Not Saved by the Bell: Non-Gaussianity and Fluid Transport Measurements in Molecular-Dynamics Simulations

In interpreting molecular-dynamics (MD) simulations, it is frequently taken for granted that measurements meet (seemingly vanilla) standards of statistical regularity, enabling the use of commonplace statistical procedures for model fitting and uncertainty quantification. In this talk, we explore several systems in which such assumptions break down in subtle and surprising ways, with a specific focus on fluid diffusion under spatial confinement. In a wide-ranging array of MD simulations reflecting systems of engineering interest, we demonstrate that distributions of mean-squared displacement exhibit significant non-Gaussianity at fixed times as well as significant heteroscedasticity over time. If unaccounted for, these statistical qualities tend to lead to underestimates of the simulation time required to characterize fluid transport and, ultimately, overconfident estimates of transport quantities. Drawing on modern tools for regression analysis of time series, we discuss strategies for ameliorating these issues. Our work highlights the unusual statistical challenges posed by (and numerous opportunities to improve the interpretation of) MD simulations of fluids, especially in confined and heterogeneous environments.