Variational Koopman models
Wu, Hao ;  Nueske, Feliks ;  Paul, Fabian ;  Klus, Stefan ;  Koltai, Peter ;  Noe, Frank

HaupttitelVariational Koopman models
TitelzusatzSlow collective variables and molecular kinetics from short off-equilibrium simulations
AutorWu, Hao
AutorNueske, Feliks
AutorPaul, Fabian
AutorKlus, Stefan
AutorKoltai, Peter
AutorNoe, Frank
Seitenzahl17 S.
Freie SchlagwörterEigenvalues; Basis sets; Relaxation times; Markov processes; Conformational dynamics
DDC530 Physik
Auch erschienen inJournal of Chemical Physics. - 146 (2017), 15, Artikel Nr. 154104
ZusammenfassungMarkov state models (MSMs) and master equation models are popular approaches to approximate molecular kinetics, equilibria, metastable states, and reaction coordinates in terms of a state space discretization usually obtained by clustering. Recently, a powerful generalization of MSMs has been introduced, the variational approach conformation dynamics/molecular kinetics (VAC) and its special case the time-lagged independent component analysis (TICA), which allow us to approximate slow collective variables and molecular kinetics by linear combinations of smooth basis functions or order parameters. While it is known how to estimate MSMs from trajectories whose starting points are not sampled from an equilibrium ensemble, this has not yet been the case for TICA and the VAC. Previous estimates from short trajectories have been strongly biased and thus not variationally optimal. Here, we employ the Koopman operator theory and the ideas from dynamic mode decomposition to extend the VAC and TICA to non-equilibrium data. The main insight is that the VAC and TICA provide a coefficient matrix that we call Koopman model, as it approximates the underlying dynamical (Koopman) operator in conjunction with the basis set used. This Koopman model can be used to compute a stationary vector to reweight the data to equilibrium. From such a Koopman-reweighted sample, equilibrium expectation values and variationally optimal reversible Koopman models can be constructed even with short simulations. The Koopman model can be used to propagate densities, and its eigenvalue decomposition provides estimates of relaxation time scales and slow collective variables for dimension reduction. Koopman models are generalizations of Markov state models, TICA, and the linear VAC and allow molecular kinetics to be described without a cluster discretization.
PDF-Datei von FUDOCS_document_000000027108
Falls Ihr Browser eine Datei nicht öffnen kann, die Datei zuerst herunterladen und dann öffnen.
Fachbereich/EinrichtungFB Physik
Dokumententyp/-SammlungenWissenschaftlicher Artikel
RechteCopyright des Verlags
Erstellt am31.05.2017 - 12:47:59
Letzte Änderung31.05.2017 - 12:48:07
Statische URLhttp://edocs.fu-berlin.de/docs/receive/FUDOCS_document_000000027108