Title
Deep Symbolic Regression for Nonlinear Dynamical Systems
Author
Thamban, Arun (TU Delft Mechanical, Maritime and Materials Engineering)
Contributor
Aragon, A.M. (mentor) 
Alijani, F. (graduation committee)
Degree granting institution
Delft University of Technology
Corporate name
Delft University of Technology
Programme
Mechanical Engineering
Date
2023-06-28
Abstract
From the motion of electrons in an atom to the orbits of celestial bodies in the cosmos, governing equations are essential to the characterisation of dynamical systems. They facilitate an understanding of the physics of a system, which enables the development of useful techniques such as predictive control. An increasingly popular method to obtain these equations is Symbolic Regression, where governing laws are discovered from observations of the system. In this work, we extend the Deep Symbolic Regression package to the identification of dynamical systems. Preliminary tests revealed the limits of the method as applied to dynamical systems, and new methods of incorporating domain knowledge to constrain the expression space are added. We test the extended package on 3 strongly nonlinear ODEs that exhibit different dynamics as their parameterisation varies. Finally, we demonstrate the working of this method in practice by discovering the governing equation of a pendulum, from a video of its oscillation. This method achieved a 100% equation recovery rate on our tests, and was able to consistently retrieve the correct equation from datasets representing a diverse range of dynamics.
Subject
Symbolic Regression
Deep Learning
Nonlinear dynamics
To reference this document use:
http://resolver.tudelft.nl/uuid:41c2a7cd-8922-44c7-a065-a0f96ee7420e
Embargo date
2025-06-27
Part of collection
Student theses
Document type
master thesis
Rights
© 2023 Arun Thamban