Review of applications of Physics-Informed Neural Networks in hydrogeology and engineering geology

Abstract

[Objective] In the research on hydrogeology and engineering geology, traditional mechanism-based numerical models often exhibit issues such as low modeling accuracy and high uncertainty when simulating complex physical processes, while machine learning models are limited by their substantial data demands and poor interpretability. Physics-Informed Neural Networks(PINNs), as a new computational method that combines physical laws and machine learning, can provide a feasible solution to the above-mentioned problems. [Methods] Firstly, recent literature from the past four years is systematically reviewed to summarize the current research status of mechanism-based numerical models, machine learning models, and mechanism-learning coupled models in the fields of hydrogeology and engineering geology. Secondly, an in-depth analysis of PINNs' latest applications in these fields is conducted. Finally, the existing limitations of PINNs in the fields of hydrogeology and engineering geology are expounded, and recommendations for future development are proposed. [Results] It is found that PINNs have partially addressed issues in numerical models and machine learning models, such as data scarcity, poor interpretability, and insufficient generalizability, demonstrating broad application prospects in hydrogeology and engineering geology. Future efforts should focus on resolving existing problems in robustness, adaptive weight allocation, and initial and boundary condition processing to further tap into their potential. [Conclusion] In future research, the following recommendations for further development are proposed. Generative models or reinforcement learning should be coupled to reduce the impact of data quality and noise on the model, thereby enhancing robustness. Adaptive learning algorithms and dynamic weight balancing mechanisms should be employed to balance the weights of each term in the loss function and ensure the output matrix of the PINNs model satisfies orthogonal conditions, thereby improving computational efficiency. Considering the actual situation, methods such as the activation function and constraint methods should be optimized for selection to achieve faster convergence and higher accuracy in PINN modeling.

Keywords

Physics-Informed Neural Networks / numerical model / machine learning / coupled model / groundwater / hydrogeology / numerical simulation / engineering geology