Table 2 The representative properties selected by their correlation graphs for different types of MLIPs

\(\delta {E}_{{\rm{f}}}^{{\rm{vacancy}}}\)

1

1

1

1

1

1

\(\delta {E}_{{\rm{f}}}^{{\rm{split}}- < 110 > }\)

1

1

1

1

1

\(\delta {E}_{{\rm{f}}}^{{\rm{tetrahedral}}}\)

1

1

1

1

1

\(\delta {E}_{{\rm{f}}}^{{\rm{hexagonal}}}\)

1

1

1

1

1

1

\(\delta {C}_{11}^{{\rm{supercell}}}\)

1

1

1

1

\(\delta {C}_{12}^{{\rm{supercell}}}\)

1

1

1

1

1

\(\delta {C}_{44}^{{\rm{supercell}}}\)

1

1

1

1

1

1

\(\delta {K}^{{\rm{supercell}}}\)

1

1

1

1

\(\delta {C}_{11}^{{\rm{vacancy}}}\)

1

1

1

1

1

\(\delta {C}_{12}^{{\rm{vacancy}}}\)

1

1

1

1

\(\delta {C}_{44}^{{\rm{vacancy}}}\)

1

1

1

1

1

1

\(\delta {K}^{{\rm{vacancy}}}\)

1

1

1

1

1

\(\delta {C}_{11}^{{\rm{split}}- < 110 > }\)

1

1

1

1

\(\delta {C}_{12}^{{\rm{split}}- < 110 > }\)

\(\delta {C}_{44}^{{\rm{split}}- < 110 > }\)

1

1

1

1

\(\delta {K}^{{\rm{split}}- < 110 > }\)

1

1

1

1

\(\delta {C}_{11}^{{\rm{tetrahedral}}}\)

1

1

1

1

\(\delta {C}_{12}^{{\rm{tetrahedral}}}\)

1

1

1

1

1

1

\(\delta {C}_{44}^{{\rm{tetrahedral}}}\)

1

1

1

1

1

\(\delta {K}^{{\rm{tetrahedral}}}\)

1

1

\(\delta {C}_{11}^{{\rm{hexagonal}}}\)

1

1

1

1

\(\delta {C}_{12}^{{\rm{hexagonal}}}\)

1

1

1

\(\delta {C}_{44}^{{\rm{hexagonal}}}\)

1

1

1

1

1

1

1

\(\delta {K}^{{\rm{hexagonal}}}\)

1

1

1

1

1

\(\delta {a}^{{\rm{unit\; cell}}}\)

1

1

1

\(\delta {a}^{{\rm{supercell}}}\)

1

1

1

1

1

1

\(\delta {a}^{{\rm{vacancy}}}\)

1

1

1

1

1

1

1

\(\delta {a}^{{\rm{split}}- < 110 > }\)

1

1

1

1

1

1

\(\delta {a}^{{\rm{tetrahedral}}}\)

1

1

1

1

1

\(\delta {a}^{{\rm{hexagonal}}}\)

1

1

1

1

1

1

\({P}_{{\rm{ranking\; error}}}^{{\mathcal{D}}1}\)

1

1

1

1

1

1

Mean \({\Delta E}_{{\rm{DFT}}}^{{\mathcal{D}}1}\)

1

1

1

Maximum \({\Delta E}_{{\rm{DFT}}}^{{\mathcal{D}}1}\)

1

1

1

1

\({P}_{{\rm{ranking\; error}}}^{{\mathcal{D}}2}\)

1

Mean \({\Delta E}_{{\rm{DFT}}}^{{\mathcal{D}}2}\)

1

1

1

1

Maximum \({\Delta E}_{{\rm{DFT}}}^{{\mathcal{D}}2}\)

1

\({P}_{{\rm{ranking\; error}}}^{{\mathcal{D}}3}\)

1

1

1

1

Mean \({\Delta E}_{{\rm{DFT}}}^{{\mathcal{D}}3}\)

1

1

Maximum \({\Delta E}_{{\rm{DFT}}}^{{\mathcal{D}}3}\)

1

1

1

1

\({P}_{{\rm{ranking\; error}}}^{{\mathcal{D}}4}\)

1

1

1

Mean \({\Delta E}_{{\rm{DFT}}}^{{\mathcal{D}}4}\)

1

1

Maximum \({\Delta E}_{{\rm{DFT}}}^{{\mathcal{D}}4}\)

1

1

1

1

\(\Delta {NAC}({{\rm{\delta }}}_{{\rm{\theta }}},{{\mathcal{D}}}^{{\rm{RE}}-{\rm{I}}})\)

1

1

1

1

\(\Delta {NAC}\left({|\delta }_{{\rm{F}}},|,,{{\mathcal{D}}}^{{\rm{RE}}-{\rm{I}}}\right)\)

\(\Delta {NAC}({{\rm{\delta }}}_{{\rm{\theta }}},{{\mathcal{D}}}^{{\rm{RE}}-{\rm{V}}})\)

1

1

1

\(\Delta {NAC}({\rm{|}}{\delta }_{{\rm{F}}}|,{{\mathcal{D}}}^{{\rm{RE}}-{\rm{V}}})\)

1

\({\sigma }_{{\rm{E}}}^{{\rm{RE}}-{\rm{I}}}\)

1

1

1

1

\({\sigma }_{{\rm{F}}}^{{\rm{RE}}-{\rm{I}}}\)

1

1

\({\sigma }_{{\rm{E}}}^{{\rm{RE}}-{\rm{V}}}\)

1

1

1

1

\({\sigma }_{{\rm{F}}}^{{\rm{RE}}-{\rm{V}}}\)

1

1

\({\sigma }_{{\rm{E}}}^{{\rm{enhanced}}-{\rm{I}}}\)

1

1

\({\sigma }_{{\rm{F}}}^{{\rm{enhanced}}-{\rm{I}}}\)

1

1

\({\sigma }_{{\rm{E}}}^{{\rm{enhanced}}-{\rm{V}}}\)

1

1

1

1

1

\({\sigma }_{{\rm{F}}}^{{\rm{enhanced}}-{\rm{V}}}\)

\(\delta {E}_{{\rm{free}}}^{{\rm{bulk}}}\left(T\right)\)

1

1

\(\delta {S}^{{\rm{bulk}}}(T)\)

1

1

\(\delta {c}^{{\rm{bulk}}}(T)\)

1

1

\(\delta {E}_{{\rm{free}}}^{{\rm{vacancy}}}(T)\)

1

1

1

\(\delta {S}^{{\rm{vacancy}}}(T)\)

1

1

\(\delta {c}^{{\rm{vacancy}}}(T)\)

1

1

1

60

21

37

30

46

31

29

29