Table 1.

Experimental results.

		Decile of population										Global metrics
		1	2	3	4	5	6	7	8	9	10	CPC	NRMSE	Corr.	JSD
England
G	Mean CPC	0.66	0.51	0.40	0.34	0.28	0.25	0.20	0.16	0.12	0.08
	std CPC	0.18	0.09	0.07	0.04	0.04	0.03	0.03	0.02	0.02	0.02	0.11	0.51	0.35	0.73
	Mean CPC	0.64	0.50	0.41	0.36	0.31	0.27	0.21	0.16	0.13	0.08
	std CPC	0.18	0.07	0.06	0.07	0.06	0.04	0.03	0.02	0.02	0.02
NG	Rel. Imp.	-1.52	-1.88	0.35	5.79	6.41	4.41	3.82	4.46	3.99	4.53	0.12	0.45	0.56	0.72
	Mean CPC	0.66	0.52	0.45	0.41	0.36	0.36	0.32	0.30	0.26	0.19
	std CPC	0.17	0.09	0.07	0.05	0.04	0.04	0.06	0.05	0.04	0.04
MFG	Rel. Imp.	1.29	1.55	13.46	20.11	26.89	43.01	61.43	87.83	105.64	139.46	0.23	0.47	0.48	0.65
	Mean CPC	0.67	0.57	0.50	0.48	0.44	0.45	41	0.39	0.35	0.28
	std CPC	0.17	0.07	0.06	0.06	0.04	0.05	0.05	0.05	0.04	0.05
DG	Rel. Imp.	3.20	11.72	24.91	41.47	54.35	75.76	108.47	143.54	174.97	246.88	0.32	0.41	0.61	0.60
Italy
G	Mean CPC	0.26	0.38	0.41	0.37	0.31	0.29	0.27	0.24	0.21	0.13
	std CPC	0.27	0.14	0.09	0.09	0.08	0.07	0.06	0.06	0.05	0.05	0.18	0.48	0.49	0.69
	Mean CPC	0.31	0.44	0.48	0.43	0.38	0.35	0.34	0.30	0.25	0.15
	std CPC	0.31	0.14	0.10	0.10	0.08	0.07	0.06	0.07	0.06	0.06
NG	Rel. Imp.	19.30	14.63	16.41	16.82	19.76	22.26	23.67	22.93	19.93	19.45	0.21	0.45	0.57	0.67
	Mean CPC	0.29	0.41	0.45	0.41	0.37	0.33	0.31	0.28	0.23	0.14
	std CPC	0.30	0.16	0.09	0.09	0.09	0.07	0.06	0.07	0.06	0.06
MFG	Rel. Imp.	10.96	5.95	10.68	10.88	15.62	14.76	14.69	15.70	13.99	14.20	0.20	0.50	0.44	0.67
	Mean CPC	0.34	51	0.55	0.49	0.46	0.43	0.41	0.37	0.31	0.21
	std CPC	0.34	0.16	0.09	0.10	0.07	0.08	0.07	0.08	0.07	0.08
DG	Rel. Imp.	30.02	31.62	32.98	33.26	43.97	48.46	49.18	52.35	51.46	66.02	0.27	0.43	0.62	0.63
New York State
G	Mean CPC	0.29	0.35	0.24	0.25	0.13	0.13	0.16	0.09	0.06	0.04
	std CPC	0.31	0.28	0.25	0.26	0.19	0.18	0.19	0.14	0.04	0.02	0.06	0.74	0.03	0.78
	Mean CPC	0.29	0.35	0.43	0.46	0.42	0.49	0.45	0.50	0.49	0.47
	std CPC	0.31	0.28	0.20	0.22	0.19	0.13	0.16	0.05	0.02	0.03
NG	Rel. Imp.	0	0	75.71	81.90	206.35	278.09	180.91	405.66	607.17	1031.14	0.68	0.26	0.93	0.34
	Mean CPC	0.29	0.35	0.36	0.37	0.31	0.33	0.28	0.28	0.27	0.18
	std CPC	0.31	0.28	0.18	0.19	0.15	0.10	0.13	0.07	0.08	0.03
MFG	Rel. Imp.	0	0	49.70	48.08	126.68	157.01	74.47	184.04	297.44	351.59	0.28	0.48	0.35	0.62
	Mean CPC	0.29	0.35	0.43	0.46	0.42	0.49	0.45	0.51	0.52	0.49
	std CPC	0.31	0.28	0.20	0.22	0.19	0.13	0.16	0.06	0.05	0.03
DG	Rel. Imp.	0	0	75.80	82.41	208.03	282.91	184.33	416.43	661.03	1076.93	0.70	0.19	0.93	0.33

Comparison of the performance, in terms of Common Part of Commuters (CPC), of Gravity (G), Nonlinear Gravity (NG), Multi-Feature Gravity (MFG), and Deep Gravity (DG), for England, Italy, and New York State, varying the decile of the population of the regions of interest (side size of 25 km). We also provide a global evaluation of the goodness of each model in terms of CPC, Pearson correlation coefficient, Normalized Root Mean Squared Error (NRMSE), and the Jensen-Shannon divergence (JSD) between the distribution of real and generated flows. For each model, and for each decile of the distribution of population, we show the average CPC and the standard deviation of the CPC obtained over five runs of the model. For NG, MFG, and DG we also show the relative improvement in terms of CPC with respect to G. We put in bold the values over the deciles that correspond to the best mean CPC and relative improvement. Regardless of the evaluation metric, DG significantly improves on the other models in all the geographic areas considered.