Table 1 Performance of four versions of the CACE-LR potentials on each test set

Version	1	2	3	4
	E+F	E+F	E+F	E+F+BEC
N_config	654	654	100	100
r_cut(Å)	5.5	4.5	4.5	4.5
E	0.22	0.25	0.26	0.19
F	18.88	21.01	23.84	25.34
\({Z}_{\alpha \alpha }^{* }\)	0.11	0.06	0.05	0.04
\({Z}_{\alpha \beta }^{* }\)	0.04	0.04	0.05	0.03
\({Z}_{\alpha \alpha }^{* }\,{R}^{2}\)	0.97	0.99	0.99	1.00
\({Z}_{\alpha \beta }^{* }\,{R}^{2}\)	0.90	0.90	0.89	0.94

Reported metrics are test root mean squared errors (RMSE)s: in meV/atom for energy (E), meV/ Å for forces (F), and e for Born effective charge (BEC) tensors, separated into diagonal (\({Z}_{\alpha \alpha }^{* }\)) and off-diagonal (\({Z}_{\alpha \beta }^{* }\) with α ≠ β) components. R² coefficients for BEC components are also included.

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