Virtual dimensions in the docking method based on tensor train decompositions

Authors

Keywords:

tensor train decomposition, virtual dimensions, cross interpolation method, global optimization, docking, computer drug design

Abstract

A modification of the docking method based on tensor train decompositions using the idea of virtual dimensions adding is proposed to find the position of the energy global minimum for the ligand-protein system. The proposed method is compared with the TTDock (docking based on tensor train decompositions) program, which uses only physical dimensions. According to the testing results, the modified method is 5–10 times faster with the same level of reliability.

Author Biographies

D.A. Zheltkov

Lomonosov Moscow State University,
Faculty of Computational Mathematics and Cybernetics
• PhD Student

E.E. Tyrtyshnikov

Institute of Numerical Mathematics of RAS (INM RAS)
• Director

References

  1. Oseledets I.V., Tyrtyshnikov E.E. Breaking the curse of dimensionality, or how to use SVD in many dimensions // SIAM J. Sci. Comput. 2009. 31, N 5. 3744-3759.
  2. Желтков Д.А., Офёркин И.В., Каткова Е.В., Сулимов А.В., Сулимов В.Б., Тыртышников Е.Е. TTDock: метод докинга на основе тензорных поездов // Вычислительные методы и программирование. 2013. 14. 279-291.
  3. Oseledets I.V., Tyrtyshnikov E.E. TT-cross approximation for multidimensional arrays // Linear Algebra Appl. 2010. 432, N 1. 70-88.
  4. Тыртышников Е.Е. Тензорные аппроксимации матриц, порожденных асимптотически гладкими функциями // Математический сборник. 2003. 194, № 6. 146-160.
  5. Oseledets I.V. Approximation of 2^d imes 2^d matrices using tensor decomposition // SIAM J. Matrix Anal. Appl. 2010. 31, N 4. 2130-2145.
  6. Khoromkij B.N., Oseledets I.V. QTT approximation of elliptic operators in higher dimensions // Rus. J. Numer. Anal. Math. Model. 2011. 26, N 3. 303-322.
  7. Oseledets I.V. Tensor-train decomposition // SIAM J. Sci. Comput. 2011. 33, N 5. 2295-2317.
  8. Goreinov S.A., Tyrtyshnikov E.E., Zamarashkin N.L. A theory of pseudo-skeleton approximations // Linear Algebra Appl. 1997. 261, N 1-3. 1-21.
  9. Tyrtyshnikov E.E. Incomplete cross approximation in the mosaic-skeleton method // Computing. 2000. 64, N 4. 367-380.
  10. Goreinov S.A., Tyrtyshnikov E.E. The maximal-volume concept in approximation by low-rank matrices // Contemporary Mathematics. 2001. 208. 47-51.
  11. Goreinov S.A., Oseledets I.V., Savostyanov D.V., Tyrtyshnikov E.E., Zamarashkin N.L. How to find a good submatrix // Matrix Methods: Theory, Algorithms, Applications / Edited by V. Olshevsky and E. Tyrtyshnikov. Hackensack: World Scientific, 2010. 247-256.
  12. GNU Scientific Library (http://www.gnu.org/software/gsl).
New computational technologies

Downloads

Published

18-06-2013

How to Cite

Желтков Д., Тыртышников Е. Virtual Dimensions in the Docking Method Based on Tensor Train Decompositions // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2013. 14. 292-294

Issue

Vol. 14 (2013): Issue 3.

Section

Section 1. Numerical methods and applications

License

Copyright (c) 2013 Вычислительные методы и программирование

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Most read articles by the same author(s)