Optimal statistical estimators for diffusivity in particle-based simulations of fluids

Although particle-based simulations are used to study a broad range of micro- and nano-scale flow phenomena, a task as seemingly simple as constructing an error bar to place on a result obtained from a particle-based simulation can be fraught with subtleties. In this talk, by performing simulations on a variety of systems of interest to micro- and nano-scale fluid mechanics, we demonstrate that traditional approaches for quantifying uncertainty in transport calculations, including and especially for diffusivity, can fail (at times dramatically) to capture the true variance of this quantity. We argue that commonplace techniques for computing standard errors in transport measurements (typically based upon ordinary-least-squares estimators) are prone to overconfident predictions. Motivated by tools used to resolve a similar problem in econometrics, we present a simple and computationally efficient scheme that can significantly alleviate these issues, yielding more confidence in particle-based simulations of fluid transport phenomena.