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A.F. Albu Application of the fast automatic differentiation to the computation of the gradient of the tersoff potential |
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Abstract.To tackle problems of computer modelling of crystal structures of materials gradient optimization methods are often used. This raises the need to determine the exact value of the gradient of the Tersoff potential using specific parameters of this potential for the modeled substance. Based on the technique of the Fast Automatic Differentiation the formulas that allow the calculation of the exact value of the above-mentioned gradient were derived. Keywords: Tersoff potential, gradient, Fast Automatic Differentiation PP. 43-49. REFERENCES 1. Abgaryan K.K., Posypkin M.A. Primenenie optimizatsionnykh metodov dlya resheniya zadach parametricheskoy identifikatsii potentsialov mezhatomnogo vzaimodeystviya. // Zh. vychisl. matem. i matem. fiziki. 2014. T. 54. № 12, S. 1994–2001. 2. Abgaryan K.K., Posypkin M.A. Programmnyy kompleks dlya resheniya zadach parametricheskoy identifikatsii potentsialov mezhatomnogo vzaimodeystviya. // International Journal of Open Information Technologies. 2014. T. 2, № 10, S. 14-19. 3. J.Tersoff. Empirical interatomic potential for silicon with improved elastic properties. \\ Phys. Rev. B. 1988, V.38, P. 9902-9905. 4. Yu.G. Yevtushenko. Optimizatsiya i bystroe avtomaticheskoe differentsirovanie. Nauchnoe izdanie. Vychislitelnyy tsentr im. A.A. Dorodnitsyna Rossiyskoy akademii nauk. Moskva. 2013. 144 S. 5. Evtushenko, Y.G. Computation of Exact Gradients in Distributed Dynamic Systems // Optimizat. Methods and Software. 1998. № 9. P. 45-75. 6. A.F. Albu, V.I. Zubov. Ob effektivnosti resheniya zadach optimalnogo upravleniya s pomoshchyu metodologii bystrogo avtomaticheskogo differentsirovaniya. //Trudy Instituta matematiki i mekhaniki UrO RAN. 2015. T. 21. № 4. S. 20-29.
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