The solution of ordinary differential equations using genetic programming with constant tuning

Rockett, P. orcid.org/0000-0002-4636-7727 (2026) The solution of ordinary differential equations using genetic programming with constant tuning. In: Hart, E., Horvath, T., Tan, Z. and Thomson, S., (eds.) Advances in Computational Intelligence Systems: Contributions Presented at The 24th UK Workshop on Computational Intelligence (UKCI 2025), September 3-5, 2025, Edinburgh, UK. 24th UK Workshop on Computational Intelligence (UKCI 2025), 03-05 Sep 2025, Edinburgh, UK. Advances in Intelligent Systems and Computing, AISC 1468. Springer Cham, pp. 103-114. ISSN: 2194-5357. EISSN: 2194-5365.

Abstract

In this paper we report the solution of a benchmark set of ordinary differential equations (ODEs) using genetic programming (GP) within a collocation framework using tuning of the embedded tree constants. We report statistical comparison with a baseline GP approach without constant tuning that indicates that parameter tuning produces statistically superior results. We obtain highly accurate solutions for almost all the benchmark ODEs, but identify a hitherto unreported issue with GP finding trivial solutions. The characteristics of the individual ODEs appear to dictate whether or not solution is problematic.

Metadata

Item Type:	Proceedings Paper
Authors/Creators:	Rockett, P. https://orcid.org/0000-0002-4636-7727
Editors:	Hart, E. Horvath, T. Tan, Z. Thomson, S.
Copyright, Publisher and Additional Information:	© 2025 The Author(s). Except as otherwise noted, this author-accepted version of a conference paper published in Advances in Computational Intelligence Systems: Contributions Presented at The 24th UK Workshop on Computational Intelligence (UKCI 2025), September 3-5, 2025, Edinburgh, UK is made available via the University of Sheffield Research Publications and Copyright Policy under the terms of the Creative Commons Attribution 4.0 International License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/
Keywords:	genetic programming; ordinary differential equations; collocation method
Dates:	Accepted: 14 July 2025 Published (online): 2 January 2026 Published: 2 January 2026
Institution:	The University of Sheffield
Academic Units:	The University of Sheffield > Faculty of Engineering (Sheffield) > School of Electrical and Electronic Engineering
Date Deposited:	23 Jul 2025 07:56
Last Modified:	05 Jan 2026 12:28
Status:	Published
Publisher:	Springer Cham
Series Name:	Advances in Intelligent Systems and Computing
Refereed:	Yes
Identification Number:	10.1007/978-3-032-07938-1_9
Related URLs:	Conference
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:229165

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The solution of ordinary differential equations using genetic programming with constant tuning

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