This article is cited in 1 paper

Optimal control

FAD technique and differentiation of a composite function

A. F. Albu^a, A. Yu. Gorchakov^ab, V. I. Zubov<sup>a

a</sup> Federal Research Center "Computer Science and Control", Russian Academy of Sciences, 119333, Moscow, Russia
^b Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudnyi, Moscow oblast, Russia

Abstract: Different approaches to the calculation of the gradient of a composite function of several variables are compared, namely, exact analytically derived formulas, formulas based on the fast automatic differentiation (FAD) technique, and standard software packages implementing the ideas of the FAD technique. The approaches are compared as applied to a composite function representing the energy of a system of atoms with the Tersoff interatomic potential. The comparison criterion is the computer time required for computing the gradient of the function. The results show that the FAD technique is superior to the analytical formulas. The standard packages take nearly the same time to compute the function gradient as the FAD technique formulas.

Key words: fast automatic differentiation, multistep process, standard software packages.

UDC: 517.23

Received: 27.04.2022
Revised: 27.04.2022
Accepted: 17.09.2022

DOI: 10.31857/S0044466923010039

 English version: Computational Mathematics and Mathematical Physics, 2023, 63:1, 57–68

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