  In molecular dynamics simulations, dynamically consistent coarse-grained (CG)
models commonly use stochastic thermostats to model friction and fluctuations
that are lost in a CG description. While Markovian, i.e., time-local,
formulations of such thermostats allow for an accurate representation of
diffusivities/long-time dynamics, a correct description of the dynamics on all
time scales generally requires non-Markovian, i.e., non-time-local,
thermostats. These thermostats are typically in the form of a Generalized
Langevin Equation (GLE) determined by a memory kernel. In this work, we use a
Markovian embedded formulation of a position-independent GLE thermostat acting
independently on each CG degree of freedom. Extracting the memory kernel of
this CG model from atomistic reference data requires several approximations.
Therefore, this task is best understood as an inverse problem. While our
recently proposed approximate Newton scheme, Iterative Optimization of memory
kernels (IOMK), allows for the iterative optimization of a memory kernel,
Markovian embedding remained potentially error-prone and computationally
expensive. In this work, we present a IOMK-Gauss-Newton scheme (IOMK-GN) based
on IOMK, that allows for the direct parameterization of a Markovian embedded
model.
