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

A system of differential-algebraic equations (DAEs) is a combination of differential equations and algebraic equations, in which the differential equations are related to the dynamical evolution of the system, and the algebraic equations are responsible for constraining the solutions that satisfy the differential and algebraic equations. DAEs serve as essential models for a wide array of physical phenomena. They find applications across various domains such as mechanical systems, electrical circuit simulations, chemical process modeling, dynamic system control, biological simulations, and control systems. Consequently, solving these intricate differential equations has remained a significant challenge for researchers. To address this, a range of techniques including numerical, analytical, and semi-analytical methods have been employed to tackle the complexities inherent in solving DAEs.