关键词: 科学范式, 物理引导, 深度学习, 模型融合, 控制方程

Abstract: While deep learning has significant achievements in addressing nonlinear high-dimensional problems, it faces challenges in complex scientific and engineering domains (such as high computational costs and data requirements, the difficulty in interpreting its black-box nature, and the lack of capabilities for following the physical laws). Therefore, a novel framework called physics-guided deep learning has emerged which enhances the performance, interpretability, and adherence to actual physical laws of deep learning by integrating domain-specific physics knowledge into the construction and training process of deep learning models. This paper reviewed and analyzed the researches (e.g., methodologies, applications, etc.) on physics-guided deep learning thoroughly. Firstly, the main motivations and theoretical foundations of the physics-guided deep learning are introduced. Secondly, a detailed discussion is conducted on the two modes: the combination of physical information with deep learning and the fusion of physical information with deep learning. The characteristics, limitations and application scenarios of the two modes are summarized and discussed. Finally, the performance of physics-guided deep learning across various applications are analyzed. Furthermore, the challenges the physics-guided deep learning are discussed from four perspectives: computational cost, convergence, biases in control equations, and dependence on observational data, aiming to provide an outlook on the future direction of this domain.

Key words: scientific paradigm, physics-guided, deep learning, model fusion, governing equations