A novel application of least squares support vector regression for solving inverse nonlinear partial differential equations

Articles in Press

Document Type : Research Article

Authors

Hassan Dana Mazraeh ¹

Alireza Afzal Aghaei ²

Kourosh Parand ²

¹ School of Mathematics and Computer Science, Damghan University, P.O.Box 36715-364, Damghan, Iran.

² Department of Computer and Data Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran.

10.22067/ijnao.2026.100348.1940

Abstract

The main objective of this research paper is to explore the capability of the least squares support vector regression in addressing the challenges associated with solving nonlinear inverse partial differential equations. To achieve this, two one-dimensional inverse formulations of Burgers' equations, an inverse form of a two-dimensional Burgers equation, an inverse form of a system of two-dimensional Burgers' equation, and an inverse form of a three-dimensional Telegraph equation are taken into consideration. In order to improve the effectiveness of least squares support vector regression, Legendre orthogonal polynomials are employed as transformation functions. In this work, we showcase a series of numerical trials aimed at illustrating the efficacy of the suggested method. The outcomes suggest that the proposed technique yields remarkably precise estimations for missing initial conditions.

Keywords

Least squares support vector regression

Legendre orthogonal polynomial

Nonlinear inverse partial differential equations

Burgers' equation

Telegraph equation

Machine learning

Subjects

• Computational Mathematics

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