Physics-Guided Deep Learning for Dynamical Systems: A Survey

TL;DR

This survey reviews physics-guided deep learning approaches that combine physical laws with neural networks to improve modeling of complex dynamical systems, addressing limitations of traditional methods and pure deep learning.

Contribution

It provides a comprehensive overview of methodologies integrating physical knowledge into deep learning for dynamical systems, highlighting challenges and future opportunities.

Findings

Physics-guided DL improves generalization over pure DL.

Combines physics-based models with neural networks effectively.

Addresses computational and interpretability limitations of traditional models.

Abstract

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.