and 6). Insets were created using the OVITO software package [@Stukowski2010]. Thus the low-fidelity LJ explores a vastly different region in phase space as compared to that of the high-fidelity Sine 7; however, even under such unfavorable conditions FUQ is able to provide some level of correction. In contrast, the solid cases have sharply peaked distributions with strong overlap and correspondingly highly accurate predictions, with the caveat of more difficult convergence of the results. Histograms for all physical cases and potentials are within the supplementary material.

The degree of similarity of phase space exploration can be further summarized by plotting the average of $\Delta U_0$ against the average of $\Delta U_1$. The closer to slope of unity, the more significant the distribution overlap. Figure \[fig:histpoints\] gives results that agree with the histograms in Fig. \[fig:hist\] and supplementary material; namely, for cases where the explored phase space for the low and high-fidelity trajectories is less similar and there is little histogram overlap, the prediction error increases, particularly for the ambient liquid. Results in this figure for the Morse (gray symbols) and hybrid LJ-Morse (white) potentials are discussed in sub-section \[sec:resultsMorse\].

Correction for the Morse potential and hybrid potential calculations {#sec:resultsMorse}
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