A comprehensive review of physics-informed deep learning and its applications in geoenergy development
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PUBLIC SUMMARY
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Physics-informed deep learning (PIDL) integrates physical laws with deep learning.
Advances in loss weighting, network design, and PDE integration enhance geoenergy simulations.
PIDL excels in surrogate modeling and inverse modeling for subsurface resource management.
Case studies highlight PIDL's potential as a powerful tool in geoenergy system modeling.
Challenges remain in PIDL's costs, generalization, tuning, and physics-AI balance for complex geoenergy systems.
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ABSTRACT
Deep learning models have been widely utilized in various scientific and engineering problems; however, their application still faces practical challenges, including high data volume requirements, limited physical consistency, and insufficient interpretability. Physics-informed deep learning (PIDL) has emerged as a promising paradigm to address these challenges by incorporating physical laws into the training process of deep learning models. By integrating data-driven approaches with physics-based constraints, PIDL enhances the accuracy and reliability of deep learning models, making it a powerful tool across diverse fields. Numerous variants of PIDL models have been developed to cater to different applications. This review provides a comprehensive examination of recent advancements in PIDL, with a particular focus on its applications in geoenergy development. We discuss key methodologies underlying PIDL, including weighting strategies in loss functions, network architectures, derivative calculations, and various forms of physical equations. Furthermore, we summarize the three most common application scenarios of PIDL models, including solving partial differential equations (PDEs), surrogate modeling, and inverse modeling. A series of case studies highlighting PIDL’s role in geoenergy development are also presented. Finally, current challenges and future directions of PIDL in the geoenergy field are summarized. This review aims to serve as a foundational and valuable resource for researchers and practitioners newly entering this field, while also highlighting the potential of PIDL in advancing geoenergy development. -
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Wang N., Chen Y. and Zhang D. (2025). A comprehensive review of physics-informed deep learning and its applications in geoenergy development. The Innovation Energy 2:100087. https://doi.org/10.59717/j.xinn-energy.2025.100087
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Wang N., Chen Y. and Zhang D. (2025). A comprehensive review of physics-informed deep learning and its applications in geoenergy development. The Innovation Energy 2:100087. https://doi.org/10.59717/j.xinn-energy.2025.100087
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Figure 1.
Timeline of the development of PINN models, based on their initial publication in arXiv preprints or peer-reviewed journals.
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Figure 2.
The role of physics-informed deep learning models in the geoenergy production process.
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Figure 3.
(A) Schematic diagram of the physics-informed neural network (PINN); (B) Automatic differentiation for fully connected neural networks (FCNN); (C) Automatic differentiation for convolutional neural networks (CNN); (D) Derivative calculation using the finite difference method for CNN.
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Figure 4.
Schematic diagram of the variational physics-informed neural network (VPINN).34
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Figure 5.
Application scenarios of physics-informed deep learning models.
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Figure 6.
(A) Surrogate modeling based on physics-informed neural network. (B) Direct inversion with multiple physics-informed neural networks.
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Figure 7.
Schematic diagram of TgCNN for two-phase flow problems.57
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Figure 8.
Schematic diagram of physics-informed LSTM for prediction of pressure, gas saturation and water production in GCS problems.93
