How to produce confidence intervals instead of confidence tricks: Representative sampling for molecular simulations of fluid self-diffusion under nanoscale confinement

Abstract

Ergodicity (or at least the tantalizing promise of it) is a core animating principle of molecular-dynamics (MD) simulations: Put simply, sample for long enough (in time), and you will make representative visits to states of a system all throughout phase space, consistent with the desired statistical ensemble. However, one is not guaranteed a priori that the chosen window of sampling in a production run is sufficiently long to avoid problematically non-ergodic observations; one is also not guaranteed that successive measurements of an observable are statistically independent of each other. In this paper, we investigate several particularly striking and troublesome examples of statistical correlations in MD simulations of nanoconfined fluids, which have profound implications on the quantification of uncertainty for transport phenomena in these systems. In particular, we show that these correlations can lead to confidence intervals on the fluid self-diffusion coefficient that are dramatically overconfident and estimates of this transport quantity that are simply inaccurate. We propose a simple approach—based on the thermally accelerated decorrelation of fluid positions and momenta—that ameliorates these issues and improves our confidence in MD measurements of nanoconfined fluid transport properties. We demonstrate that the formation of faithful confidence intervals for measurements of self-diffusion under nanoscale confinement typically requires at least 20 statistically independent samples, and potentially more depending on the sampling technique used.