quantified uncertainties. Examples of input functions with varying degrees of accuracy include exchange and correlation functionals used in density functional theory calculations [@Mortensen2005; @Aldegunde2016], interatomic potentials for molecular dynamics (MD) [@Rizzi2012p2; @Rizzi2013p2; @Farrell2015], generalized stacking faults used in dislocation dynamics [@Cao2015], and constitutive laws for micromechanical simulations. In this paper we use functional derivatives (FD), recently proposed as a mathematical framework to quantify uncertainties that arise from constitutive models used in simulations [@Strachan2013], to quantify and correct uncertainties that originate from the interatomic potential used in MD simulations.

Functional uncertainty quantification (FUQ) can, in principle, be used to assess the uncertainties originating from approximate input constitutive laws, correct predictions if a more accurate function becomes available, and rank when and where to replace a low-fidelity model used in a simulation with one of higher fidelity in order to reduce prediction error by running additional simulations. This paper introduces a computationally efficient method to compute FDs in MD simulations involving two-body interatomic potentials, extending ideas from thermodynamic integration and free-energy perturbation methods [@Frenkel2001; @Chipot2007]. The FD quantifies how a quantity of interest (QoI) – in this case the total potential energy or pressure computed from an MD simulation in the canonical 