Modeling complex physical dynamics is a fundamental task in science and
engineering. Traditional physics-based models are sample efficient, and
interpretable but often rely on rigid assumptions. Furthermore, direct
numerical approximation is usually computationally intensive, requiring
significant computational resources and expertise, and many real-world systems
do not have fully-known governing laws. While deep learning (DL) provides novel
alternatives for efficiently recognizing complex patterns and emulating
nonlinear dynamics, its predictions do not necessarily obey the governing laws
of physical systems, nor do they generalize well across different systems.
Thus, the study of physics-guided DL emerged and has gained great progress.
Physics-guided DL aims to take the best from both physics-based modeling and
state-of-the-art DL models to better solve scientific problems. In this paper,
we provide a structured overview of existing methodologies of integrating prior
physical knowledge or physics-based modeling into DL, with a special emphasis
on learning dynamical systems. We also discuss the fundamental challenges and
emerging opportunities in the area.

本文概述了将先验物理知识或基于物理建模方法与深度学习相结合的现有方法，并重点讨论了在学习动力系统方面所面对的基本挑战和新兴机遇。