bibliography:
- 'bibtex/Reeve-Strachan-2016\_main.bib'
title: 'Error correction in multi-fidelity molecular dynamics simulations using functional uncertainty quantification'
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uncertainty quantification ,functional derivative ,molecular dynamics ,interatomic potential ,free energy calculation

Introduction
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Uncertainty quantification (UQ) is becoming increasingly important in predictive simulations of materials and devices [@Chernatynskiy2013]. While the majority of the early UQ work focused on solid and fluid mechanics, there is growing interest in applying and extending UQ techniques to simulations at the material level, including density functional theory [@Mortensen2005; @Anderson2012], molecular dynamics (MD) [@Rizzi2012p1; @Rizzi2013p1; @Angelikopoulos2013; @Karniadakis2015; @Patrone2016], and multiscale methods [@Koslowski2011; @Kim2013; @Vedula2013]. These efforts highlighted the importance of acknowledging uncertainties in model parameters, from measurement or averaging techniques, as well as intrinsic variability of the systems or processes under investigation. These studies, and most UQ work thus far, examined uncertainties in input parameters and specialized software packages have been developed for this task: examples include DAKOTA [@Adams2014], PUQ [@Hunt2015], and $\Pi$4U [@Hadjidoukas2015]. However, in many applications – especially those involving complex physics – accounting for uncertainty in parameters is not enough, as the functional forms of the constitutive models themselves are approximate. This is particularly true in materials modeling where lack of knowledge leads to unquantified or poorly 