An Orthogonal Polynomial Kernel-Based Machine Learning Model for
  Differential-Algebraic Equations
Tayebeh Taheri Alireza Afzal Aghaei Kourosh Parand
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.