Display options
Cite
Bittracher A, Koltai P, Klus S, et al. Transition Manifolds of Complex Metastable Systems: Theory and Data-Driven Computation of Effective Dynamics. J Nonlinear Sci. 2017;28(2):471-512doi: 10.1007/s00332-017-9415-0.
Bittracher, A., Koltai, P., Klus, S., Banisch, R., Dellnitz, M., & Schütte, C. (2018). Transition Manifolds of Complex Metastable Systems: Theory and Data-Driven Computation of Effective Dynamics. Journal of nonlinear science, 28(2), 471-512. https://doi.org/10.1007/s00332-017-9415-0
Bittracher, Andreas, et al. "Transition Manifolds of Complex Metastable Systems: Theory and Data-Driven Computation of Effective Dynamics." Journal of nonlinear science vol. 28,2 (2018): 471-512. doi: https://doi.org/10.1007/s00332-017-9415-0
Bittracher A, Koltai P, Klus S, Banisch R, Dellnitz M, Schütte C. Transition Manifolds of Complex Metastable Systems: Theory and Data-Driven Computation of Effective Dynamics. J Nonlinear Sci. 2018;28(2):471-512. doi: 10.1007/s00332-017-9415-0. Epub 2017 Oct 12. PMID: 29527099; PMCID: PMC5835149.
Copy Download .nbib Format: NLM
Share it on

J Nonlinear Sci. 2018;28(2):471-512. doi: 10.1007/s00332-017-9415-0. Epub 2017 Oct 12.

Transition Manifolds of Complex Metastable Systems: Theory and Data-Driven Computation of Effective Dynamics.

Journal of nonlinear science

Andreas Bittracher, Péter Koltai, Stefan Klus, Ralf Banisch, Michael Dellnitz, Christof Schütte

Affiliations

  1. 1Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany.
  2. 2Department of Mathematics, Paderborn University, Paderborn, Germany.
  3. 3Zuse Institute Berlin, Berlin, Germany.

PMID: 29527099 PMCID: PMC5835149 DOI: 10.1007/s00332-017-9415-0

Abstract

We consider complex dynamical systems showing metastable behavior, but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics.

Keywords: Coarse graining; Effective dynamics; Metastability; Reaction coordinate; Transfer operator; Whitney embedding theorem

References

  1. Faraday Discuss. 2016 Dec 22;195:365-394 - PubMed
  2. Methods. 2010 Sep;52(1):99-105 - PubMed
  3. J Chem Phys. 2004 Jun 15;120(23):10880-9 - PubMed
  4. Proc Natl Acad Sci U S A. 2002 Oct 1;99(20):12562-6 - PubMed
  5. Proc Natl Acad Sci U S A. 2017 Jul 11;114(28):E5494-E5503 - PubMed
  6. J Chem Phys. 2012 May 7;136(17):174118 - PubMed
  7. J Chem Phys. 2013 Jul 7;139(1):015102 - PubMed
  8. Proc Natl Acad Sci U S A. 2009 Sep 22;106(38):16090-5 - PubMed
  9. Science. 2000 Dec 22;290(5500):2319-23 - PubMed
  10. J Chem Phys. 2017 Mar 28;146(12 ):124133 - PubMed
  11. J Chem Phys. 2014 Jul 28;141(4):044109 - PubMed
  12. J Chem Phys. 2012 May 7;136(17):174101 - PubMed
  13. Annu Rev Phys Chem. 2010;61:391-420 - PubMed
  14. Chemphyschem. 2005 Sep 5;6(9):1809-14 - PubMed
  15. J Chem Phys. 2011 May 28;134(20):204105 - PubMed
  16. Annu Rev Phys Chem. 2009;60:321-44 - PubMed
  17. Mol Simul. 2014;40(10-11):784-793 - PubMed
  18. Proc Natl Acad Sci U S A. 2009 Nov 10;106(45):19011-6 - PubMed
  19. J Chem Phys. 2008 Apr 14;128(14):144120 - PubMed
  20. Proc Natl Acad Sci U S A. 2010 Jan 19;107(3):1088-93 - PubMed
  21. J Phys Chem B. 2005 Apr 14;109(14):6769-79 - PubMed
  22. J Chem Phys. 2005 Oct 1;123(13):134109 - PubMed
  23. J Chem Phys. 2017 Jan 28;146(4):044109 - PubMed
  24. Proc Natl Acad Sci U S A. 1993 Jul 1;90(13):6369-72 - PubMed
  25. Curr Opin Struct Biol. 2014 Apr;25:135-44 - PubMed

Publication Types