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.

利用最小二乘支持向量回归算法，将其应用于解决常微分代数方程组（DAEs），通过建立最小二乘支持向量回归、加权残差法和 Legendre 正交多项式之间的联系，提出了一种新颖的以算子形式求解 DAEs 的方法。通过模拟各种 DAE 场景，如非线性系统、分数阶导数、积分微分和偏微分 DAE，评估了所提出方法的有效性，并与现有的先进方法进行了比较，显示其可靠性和有效性。