Yves van Gennip
[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.
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