An Orthogonal Polynomial Kernel-Based Machine Learning Model for Differential-Algebraic Equations
This provides a machine learning-based solution for differential-algebraic equations, which are important in engineering and physics, but appears incremental as it extends an existing algorithm to a new problem type.
The authors tackled solving systems of differential-algebraic equations (DAEs) by extending the Least-Squares Support Vector Regression algorithm, demonstrating reliability and effectiveness through simulations of various DAE scenarios and comparisons with state-of-the-art methods.
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.