An Orthogonal Polynomial Kernel-Based Machine Learning Model for Differential-Algebraic Equations

2024/01/25 by Tayebeh Taheri, Taheri, Tayebeh, Alireza Afzal Aghaei +3 · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Computer science #Differential (mechanical device) #Engineering #FOS: Computer and information sciences #FOS: Mathematics #Kernel (algebra) #Kernel method #Legendre polynomials #Machine Learning (cs.LG) #Mathematical analysis #Mathematics #Model Reduction and Neural Networks #Nonlinear system #Numerical Analysis (math.NA) #Numerical methods for differential equations #Orthogonal polynomials #Polynomial #Polynomial and algebraic computation #Pure mathematics #Residual #Support vector machine

paper · pdf · doi:10.48550/arxiv.2401.14382

openalex publication_date 2024/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The recent introduction of the Least-Squares Support Vector Regression (LS-SVR) algorithm for solving differential and integral equations has sparked interest. In this study, we expand the application of this algorithm to address systems of differential-algebraic equations (DAEs). Our work presents a novel approach to solving general DAEs in an operator format by establishing connections between the LS-SVR machine learning model, weighted residual methods, and Legendre orthogonal polynomials. To assess the effectiveness of our proposed method, we conduct simulations involving various DAE scenarios, such as nonlinear systems, fractional-order derivatives, integro-differential, and partial DAEs. Finally, we carry out comparisons between our proposed method and currently established state-of-the-art approaches, demonstrating its reliability and effectiveness.

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