FAD Technique and Differentiation of a Composite Function
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 techn...
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| Veröffentlicht in: | Computational mathematics and mathematical physics 2023, Vol.63 (1), p.57-68 |
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| creator | Albu, A. F. Gorchakov, A. Yu Zubov, V. I. |
| description | 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. |
| doi_str_mv | 10.1134/S0965542523010037 |
| format | Article |
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| subjects | Composite functions Computational Mathematics and Numerical Analysis Differentiation Mathematics Mathematics and Statistics Optimal Control Packages |
| title | FAD Technique and Differentiation of a Composite Function |
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