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

摘要： 尽管深度学习在处理非线性高维问题时展现出强大的能力，但在复杂科学与工程问题中仍面临诸多挑战，如高昂的计算成本、大量的数据需求、难以解释的黑盒特性，以及缺乏对物理规律的建模能力.为此，近年来涌现了一种新的框架——物理引导深度学习，通过将领域内的物理知识融入深度学习模型的构建和训练过程中，旨在增强模型的性能、可解释性及其物理一致性.本文对国内外关于物理引导深度学习的相关工作进行了全面梳理与分析.首先，介绍了物理引导深度学习框架的主要动机与理论基础.其次，对物理信息组合与物理信息融合两种模式进行了详细讨论，总结了各方法的特点、局限性与应用场景.最后，分析了物理引导深度学习在多领域应用中的表现，并从计算复杂性与优化收敛问题、控制方程偏离问题、观测数据依赖问题与知识融合困难问题四个方面探讨了该框架目前面临的挑战，并基于此展望该领域未来的发展方向，为未来研究者提供了借鉴思路及多维度视角.

关键词: 科学范式, 物理引导, 深度学习, 模型融合, 控制方程