A Quantitative Approach to Universal Numerical Integrators (UNIS) with Computational Application

Abstract In this paper, we examine the mathematics that makes it possible to couple a conventional numerical integrator (e.g., Euler, Runge-Kutta, among others) with some universal approximator of functions (e.g., artificial neural networks, fuzzy inference systems, among others). These hybrid structures, known as Universal Numerical Integrators (UNIs), are analyzed through a set of significant properties essential for their proper design. Theoretical foundations are complemented by numerical and computational experiments, validating the proposed UNI models. We also hope that the theoretical content in this article can help guide researchers aiming to computationally design general problems related to some Universal Numerical Integrator (UNI).