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From Data-Driven to Geology-Informed Learning: Geometry-Aware Graph Transformer Learning for Geo-Energy Systems
1
Lincoln University College, Petaling Jaya 47301, Selangor, Malaysia
* Corresponding Author:
Jinghan Li,
[email protected]
Volume 3, Issue 1
2027
Received: 25 August 2026
Revised: 19 September 2026
Accepted: 29 September 2026
Published: 22 October 2026
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CC BY 4.0 License
Article Information
Abstract
Geo-energy systems involve heterogeneous subsurface properties, irregular spatial structures, and complex interactions. Conventional data-driven models either treat observations independently or rely on graph connectivity without explicitly encoding relative geometry, which limits their ability to distinguish spatially different configurations. This study develops a Geometry-Aware Graph Transformer (GAGT) that integrates node attributes, graph structure, and relative geometric information through a learnable geometric bias in the attention mechanism. A controlled synthetic experiment with 300 irregularly distributed three-dimensional nodes compares a multilayer perceptron (MLP), a Graph Transformer (GT), and GAGT under identical settings. Across 10 random seeds, GAGT achieved a mean absolute error (MAE) of 0.1569, a root mean square error (RMSE) of 0.2152, and a coefficient of determination ($R^2$) of 0.8678, reducing MAE and RMSE by 35.77% and 33.95%, respectively, relative to GT. In this controlled setting, explicit geometry therefore carries predictive information that graph connectivity alone does not provide. GAGT can serve as a geometry-aware representation layer between purely data-driven learning and more comprehensive geology-informed modeling; validation with real geological data and physically constrained simulations is still required.
Graphical Abstract
Keywords
geo-energy systems
geometry-aware learning
graph Transformer
subsurface modeling
geology-informed artificial intelligence
Data Availability Statement
The data generated and analyzed in this study are available from the corresponding author upon reasonable request. The synthetic data can be regenerated from the settings described in Section 4.
Funding
This work was supported without any funding.
Conflicts of Interest
The author declares no conflicts of interest.
AI Use Statement
The author declares that no generative AI was used in the preparation of this manuscript.
Ethical Approval and Consent to Participate
Not applicable. This study did not involve human participants, animals, personal data, or identifiable individual information.
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APA Style
Li, J. (2026). From Data-Driven to Geology-Informed Learning: Geometry-Aware Graph Transformer Learning for Geo-Energy Systems. Journal of Geo-Energy and Environment, 3(1), 72-83. https://doi.org/10.62762/JGEE.2026.158449
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TY - JOUR AU - Li, Jinghan PY - 2026 DA - 2026/10/22 TI - From Data-Driven to Geology-Informed Learning: Geometry-Aware Graph Transformer Learning for Geo-Energy Systems JO - Journal of Geo-Energy and Environment T2 - Journal of Geo-Energy and Environment JF - Journal of Geo-Energy and Environment VL - 3 IS - 1 SP - 72 EP - 83 DO - 10.62762/JGEE.2026.158449 UR - https://www.icck.org/article/abs/JGEE.2026.158449 KW - geo-energy systems KW - geometry-aware learning KW - graph Transformer KW - subsurface modeling KW - geology-informed artificial intelligence AB - Geo-energy systems involve heterogeneous subsurface properties, irregular spatial structures, and complex interactions. Conventional data-driven models either treat observations independently or rely on graph connectivity without explicitly encoding relative geometry, which limits their ability to distinguish spatially different configurations. This study develops a Geometry-Aware Graph Transformer (GAGT) that integrates node attributes, graph structure, and relative geometric information through a learnable geometric bias in the attention mechanism. A controlled synthetic experiment with 300 irregularly distributed three-dimensional nodes compares a multilayer perceptron (MLP), a Graph Transformer (GT), and GAGT under identical settings. Across 10 random seeds, GAGT achieved a mean absolute error (MAE) of 0.1569, a root mean square error (RMSE) of 0.2152, and a coefficient of determination ($R^2$) of 0.8678, reducing MAE and RMSE by 35.77% and 33.95%, respectively, relative to GT. In this controlled setting, explicit geometry therefore carries predictive information that graph connectivity alone does not provide. GAGT can serve as a geometry-aware representation layer between purely data-driven learning and more comprehensive geology-informed modeling; validation with real geological data and physically constrained simulations is still required. SN - 3069-3268 PB - Institute of Central Computation and Knowledge LA - English ER -
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@article{Li2026From,
author = {Jinghan Li},
title = {From Data-Driven to Geology-Informed Learning: Geometry-Aware Graph Transformer Learning for Geo-Energy Systems},
journal = {Journal of Geo-Energy and Environment},
year = {2026},
volume = {3},
number = {1},
pages = {72-83},
doi = {10.62762/JGEE.2026.158449},
url = {https://www.icck.org/article/abs/JGEE.2026.158449},
abstract = {Geo-energy systems involve heterogeneous subsurface properties, irregular spatial structures, and complex interactions. Conventional data-driven models either treat observations independently or rely on graph connectivity without explicitly encoding relative geometry, which limits their ability to distinguish spatially different configurations. This study develops a Geometry-Aware Graph Transformer (GAGT) that integrates node attributes, graph structure, and relative geometric information through a learnable geometric bias in the attention mechanism. A controlled synthetic experiment with 300 irregularly distributed three-dimensional nodes compares a multilayer perceptron (MLP), a Graph Transformer (GT), and GAGT under identical settings. Across 10 random seeds, GAGT achieved a mean absolute error (MAE) of 0.1569, a root mean square error (RMSE) of 0.2152, and a coefficient of determination (\$R^2\$) of 0.8678, reducing MAE and RMSE by 35.77\% and 33.95\%, respectively, relative to GT. In this controlled setting, explicit geometry therefore carries predictive information that graph connectivity alone does not provide. GAGT can serve as a geometry-aware representation layer between purely data-driven learning and more comprehensive geology-informed modeling; validation with real geological data and physically constrained simulations is still required.},
keywords = {geo-energy systems, geometry-aware learning, graph Transformer, subsurface modeling, geology-informed artificial intelligence},
issn = {3069-3268},
publisher = {Institute of Central Computation and Knowledge}
}
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