somewhat limited (e.g., by nucleating lattices that are incommensurate with the supercell, or by formation of frustrated polycrystals), and it is possible that enhancements to the sampling strategy could yield better prediction of elastic constants. For example, future work might employ time-varying applied strains of the supercell, in addition to the time-varying temperatures employed in the present study.

Lack of DFT convergence may also be a limiting factor. Our choice of a $3\times 3\times 3$ $k$-space basis was, in retrospect, too small, given that our supercells have linear dimensions up to [${17}\,\mathrm{{\textup{\AA}}}$]{}. Consequently, we observed an artificial dependence of calculated DFT properties on the size of the supercell. Note, however, that the errors in ANI-Al predicted elastic constants are roughly the same order as good DFT/PBE calculations. For example, prior theoretical work calculated $C_{44} = {{29.5}\,\mathrm{GPa}}$ [@Pham2011Finite-temperatureMeasurements], which is in line with the ANI-Al result, [${30.4}\,\mathrm{GPa}$]{}, both predictions being smaller than experiment, [${31.6}\,\mathrm{GPa}$]{}.

For the task of predicting elastic constants, ANI-Al accuracy is on par with many classical potentials (see Fig. S1 in the supplemental information). Whereas classical potentials are explicitly *designed* to reproduce experimental elastic constants, in ANI-Al this capability is an *emergent* property. Our active learning sampling discovers 