Learning dynamical systems from data: An introduction to physics-guided deep learning

Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are first-principled, explainable, and sample-efficient. However, they often rely on strong modeling assumptions and expensive numerical integration, requiring significant computational resources and domain expertise. While deep learning (DL) provides efficient alternatives for modeling complex dynamics, they require a large amount of labeled training data. Furthermore, its predictions may disobey the governing physical laws and are difficult to interpret. Physics-guided DL aims to integrate first-principled physical knowledge into data-driven methods. It has the best of both worlds and is well equipped to better solve scientific problems. Recently, this field has gained great progress and has drawn considerable interest across discipline Here, we introduce the framework of physics-guided DL with a special emphasis on learning dynamical systems. We describe the learning pipeline and categorize state-of-the-art methods under this framework. We also offer our perspectives on the open challenges and emerging opportunities.