  We introduce a scheme for deriving an optimally-parametrised Langevin
dynamics of few collective variables from data generated in molecular dynamics
simulations. The drift and the position-dependent diffusion profiles 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 a external
time-dependent force (as opposed to canonically-equilibrated trajectories).
Secondly, it provides an explicit control on the statistical uncertainty of the
drift and diffusion profiles. These features lend to the possibility of
designing the external force driving the system so to maximize the accuracy of
the drift and diffusions profile throughout the phase space of interest.
Quantitative criteria are also provided to assess a posteriori the
satisfiability of the requisites for applying the method, namely the Markovian
character of the stochastic dynamics of the collective variables.
