We introduce a parameter estimation method that utilizes microscopic data, specifically averages and correlations of selected microscopic observables, to determine the parameters of a stochastic differential equation governing coarse-grained degrees of freedom. The method is not only limited to static parameters found in the reversible part of the coarse-grained dynamics, such as those in the free energy function or potential of mean force but also extends to dynamic parameters, including friction coefficients. The method couples the stochastic differential equation with free parameters to dynamic equations for the parameters. The coupled system self-averages, according to Anosov-Kifer's theorem, in such a way that the final state of the parameters gives coincidence between the microscopic and mesoscopic averages and correlations of selected observables. The method is validated in two examples: a Brownian particle in a harmonic potential, and a set of Brownian particles interacting hydrodynamically with the Rotne-Prager-Yamakawa mobility tensor. This latter case illustrates how the method can be used not only to determine coefficients but also state dependent transport properties-in this case, the position dependent form of the mobility tensor. The parameter estimation for these two models yields excellent results. Subsequently, we use the methodology to study a bimodal-mass Lennard-Jones fluid for which we infer both the potential of mean force between the heavy particles and its hydrodynamic mobility tensor.
Monago et al. (Wed,) studied this question.