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The recent introduction of the Least-Squares Support Vector Regression(LS-SVR) algorithm for solving differential and integral equations has sparkedinterest. In this study, we expand the application of this algorithm to addresssystems of differential-algebraic equations (DAEs). Our work presents a novelapproach to solving general DAEs in an operator format by establishingconnections between the LS-SVR machine learning model, weighted residualmethods, and Legendre orthogonal polynomials. To assess the effectiveness ofour 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 methodand currently established state-of-the-art approaches, demonstrating itsreliability and effectiveness.

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