Title: Solving differential equations with global optimisation techniques

Authors: Ioannis G. Tsoulos; Alexandros Tzallas; Dimitrios Tsalikakis

Addresses: Department of Informatics and Telecommunications, University of Ioannina, 47100 Arta, Greece ' Department of Informatics and Telecommunications, University of Ioannina, 47100 Arta, Greece ' Department of Engineering Informatics and Telecommunications, University of Western Macedonia, 50100 Kozani, Greece

Abstract: The solution of differential equations finds many applications in a huge range of problems, and many techniques have been developed to approximate their solutions. For example, differential equations can be applied to physics problems, chemistry problems, economics, modelling, etc. This manuscript presents a number of global optimisation techniques that have been successfully applied to train machine learning models to approximate differential equation solutions. More specifically, two modified versions of genetic algorithms and particle swarm optimisation methods are proposed here. These methods have been successfully applied to solving ordinary differential equations and systems of differential equations as well as partial differential equations with Dirichlet boundary conditions.

Keywords: differential equations; global optimisation; stochastic methods; machine learning.

DOI: 10.1504/IJCISTUDIES.2024.144044

International Journal of Computational Intelligence Studies, 2024 Vol.13 No.1/2, pp.1 - 22

Received: 30 Sep 2022
Accepted: 12 Oct 2023
Published online: 22 Jan 2025 *

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