Work

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

Year: 2024

Type: article

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).

Source: Human-Centric Intelligent Systems

DOI: 10.1007/s44230-024-00084-0

Authors: Paulo M. Tasinaffo, Luiz A. V. Dias, Adilson M. da Cunha

Institution: Instituto Tecnológico de Aeronáutica

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4404024834

FWCI: 0.383

Cites: 43

Cited by: 1

Related to: 10