Accurate Estimation of Diffusion Coefficients and their Uncertainties from Computer Simulation

TL;DR

This paper introduces a Bayesian regression-based scheme for accurately estimating diffusion coefficients and their uncertainties from molecular dynamics simulations, optimizing statistical efficiency and uncertainty quantification.

Contribution

The authors develop a novel Bayesian approach that models MSDs as a multivariate normal distribution, enabling precise estimation of diffusion coefficients and uncertainties from a single simulation.

Findings

High statistical efficiency in estimating D*

Accurate uncertainty quantification achieved

Applicable to single simulation trajectories

Abstract

Self-diffusion coefficients, $D^*$, are routinely estimated from molecular dynamics simulations by fitting a linear model to the observed mean-squared displacements (MSDs) of mobile species. MSDs derived from simulation exhibit statistical noise that causes uncertainty in the resulting estimate of $D^*$. An optimal scheme for estimating $D^*$ minimises this uncertainty, i.e., it will have high statistical efficiency, and also gives an accurate estimate of the uncertainty itself. We present a scheme for estimating $\D$ from a single simulation trajectory with high statistical efficiency and accurately estimating the uncertainty in the predicted value. The statistical distribution of MSDs observable from a given simulation is modelled as a multivariate normal distribution using an analytical covariance matrix for an equivalent system of freely diffusing particles, which we parameterise from the available simulation data. We use Bayesian regression to sample the distribution of linear models that are compatible with this multivariate normal distribution, to obtain a statistically efficient estimate of $D^*$ and an accurate estimate of the associated statistical uncertainty.