A Molecular-Dynamicist Walks into an Error Bar: Rigorously Quantifying Uncertainties in Simulations of Transport under Confinement

All scientists and engineers should agree that carefully quantifying uncertainties is the right thing to do, but as the adage goes, "the right thing is not always the easy thing." This is especially true in the field of molecular dynamics (MD), in which a task as nominally simple as computing a standard error is fraught with subtlety. And yet, as MD simulation continues to grow in popularity, and as advances in computing enable unprecedentedly large MD simulations, it is increasingly important that our community demands rigorous uncertainty quantification. In this talk, we highlight this principle in the context of a deceptively straightforward problem, namely, computing the diffusion coefficient of a fluid under nanoscale confinement. As compared to their unconfined (bulk) counterparts, confined systems exhibit persistent correlations that reduce the number of independent samples produced per unit of simulation time. We demonstrate that common approaches to computing standard errors in diffusivity measurements, used widely throughout the literature, frequently overstate confidence in the diffusion coefficient. We conclude by exhibiting a simple scheme that inexpensively achieves sufficient decorrelation, enabling accurate quantification of uncertainty in confined systems.