Predicting elastic constants
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We can compare ANI-Al predicted elastic constants against experimental data. A particularly important property is the bulk modulus, which corresponds to the curvature of the FCC cold curve at its minimum (Fig. \[fig:coldcurveAl\]b). Experimentally, the FCC bulk modulus is measured to be [${79}\,\mathrm{GPa}$]{} [@Simmons1971SingleHandbook], whereas the ANI-Al prediction is [${77.3}\,\mathrm{GPa}$]{}. The full set of FCC elastic constants is measured experimentally to be, $C_{11}={{114}\,\mathrm{GPa}}$, $C_{12}={{61.9}\,\mathrm{GPa}}$, and $C_{44}={{31.6}\,\mathrm{GPa}}$ [@Simmons1971SingleHandbook]. For ANI-Al, we predict $C_{11}={{117}\,\mathrm{GPa}}$, $C_{12}={{57.2}\,\mathrm{GPa}}$, and $C_{44}={{30.4}\,\mathrm{GPa}}$.

There are several possible sources for the disagreement between ANI-Al and experiment: (1) Incomplete sampling of FCC crystal configurations, (2) failure of the ML model to capture the training data, (3) inconsistency of the DFT data due to lack of convergence in $k$-space basis set, and (4) inaccuracy of the DFT functional itself.

The largest discrepancy in the ANI-Al predicted elastic constants is observed in $C_{12}$, for which the relative error is 8%. This elastic constant measures the linear response of a normal stress to a strain in an orthogonal direction. For the ML model to precisely capture $C_{12}$, the training data should ideally contain bi-axially strained FCC configurations. The mechanisms by which our active learning can generate strained FCC are 