We introduce a scheme for deriving an optimally parametrized Langevin dynamics of a few collective variables from data generated in molecular dynamics simulations. The drift- and the position-dependent diffusion pro?les governing the Langevin dynamics are expressed as explicit averages over the input trajectories. The proposed strategy is applicable to cases when the input trajectories are generated by subjecting the system to an external time-dependent force as opposed to canonically equilibrated trajectories. Second, it provides an explicit control on the statistical uncertainty in the drift and diffusion pro?les. These features lend to the possibility of designing the external force driving the system to maximize the accuracy of the drift and diffusion pro?les throughout the phase space of interest. Quantitative criteria are also provided to assess a posteriori the satis?ability of the requisites for applying the method, namely, the Markovian character of the stochastic dynamics of the collective variables.
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