Physics-Guided Deep Learning for Dynamical Systems: A Survey

Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are interpretable but rely on rigid assumptions. And the direct numerical approximation is usually computationally intensive, requiring significant computational resources and expertise. While deep learning (DL) provides novel alternatives for efficiently recognizing complex patterns and emulating nonlinear dynamics, it does 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. It 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 and discuss the emerging opportunities.