Table 1.
Mean absolute errors for atomisation energies 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)
| References | ML method/descriptor | Dataset | (Training–Test sizes) | 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 | – | – |
CV denotes a cross validation procedure. Since NN descriptors can be quite complex, they have been omitted