Deep Symbolic Regression for Nonlinear Dynamical Systems

Master thesis (2023)

Authors

A. Thamban Mechanical Engineering

Contributors

A.M. Aragon Computational Design and Mechanics - Mechanical, Maritime and Materials Engineering (supervisor 1)
F. Alijani Dynamics of Micro and Nano Systems - Mechanical, Maritime and Materials Engineering (supervisor 2)
Faculty
Mechanical Engineering
Copyright: © 2023 Arun Thamban
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Published Date

28-06-2023

Language

English

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Faculty

Mechanical Engineering

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.