科学与工程计算系列讨论班—Computing ergodic limits and stochastic geometric integration
主 题: 科学与工程计算系列讨论班—Computing ergodic limits and stochastic geometric integration
报告人: Prof. M. Tretyakov (University of Nottingham, UK)
时 间: 2017-04-24 10:30-11:30
地 点: 理科1号楼1418
Abstract: For many applications (especially, in molecular dynamics and Bayesian statistics), it is of interest to compute the mean of a given function with respect to the invariant law of the diffusion, i.e. the ergodic limit. To evaluate these mean values in situations of practical interest, one has to integrate large dimensional systems of stochastic differential equations over long time intervals. Computationally, this is a challenging problem. In the talk, theoretical results for computing ergodic limits will be briefly discussed. Then stochastic geometric integrators, which play an important role in long-time simulation of dynamical systems with high accuracy and relatively low cost, will be considered. We will illustrate geometric integration ideas using such examples as stochastic Landau-Lifshitz equation, stochastic thermostats for rigid body dynamics and Langevin equations for systems with hydrodynamic interactions.