predictive models must explicitly account for intrinsic material properties and fundamental physical constraints. We present a thermodynamics-informed, physics-regularized neural network framework designed to improve predictive accuracy and cross-lithology generalization. The framework integrates three core components: a seven-category physics-informed feature engineering scheme generating 62 thermodynamically meaningful descriptors, a multiterm loss function enforcing saturation limits and monotonic pressure responses through penalty-weighted terms, and an architecture-diverse ten-member ensemble with post hoc temperature-scaling calibration to provide reliable uncertainty estimates. Van’t Hoff temperature dependence is incorporated through thermodynamic feature engineering, with all model components integrated within a three-phase curriculum training strategy that progressively introduces physical regularization. On a random-split holdout set, the framework achieves R2 = 0.9544, RMSE = 0.0484 mmol/g, and MAE = 0.0231 mmol/g, with a 98.6% monotonicity satisfaction rate and zero nonphysical negative predictions. Because random splits primarily evaluate interpolation within the observed distribution, we prioritize leave-one-lithology-out (LOLO) validation to assess physical generalization under distribution shift. When entire geological classes are withheld from training, the framework retains R2 = 0.723 for coal and 0.794 for shale, outperforming a well-tuned random forest baseline (R2 = 0.631 and 0.712, respectively) by 14.6% and 11.5%, respectively. These results support the effectiveness of thermodynamic constraints as a generalization scaffold across geological boundaries, providing a practical foundation for evaluating formations whose lithological classes are absent from the training data.