Self-averaging parameter estimation for coarse-grained particle models

TL;DR

This paper presents a novel parameter estimation approach for coarse-grained stochastic models using microscopic data, capable of determining static and dynamic parameters, validated through multiple particle system examples.

Contribution

The method extends parameter estimation to dynamic parameters and state-dependent properties, coupling stochastic equations with parameter dynamics for self-averaging.

Findings

Accurately estimates parameters in particle models including mobility tensors.

Validates the approach with Brownian particles in harmonic potential.

Successfully infers potential and mobility in Lennard-Jones fluid.

Abstract

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 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.