TY - GEN
A1 - Quer, Jannes
A1 - Donati, Luca
A1 - Keller, Bettina
A1 - Weber, Marcus
T1 - An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates
N2 - In this article we propose an adaptive importance sampling scheme for dynamical quantities of high dimensional complex systems which are metastable. The main idea of this article is to combine a method coming from Molecular Dynamics Simulation, Metadynamics, with a theorem from stochastic analysis, Girsanov's theorem. The proposed algorithm has two advantages compared to a standard estimator of dynamic quantities: firstly, it is possible to produce estimators with a lower variance and, secondly, we can speed up the sampling. One of the main problems for building importance sampling schemes for metastable systems is to find the metastable region in order to manipulate the potential accordingly. Our method circumvents this problem by using an assimilated version of the Metadynamics algorithm and thus creates a non-equilibrium dynamics which is used to sample the equilibrium quantities.
T3 - ZIB-Report - 17-09
KW - Adaptive Importance Sampling
KW - Molecular Dynamics
KW - Metastability
KW - Variance Reduction
KW - Non Equilibrium Sampling
KW - Metadynamics
KW - Girsanov
Y1 - 2017
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62075
SN - 1438-0064
ER -
TY - JOUR
A1 - Donati, Luca
A1 - Heida, Martin
A1 - Keller, Bettina G.
A1 - Weber, Marcus
T1 - Estimation of the infinitesimal generator by square-root approximation
JF - J. Phys.: Condens. Matter
N2 - In recent years, for the analysis of molecular processes, the estimation of time-scales and transition rates has become fundamental. Estimating the transition rates between molecular conformations is—from a mathematical point of view—an invariant subspace projection problem. We present a method to project the infinitesimal generator acting on function space to a low-dimensional rate matrix. This projection can be performed in two steps. First, we discretize the conformational space in a Voronoi tessellation, then the transition rates between adjacent cells is approximated by the geometric average of the Boltzmann weights of the Voronoi cells. This method demonstrates that there is a direct relation between the potential energy surface of molecular structures and the transition rates of conformational changes. We will show also that this approximation is correct and converges to the generator of the Smoluchowski equation in the limit of infinitely small Voronoi cells. We present results for a two dimensional diffusion process and alanine dipeptide as a high-dimensional system.
Y1 - 2018
U6 - http://dx.doi.org/10.1088/1361-648X/aadfc8
VL - 30
IS - 42
SP - 425201
EP - 425201
ER -
TY - JOUR
A1 - Quer, Jannes
A1 - Donati, Luca
A1 - Keller, Bettina
A1 - Weber, Marcus
T1 - An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates
JF - SIAM Journal on Scientific Computing
N2 - In this article we propose an adaptive importance sampling scheme for dynamical quantities of high dimensional complex systems which are metastable. The main idea of this article is to combine a method coming from Molecular Dynamics Simulation, Metadynamics, with a theorem from stochastic analysis, Girsanov's theorem. The proposed algorithm has two advantages compared to a standard estimator of dynamic quantities: firstly, it is possible to produce estimators with a lower variance and, secondly, we can speed up the sampling. One of the main problems for building importance sampling schemes for metastable systems is to find the metastable region in order to manipulate the potential accordingly. Our method circumvents this problem by using an assimilated version of the Metadynamics algorithm and thus creates a non-equilibrium dynamics which is used to sample the equilibrium quantities.
Y1 - 2018
VL - 40
IS - 2
SP - A653
EP - A670
ER -