Table 1.

Energy errors for the 1D data set

M	ML-OF						ML-HK (grid)						ML-HK (other)
	ΔE		ΔE F		ΔE D		ΔE		ΔE D		Δ$E_{\mathbf{D}}^{\mathbf{ML}}$		ΔE D (Fourier)		ΔE D (KPCA)
	MAE	Max	MAE	Max	MAE	Max	MAE	Max	MAE	Max	MAE	Max	MAE	Max	MAE	Max
20	7.7	47	7.7	60	8.8	87	3.5	27	0.76	8.9	9.7	70	0.58	8	0.15	2.9
50	1.6	30	1.3	7.3	1.4	31	1.2	7.1	0.079	0.92	0.27	2.4	0.078	0.91	0.011	0.17
100	0.74	17	0.2	2.6	0.75	17	0.19	2.1	0.027	0.43	0.18	2.4	0.031	0.42	0.0012	0.028
200	0.17	2.9	0.039	0.6	0.17	2.9	0.042	0.59	0.0065	0.15	0.02	0.46	0.017	0.14	0.00055	0.015

Errors are given in kcal/mol for various M, the number of training points. Displayed are the energy error, ΔE, the functional-driven error, ΔE _F, the density-driven error, ΔE _D, and its approximation, $\Delta E_{\mathrm{D}}^{\mathrm{ML}}$