  Stochastic dynamics, such as molecular dynamics, are important in many
scientific applications. However, summarizing and analyzing the results of such
simulations is often challenging, due to the high dimension in which
simulations are carried out, and consequently to the very large amount of data
that is typically generated. Coarse graining is a popular technique for
addressing this problem by providing compact and expressive representations.
Coarse graining, however, potentially comes at the cost of accuracy, as
dynamical information is in general lost when projecting the problem in a lower
dimensional space. This article shows how to eliminate coarse-graining error
using two key ideas. First, we represent coarse-grained dynamics as a Markov
renewal process. Second, we outline a data-driven, non-parametric Mori-Zwanzig
approach for computing jump times of the renewal process. Numerical tests on a
small protein illustrate the method.
