DFT, for crystal structure $x$ at its energy-minimizing volume. By definition, we employ energy shifts such that $\epsilon_\textrm{fcc} = 0$. After FCC, the second lowest energy structure is HCP, for which the ANI-Al error is $\epsilon_\textrm{hcp} = 0.42\,\textrm{meV}/\textrm{atom}$. Note that FCC and HCP are competing close-packed structures, and both can reasonably be expected to emerge in our active learning dynamics. Specifically, HCP can be viewed, locally, as a stacking fault within FCC, and it is plausible that such configurations are contained within our training dataset. BCC, by contrast, is only physical in aluminum at much higher densities, far beyond the range of our active learning sampling. It is not surprising, therefore, that the ANI-Al error for BCC is an order of magnitude larger, $\epsilon_\textrm{bcc} = 5.3\,\textrm{meV}/\textrm{atom}$. Simple cubic and diamond crystals are less physical still, and we observe $\epsilon_\textrm{sc} = 37\,\textrm{meV}/\textrm{atom}$ and $\epsilon_\textrm{diamond} = - 44\,\textrm{meV}/\textrm{atom}$. Nonetheless, the agreement between ANI-Al and DFT observed in Fig. \[fig:coldcurveAl\] is remarkable. We emphasize that ANI-Al is not explicitly trained to any of these crystal structures. Also note that ANI-Al is capable of extrapolating beyond the range of densities (yellow region) contained in the training data. Similar observations were found in Ref. .

