. 2017 Feb 17;8:14282. doi: 10.1038/ncomms14282

Table 7. DFT aided validation for nine randomly selected RP oxides that were predicted to have an NCS ground state structure from ML.

RP oxides	DFT ground state	NCS ground state (in %)	Predicted space groups from ML [irrep label]					ΔE^D
		as predicted from ML	Tree 1	Tree 2	Tree 3	Tree 4	Tree 5
NaLaHfO₄	P2₁m (NCS)	100	Pca2₁ [⊕]	P2₁2₁2 [(η₁,η₂)]	P2₁m [(η₁,η₁)]	Pca2₁ [⊕]	P2₁2₁2 [(η₁,η₂)]	−17.9

NaLaZrO₄	P2₁m (NCS)	80	Pca2₁ [⊕]	P2₁2₁2 [(η₁,η₂)]	Pbcm [(0,η₁)]	Pca2₁ [⊕]	P2₁2₁2 [(η₁,η₂)]	−22.6

NaLaIrO₄ (FM)	P2₁m (NCS)	100	Pca2₁ [⊕]	P2₁2₁2 [(η₁,η₂)]	P2₁m [(η₁,η₁)]	Pca2₁ [⊕]	P2₁2₁2 [(η₁,η₂)]	+204.6

KLaIrO₄ (FM)	Pbcm (CS)	80	Pca2₁ [⊕]	P2₁m [(η₁,η₁)]	Pca2₁ [⊕]	Pca2₁ [⊕]	Ibca [P₄]	+135.4

KBaNbO₄	P2₁ (NCS)	100	Pca2₁ [⊕]	P2₁m [(η₁,η₁)]	Pca2₁ [⊕]	Pca2₁ [⊕]	Pca2₁ [⊕]	−832

NaCaTaO₄	Pca2₁ (NCS)	100	Pca2₁ [⊕]	Pca2₁ [⊕]	P2₁m [(η₁,η₁)]	Pca2₁ [⊕]	P2₁2₁2 [(η₁,η₂)]	+15.9

SrLaInO₄	P2₁m (NCS)	100	Pca2₁ [⊕]	P2₁2₁2 [(η₁,η₂)]	P2₁2₁2 [(η₁,η₂)]	P2₁2₁2 [(η₁,η₂)]	P2₁2₁2 [(η₁,η₂)]	+38.9

SrYGaO₄	P2₁ (NCS)	80	P2₁2₁2 [(η₁,η₂)]	φ	P2₁2₁2 [(η₁,η₂)]	P2₁2₁2 [(η₁,η₂)]	Pca2₁ [⊕]	+26.4

BaLaGaO₄	P4/nmm (CS)	60	Pbcm [(0,η₁)]	P2₁2₁2 [(η₁,η₂)]	Pbcm [(0,η₁)]	P2₁2₁2 [(η₁,η₂)]	P2₁2₁2 [(η₁,η₂)]	−51.1

CS, centrosymmetric; DFT, density-functional theory; FM, ferromagnetic spin order imposed on the Ir-atom; ML, machine learning; NCS, noncentrosymmetric structures.

Note that in a vast majority of compounds the DFT energy difference between space groups P2₁2₁2 and P Inline graphic 2₁m is of the order of few tenths of meV per atom. Additional details are given in Supplementary Table 3 and Supplementary Note 4. For KBaNbO₄, the structure initialized with Pca2₁ symmetry converged to P2₁ in our DFT calculations. ΔE^D (in meV per atom) is the decomposition energy for a chemical reaction given in Supplementary Note 4. Negative and positive values for ΔE^D indicate that the compound is thermodynamically stable and unstable, respectively.