Thermodynamically Constrained Deep Learning for Hydrogen Sorption Prediction: Overcoming Classical Isotherm Generalization Failure through Physics-Informed Cross-Lithology Transferability
- 1University of Oslo , , P.O. Box 1047 Blindern , ,
- 2SINTEF Industry , , S P Andersens Vei 15B , ,
- 3China University of Petroleum (Beijing) , , ,
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.
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BibTeX
@article{nooraiepour2026thermodynamically,
title = {{Thermodynamically Constrained Deep Learning for Hydrogen Sorption Prediction: Overcoming Classical Isotherm Generalization Failure through Physics-Informed Cross-Lithology Transferability}},
author = {Mohammad Nooraiepour and Mohammad Masoudi and Zezhang Song and Helge Hellevang},
journal = {ACS Omega},
year = {2026},
month = nov,
doi = {10.1021/acsomega.6c08678},
url = {https://pubs.acs.org/acsodf/article/doi/10.1021/acsomega.6c08678/5462543/Thermodynamically-Constrained-Deep-Learning-for},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Thermodynamically Constrained Deep Learning for Hydrogen Sorption Prediction: Overcoming Classical Isotherm Generalization Failure through Physics-Informed Cross-Lithology Transferability
AU - Mohammad Nooraiepour
AU - Mohammad Masoudi
AU - Zezhang Song
AU - Helge Hellevang
PY - 2026
DA - 2026/11/03
JO - ACS Omega
DO - 10.1021/acsomega.6c08678
UR - https://pubs.acs.org/acsodf/article/doi/10.1021/acsomega.6c08678/5462543/Thermodynamically-Constrained-Deep-Learning-for
AB - 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.
SN - 2470-1343
ER -