Una metodolog\'ia para realizar Diferenciaci\'on Autom\'atica Anidada

TL;DR

This paper introduces a new structure called SuperAdouble for nested automatic differentiation in the forward mode, compatible with any operator-overloading AD library, enabling accurate computation of nested derivatives.

Contribution

The paper presents SuperAdouble, a novel structure that facilitates nested automatic differentiation using existing operator-overloading AD libraries.

Findings

SuperAdouble ensures correct nested derivative calculations.

Compatible with any operator-overloading AD library.

Enables accurate evaluation of nested derivatives in analytic functions.

Abstract

En este trabajo se presenta una propuesta para realizar Diferenciaci\'on Autom\'atica Anidada utilizando cualquier biblioteca de Diferenciaci\'on Autom\'atica que permita sobrecarga de operadores. Para calcular las derivadas anidadas en una misma evaluaci\'on de la funci\'on, la cual se asume que sea anal\'itica, se trabaja con el modo forward utilizando una nueva estructura llamada SuperAdouble, que garantiza que se aplique correctamente la Diferenciaci\'on Autom\'atica y se calculen el valor y la derivada que se requiera. This paper proposes a framework to apply Nested Automatic Differentiation using any library of Automatic Differentiation which allows operator overloading. To compute nested derivatives of a function while it is being evaluated, which is assumed to be analytic, a new structure called SuperAdouble is used in the forward mode. This new class guarantees the correct application of Automatic Differentiation to calculate the value and derivative of a function where is required.