  This work presents a systematic methodology for describing the transient
dynamics of coarse-grained molecular systems inferred from all-atom simulated
data. We suggest Langevin-type dynamics where the coarse-grained interaction
potential depends explicitly on time to efficiently approximate the transient
coarse-grained dynamics. We apply the path-space force matching approach at the
transient dynamics regime to learn the proposed model parameters. In
particular, we parameterize the coarse-grained potential both with respect to
the pair distance of the CG particles and the time, and we obtain an evolution
model that is explicitly time-dependent. Moreover, we follow a data-driven
approach to estimate the friction kernel, given by appropriate correlation
functions directly from the underlying all-atom molecular dynamics simulations.
To explore and validate the proposed methodology we study a benchmark system of
a moving particle in a box. We examine the suggested model's effectiveness in
terms of the system's correlation time and find that the model can approximate
well the transient time regime of the system, depending on the correlation time
of the system. As a result, in the less correlated case, it can represent the
dynamics for a longer time interval. We present an extensive study of our
approach to a realistic high-dimensional water molecular system. Posing the
water system initially out of thermal equilibrium we collect trajectories of
all-atom data for the, empirically estimated, transient time regime. Then, we
infer the suggested model and strengthen the model's validity by comparing it
with simplified Markovian models.
