and HCP are competing close packed structures). The generalized stacking fault energy (GSFE) slip path provides an estimate of the resistance for dislocation slip and the energy per unit area required to form a single stacking fault. The GSFE twinning path (also known as the Generalized Planar Fault Energy) is an extension of the slip path and provides an estimate of the energy per unit area required to form $n$-layer faults (twins) by shearing $n$ successive $\{111\}$ layers along $\langle 112 \rangle$. We calculated the GSFE slip path and the twinning paths using standard methods [@Vitek1968IntrinsicCrystals; @Duesbery1998OverviewMetals; @Tadmor2004ACrack; @VanSwygenhoven2004StackingMetals].

Figures \[fig:bain\_sf\]b and \[fig:bain\_sf\]c show energies along the GSFE slip and twin paths, respectively. As before, we compare with seven EAM-based potentials. The ANI-Al potential agrees quite well with the reference DFT data for all measurements in Fig. \[fig:bain\_sf\]. To quantify this agreement, we calculate the root mean squared error (RMSE), formed as an average over the Bain, GFSE slip, and GFSE twinning paths. ANI-Al achieves RMSE values of [${4.5}\,\mathrm{meV/atom}$]{}, [${16.6}\,\mathrm{mJ/m^2}$]{}, and [${11.4}\,\mathrm{mJ/m^2}$]{}, respectively. For predicting these paths, the best classical potential is by Mishin et al.[@Mishin1999InteratomicCalculations], which achieves errors of [${4.3}\,\mathrm{meV/atom}$]{}, [${52.5}\,\mathrm{mJ/m^2}$]{}, and [${15.9}\,\mathrm{mJ/m^2}$]{}. Figure S2 of the SI provides 