A method to derive self-consistent NLTE astrophysical parameters for four million high-resolution 4MOST stellar spectra in half a day with invertible neural networks

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Volume 708 (April 2026)

A&A, 708 (2026) A118

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Table A.1

Overview of the cINN predictive performance in terms of the mean and standard deviation, ${\bar{Δ}}_{cINN-GT} \pm σ_{cINN-GT}$ $Mathematical equation: $\bar{\Delta}_{\text {cINN-GT }} \pm \sigma_{\text {cINN-GT}}$$ , of the residuals of the target parameters with respect to the ground truth on synthetic test data for different S/N.

S/N (Å⁻¹)	T_eff (K)	$log (\frac{g}{{cms}^{- 2}})$ $Mathematical equation: $\log \left(\frac{g}{\mathrm{cms}^{-2}}\right)$$	[Fe/H]	v_broad (kms⁻¹)	v_mic (kms⁻¹)	Ca	[x/Fe] Mg	Li
1000	2.00 ± 32	0.003 ± 0.15	0.01 ± 0.11	0.05 ± 1.19	−0.029 ± 0.27	−0.006 ± 0.09	−0.005 ± 0.10	0.010 ± 0.49
250	1.46 ± 33	0.005 ± 0.16	0.01 ± 0.12	0.02 ± 1.27	−0.028 ± 0.27	−0.007 ± 0.10	−0.008 ± 0.11	0.018 ± 0.51
180	0.86 ± 36	0.005 ± 0.17	0.01 ± 0.12	0.03 ± 1.33	−0.029 ± 0.27	−0.007 ± 0.10	−0.007 ± 0.11	0.016 ± 0.52
130	1.07 ± 39	0.003 ± 0.19	0.01 ± 0.12	0.05 ± 1.52	−0.025 ± 0.28	−0.005 ± 0.11	−0.007 ± 0.12	0.014 ± 0.53
100	1.58 ± 44	−0.002 ± 0.21	0.01 ± 0.13	0.05 ± 1.65	−0.026 ± 0.29	−0.007 ± 0.12	−0.007 ± 0.13	0.012 ± 0.55
80	0.56 ± 49	−0.002 ± 0.23	0.01 ± 0.14	0.04 ± 1.83	−0.023 ± 0.29	−0.008 ± 0.12	−0.004 ± 0.14	0.011 ± 0.57
50	2.68 ± 62	−0.006 ± 0.29	0.01 ± 0.16	0.04 ± 2.64	−0.023 ± 0.31	−0.008 ± 0.14	−0.007 ± 0.17	−0.004 ± 0.63
45	2.37 ± 68	−0.009 ± 0.31	0.02 ± 0.18	0.03 ± 2.95	−0.020 ± 0.32	−0.009 ± 0.15	−0.007 ± 0.17	0.002 ± 0.64
40	4.23 ± 73	−0.010 ± 0.31	0.02 ± 0.18	0.06 ± 3.10	−0.023 ± 0.33	−0.012 ± 0.16	−0.008 ± 0.18	−0.002 ± 0.66
35	3.95 ± 81	−0.005 ± 0.34	0.02 ± 0.20	−0.04 ± 3.74	−0.026 ± 0.33	−0.009 ± 0.16	−0.010 ± 0.18	−0.013 ± 0.68
30	5.35 ± 90	−0.007 ± 0.38	0.02 ± 0.20	−0.02 ± 3.88	−0.030 ± 0.35	−0.015 ± 0.17	−0.013 ± 0.19	−0.008 ± 0.71
26	7.29 ± 100	0.008 ± 0.39	0.03 ± 0.23	−0.06 ± 4.41	−0.031 ± 0.36	−0.016 ± 0.18	−0.015 ± 0.20	−0.020 ± 0.74
23	7.88 ± 111	0.012 ± 0.42	0.04 ± 0.25	−0.07 ± 5.01	−0.035 ± 0.37	−0.017 ± 0.19	−0.014 ± 0.21	−0.031 ± 0.76
20	11.4 ± 127	0.018 ± 0.46	0.05 ± 0.28	−0.13 ± 5.93	−0.036 ± 0.38	−0.017 ± 0.19	−0.014 ± 0.21	−0.035 ± 0.79
18	12.4 ± 138	0.022 ± 0.48	0.06 ± 0.30	−0.10 ± 6.42	−0.036 ± 0.39	−0.018 ± 0.20	−0.014 ± 0.22	−0.057 ± 0.80
16	17.7 ± 149	0.023 ± 0.51	0.07 ± 0.33	0.06 ± 7.29	−0.041 ± 0.39	−0.016 ± 0.20	−0.015 ± 0.22	−0.051 ± 0.83
14	17.3 ± 172	0.014 ± 0.55	0.08 ± 0.36	−0.02 ± 7.59	−0.039 ± 0.40	−0.024 ± 0.21	−0.014 ± 0.23	−0.080 ± 0.85
12	24.1 ± 196	0.013 ± 0.60	0.11 ± 0.39	0.09 ± 8.28	−0.034 ± 0.42	−0.022 ± 0.21	−0.013 ± 0.23	−0.113 ± 0.89
10	17.5 ± 233	−0.002 ± 0.64	0.12 ± 0.46	0.23 ± 9.59	−0.017 ± 0.43	−0.026 ± 0.22	−0.014 ± 0.24	−0.163 ± 0.94

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