A comprehensive review of physics-informed deep learning and its applications in geoenergy development

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.