Year: 2026
Type: book-chapter
Abstract: Learning dynamic equations from data has shown great promise in various fields of research, such as physics, engineering, and biology. This short review provides a comprehensive overview of the methods, challenges, and applications involved in learning governing equations from time-series data. We begin by highlighting the importance of dynamic equations in modeling complex systems. Subsequently, we present different approaches used for learning dynamic equations, including symbolic regression and neural networks. These methods are contextualized within different modeling scopes, which here are largely defined by the properties of the underlying differential equations. We explore the advantages and limitations of these methods, with a particular focus on symbolic regression. Through various studies and examples, we demonstrate the utility of learning dynamic equations from data and showcase their applicability in the domain of density functional theory. Finally, we identify promising directions for future research and discuss potential applications of this methodology in advancing scientific understanding and solving real-world problems.
Authors: Oliver Kamps, Tim W. Kroll, Oliver Mai
Institution: University of Münster
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7123364343