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Table 1 Mean absolute errors for atomisation energies \(U_0\) in kcal/mol, HOMO and LUMO energies (in eV) for several models Kernel Ridge regression (KRR), Elastic Net (EN), Gaussian process regression (KRR), and neural networks (NN) reported in the literature (from oldest to most recent)

From: Dataset’s chemical diversity limits the generalizability of machine learning predictions

References ML method/descriptor Dataset (Training–Test sizes) \(U_0\) HOMO LUMO
Rupp [12] KRR/CM QM7 (7000–165) 10.0
Montavon [21] multitask NN QM7b (CV 5000–2211) 3.7 0.15 0.13
Hansen [14] KRR/BoB QM7 (CV 5732–1433) 1.5
Huang [16] KRR/BoB QM7b (5011–2200) 1.8 0.15 0.16
Huang [16] KRR/BAML QM7b (5011–2200) 1.2 0.10 0.11
Faber [17] EN/CM QM9 (CV 118k–13k) 21.0 0.34 0.63
Faber [17] EN/BoB QM9 (CV 118k–13k) 13.9 0.28 0.52
Faber [17] KRR/CM QM9 (CV 118k–13k) 3.0 0.13 0.18
Faber [17] KRR/BoB QM9 (CV 118k–13k) 1.5 0.09 0.12
Faber [17] KRR/BAML QM9 (CV 118k–13k) 1.2 0.09 0.12
Bartók [19] GPR/SOAP-GAP QM7b (5411–1800) 0.40
Bartók [19] GPR/SOAP-GAP QM9 (100k–31k) 0.28
Gilmer [23] NMP NN QM9 (120k–10k) 0.45 0.04 0.04
Smith [22] ANI-1 NN ANI (13.7M–1.7M) <1.5
Hou [26] multitask NN QM9 (119k–13k) 44.0 0.38 0.63
Schütt [24] SchNet NN QM9 (CV 110k–10k) 0.32 0.04 0.03
Lubbers [27] HIP-NN QM9 (CV 110k–20k) 0.26
Unke [28] HDNN QM9 (CV 100k–30k) 0.41
Willatt [30] KRR/SOAP QM9 (CV 100k–30k) 0.14
Unke [2] PhysNet NN QM9 (CV 110k–20k) 0.14
  1. CV denotes a cross validation procedure. Since NN descriptors can be quite complex, they have been omitted