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

Area of Science:

• Scientific modeling
• Dynamical systems
• Computational science

Background:

• Traditional physics-based models offer explainability but require significant resources and expertise.
• Deep learning (DL) models are efficient but demand extensive data and may violate physical laws.
• Existing methods struggle to balance accuracy, interpretability, and data efficiency in complex dynamics modeling.

Purpose of the Study:

• Introduce a framework for physics-guided deep learning (DL) tailored for dynamical systems.
• Categorize and analyze state-of-the-art methods within this framework.
• Identify challenges and opportunities in physics-guided DL for scientific applications.

Main Methods:

• Integrating first-principles physical knowledge into data-driven DL approaches.
• Developing a learning pipeline specifically for dynamical systems.
• Systematic review and categorization of current physics-guided DL techniques.

Main Results:

• Demonstrated the potential of physics-guided DL to overcome limitations of traditional and pure DL methods.
• Provided a structured overview of existing methodologies in the field.
• Highlighted the synergistic benefits of combining physical laws with data-driven learning.

Conclusions:

• Physics-guided DL offers a powerful paradigm for modeling complex physical dynamics.
• The framework facilitates the development of more robust, interpretable, and efficient scientific models.
• Future research directions include addressing open challenges and exploring new opportunities in this rapidly advancing field.