Table 2 Prediction errors for energies (meV/atom) and forces (meV/Å) by system, level, and potential

From: Machine learned interatomic potentials for ternary carbides trained on the AFLOW database

Alloy

Energy errors (meV/atom)

Force errors (meV/Å)

Level 10

Robust potential

Accurate potential

Robust potential

Accurate potential

CHfTa

45 (75)

24 (36)

89 (281)

82 (270)

CHfZr

55 (87)

37 (62)

81 (255)

57 (170)

CMoW

53 (105)

88 (155)

99 (318)

88 (273)

CTaTi

51 (85)

53 (70)

99 (303)

76 (220)

Level 16

Robust potential

Accurate potential

Robust potential

Accurate potential

CHfTa

42 (72)

29 (90)

79 (238)

53 (169)

CHfZr

43 (77)

22 (30)

68 (211)

42 (112)

CMoW

46 (96)

76 (129)

88 (278)

55 (167)

CTaTi

41 (60)

45 (59)

90 (285)

56 (161)

Level 22

Robust potential

Accurate potential

Robust potential

Accurate potential

CHfTa

44 (70)

21 (57)

85 (270)

23 (71)

CHfZr

39 (62)

29 (91)

61 (197)

18 (59)

CTaTi

36 (58)

82 (218)

73 (223)

25 (79)

Level 16*

Robust potential

Accurate potential

Robust potential

Accurate potential

CHfTa

126 (156)

16 (19)

129 (381)

50 (150)

CHfZr

78 (107)

24 (37)

93 (278)

40 (114)

CMoW

91 (131)

67 (120)

108 (336)

52 (196)

CTaTi

119 (153)

92 (112)

110 (345)

45 (134)

  1. Each box contains the mean absolute-error (MAE) and, in parentheses, the root-mean-squared error (RMSE). Only the Robust Potential (RP) and the Accurate Potential (AP) developed during the active learning scheme (ALS) as illustrated in Fig. 1 are shown here; training data for the pre-Robust Potential is provided in Supplementary Table 1. The errors for the RP are calculated by comparing the energies of the final relaxed structures found within AFLOW to their RP-predicted energies and forces. The errors for the AP are calculated in a similar fashion, except only the structures whose AFLOW energies are within 50 meV/atom of the most stable configuration for a particular stoichiometry were considered.
  2. *Calculations performed without pre-training the MTP on the AFLOW data (gray box in Fig. 1).