School of Mathematical Sciences
   
   
  

External Seminar: Hong Duong

Location
Phys C27
Date(s)
Wednesday 20th June 2018 (13:00-14:00)
Contact

Matteo Icardi

Yves van Gennip

Description

[Joint Industrial and Applied Mathematics/Algebra and Analysis Seminar]

Hong Duong (Imperial College London)

Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics

Coarse-graining or dimension reduction is the procedure of approximating a large and complex system by a simpler and lower dimensional one, where the variables in the reduced model are called coarse grained or collective variables. Such a reduction is necessary from a computational point of view since an all-atom molecular simulation of the complex system is often unable to access information about relevant temporal and/or spatial scales. Further this is also relevant from a modelling point of view as the quantities of interest are often described by a smaller class of features. For these reasons coarse graining has gained importance in various fields and especially in molecular dynamics. In this work, we will study and quantify the coarse-graining error between the coarse-grained dynamics and an effective dynamics. The effective dynamics is a Markov process on the coarse-grained state space obtained by a closure procedure from the coarse-grained coefficients. We obtain error estimates both in relative entropy and Wasserstein distance, for both Langevin and overdamped Langevin dynamics. The approach allows for vectorial coarse-graining maps. Hereby, the quality of the chosen coarse-graining is measured by certain functional inequalities encoding the scale separation of the Gibbs measure. The method is based on error estimates between solutions of (kinetic) Fokker-Planck equations in terms of large-deviation rate functionals. This is joint work with A. Lamacz, M. Peletier, A. Schlichting, and U. Sharma.

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

For all enquiries please visit:
www.nottingham.ac.uk/enquire