On the Effectiveness of the Fast Automatic Differentiation Methodology
In this paper, we compare the three approaches for calculating the gradient of a complex function of many variables. The compared approaches are: the use of precise, analytically derived formulas; the usage of formulas derived with the aid of the Fast Automatic Differentiation methodology; the use of standard software packages that implement the ideas of Fast Automatic Differentiation methodology. Comparison of approaches is carried out with the help of a complex function that represents the energy of atoms system whose interaction potential is the Tersoff potential. As a comparison criterion, the computer time required to calculate the gradient of the function is used. The results show the superiority of the Fast Automatic Differentiation methodology in comparison with the approach using analytical formulas. Standard packages compute the function gradient around the same time as using the formula of the Fast Automatic Differentiation methodology.
KeywordsFast Automatic Differentiation Standard software packages Tersoff potential
- 3.Albu, A.F.: Application of the fast automatic differentiation to the computation of the gradient of the tersoff potential. Informacionnye tekhnologii i vychislitel’nye sistemy 1, 43–49 (2016)Google Scholar
- 5.Evtushenko, Y., Lurie, S., Posypkin, M.: New optimization problems arising in modelling of 2D-crystal lattices. In: AIP Conference Proceedings, vol. 1776 (2016). https://doi.org/10.1063/1.4965341
- 6.Albring, T., et al.: An aerodynamic design framework based on algorithmic differentiation. ERCOFTAC Bull. 102, 10–16 (2015)Google Scholar
- 8.Gorchakov, A.Y.: On software packages of fast automatic differentiation. Informacionnye tekhnologii i vychislitel’nye sistemy 1, 30–36 (2018)Google Scholar