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

TL;DR

This paper develops a method to quantify the error introduced by coarse-graining in Langevin and overdamped Langevin dynamics, providing error estimates in relative entropy and Wasserstein distance for high-dimensional Gibbs measures.

Contribution

It introduces a novel approach to measure coarse-graining errors using functional inequalities and large-deviation principles, applicable to vectorial coarse-graining maps.

Findings

Error estimates in relative entropy and Wasserstein distance for Langevin dynamics

Quantification of coarse-graining quality via functional inequalities

Applicability to high-dimensional Gibbs measures and vectorial coarse-graining

Abstract

In molecular dynamics and sampling of high dimensional Gibbs measures coarse-graining is an important technique to reduce the dimensionality of the problem. 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.