Bottom-up transient time models in coarse-graining molecular systems

Abstract: 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.