here to obtain the functional derivatives.

This work demonstrates FUQ in equilibrium simulations. Continuing work should include investigation of functional derivatives in non-equilibrium processes as an analog of the relationships between free energy perturbation and non-equilibrium work methods in free energy calculations. The method can be generally used in equilibrium MD simulations and numerous other physics problems including multi-scale simulations. Ongoing investigations will include using FUQ to correct predictions in solid mechanics with the plasticity model as the input constitutive law.

An important advantage of FUQ over uncertainty propagation in parameters is that it enables changes in the actual functional forms used in the simulation. In our example, we are not limited to Lennard-Jones potentials with different parameters but can change the shape of the potential (with the limitations discussed above).

Conclusions
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In summary we demonstrated the ability to calculate functional derivatives of a quantity of interest predicted by a non-trivial physics simulation with respect to its input laws. This information can be used to quantify the uncertainties originating in the simulation due to the use of the input function or to correct the prediction if a more accurate model becomes available. We developed a computationally efficient approach to 