@misc{QuerDonatiKelleretal., author = {Quer, Jannes and Donati, Luca and Keller, Bettina and Weber, Marcus}, title = {An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62075}, abstract = {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.}, language = {en} } @article{DonatiHartmannKeller, author = {Donati, Luca and Hartmann, Carsten and Keller, Bettina G.}, title = {Girsanov reweighting for path ensembles and Markov state models}, series = {The Journal of Chemical Physics}, volume = {146}, journal = {The Journal of Chemical Physics}, number = {24}, doi = {10.1063/1.4989474}, pages = {244112}, abstract = {The sensitivity of molecular dynamics on changes in the potential energy function plays an important role in understanding the dynamics and function of complex molecules. We present a method to obtain path ensemble averages of a perturbed dynamics from a set of paths generated by a reference dynamics. It is based on the concept of path probability measure and the Girsanov theorem, a result from stochastic analysis to estimate a change of measure of a path ensemble. Since Markov state models (MSMs) of the molecular dynamics can be formulated as a combined phase-space and path ensemble average, the method can be extended to reweight MSMs by combining it with a reweighting of the Boltzmann distribution. We demonstrate how to efficiently implement the Girsanov reweighting in a molecular dynamics simulation program by calculating parts of the reweighting factor "on the fly" during the simulation, and we benchmark the method on test systems ranging from a two-dimensional diffusion process and an artificial many-body system to alanine dipeptide and valine dipeptide in implicit and explicit water. The method can be used to study the sensitivity of molecular dynamics on external perturbations as well as to reweight trajectories generated by enhanced sampling schemes to the original dynamics.}, language = {en} }