of the functional sensitivity (the FD) and functional discrepancy $(g(z)-f(z))$. We call this product the functional error and the correction for the QoI is: $$\label{eq:correct}
\Delta Q = \int \frac{\delta Q[f]}{\delta f(z)} \cdot (g(z)-f(z)) dz$$ In the absence of a high-fidelity model Eq. \[eq:correct\] can alternatively be used for uncertainty propagation by replacing the discrepancy with the uncertainty in $f(z)$ and taking the absolute value of the functional derivative [@Strachan2013]. This procedure returns a first order bound of the uncertainty in Q.

Additionally, this equation can be used to rank high-fidelity simulations in order of their functional error to optimally reduce the error in the predicted QoI, recently demonstrated with calculation of the functional derivative for the restoring force in a multi-fidelity radio frequency MEMS switch simulation [@Strachan2013]. This functional derivative was used to rank model evaluations and minimize the necessary computational cost to maximize error correction in the simulation. In Section 3 we extend the formulation to a significantly more challenging problem: molecular dynamics simulations.

Functional derivatives in molecular dynamics
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Systems of interest and simulation details
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We demonstrate the FUQ method in molecular dynamics simulations where the input function is the pairwise interatomic potential and the QoIs 