described in Sec. \[Methods\], ANI-Al is trained from over 6,000 DFT calculations that were carefully selected using an iterative “active learning” procedure.

![Crystal energies (per atom) as a function of volume (per atom), relative to the ground state. Solid lines represent ANI-Al predictions and circles represent DFT reference calculations. Vertical bars represent sample variance of the eight neural networks comprising the (ensembled) ANI-Al model. Panel (b) is a magnification of panel (a) near the energy minima. The yellow region, from 11 to [${25}\,\mathrm{{\textup{\AA}}^3/atom}$]{}, indicates the approximate sampling range of the training data. Crystal structures explored: Diamond, simple cubic (SC), body centered cubic (BCC), hexagonal close packed (HCP), and face centered cubic (FCC).[]{data-label="fig:coldcurveAl"}](images/cold_curve_Al_AL_vert.pdf){width="\linewidth"}

Predicting crystal energies
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Figure \[fig:coldcurveAl\] shows ANI-Al predicted energies (solid lines) for select crystal structures. ANI-Al correctly predicts that FCC is the lowest energy structure for aluminum. Vertical bars show the sample variance over the eight neural networks that comprise a single ANI-Al model (i.e., the uncertainty measure used within the active learning procedure). DFT reference data is shown in circles.

For both ANI-Al and DFT calculations, energies are measured relative to the FCC ground state. Let $\epsilon_x$ represent the error in the ANI-Al prediction, relative to 