TCBG Seminar

"A mathematical viewpoint on some numerical methods used in molecular dynamics"

Dr. Tony Lelievre
Ecole des Ponts ParisTech, CERMICS
Marne la Vallee Cedex 2, France

Monday, January 27, 2014
3:00 pm (CT)
3269 Beckman Institute


Molecular dynamics is now a very widely used tool to study the matter at the molecular level. It is used in various fields, such as biology, chemistry or materials science. The aim is in particular to understand the relationships between the macroscopic properties of a molecular system and its atomistic features. One of the difficulty to reach this aim is related to timescales: the typical timescale of a molecular dynamics simulation is much smaller than the typical timescale at which the crucial events, from a macroscopic viewpoint, occur. This is related to the metastability of a molecular dynamics trajectory: the system stays for a very long time in some regions of the configuration space (called metastable state), before hopping to another one, and it is difficult to observe and simulate such rare events. An associated feature is the multimodality of the statistical ensemble (a probability measure) sampled by the molecular dynamics trajectories. Many methods have been proposed in the molecular dynamics community to deal with these difficulties, and we will focus on two prototypical ones for which a mathematical analysis gives useful insights. We will first present adaptive importance sampling techniques, which have been proposed to sample efficiently statistical ensembles and to compute free energy differences. Then, we will propose a mathematical analysis of the accelerated dynamics methods which have been introduced by A.F. Voter to generate efficiently metastable dynamics.

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