Inferring stellar parameters and their uncertainties from high-resolution spectroscopy using invertible neural networks

Context: New spectroscopic surveys will increase the number of astronomical objects requiring characterization by over tenfold.. Machine learning tools are required to address this data deluge in a fast and accurate fashion. Most machine learning algorithms can not estimate error directly, making them unsuitable for reliable science. Aims: We aim to train a supervised deep-learning algorithm tailored for high-resolution observational stellar spectra. This algorithm accurately infer precise estimates while providing coherent estimates of uncertainties by leveraging information from both the neural network and the spectra. Methods: We train a conditional Invertible Neural Network (cINN) on observational spectroscopic data obtained from the GIRAFFE spectrograph (HR10 and HR21 setups) within the Gaia-ESO survey. A key features of cINN is its ability to produce the Bayesian posterior distribution of parameters for each spectrum. By analyzing this distribution, we inferred parameters and their uncertainties. Several tests have been applied to study how parameters and errors are estimated. Results: We achieved an accuracy of 28K in $T_{\text{eff}}$, 0.06 dex in $\log g$, 0.03 dex in $[\text{Fe/H}]$, and between 0.05 dex and 0.17 dex for the other abundances for high quality spectra. Accuracy remains stable with low signal-to-noise ratio spectra. The uncertainties obtained are well within the same order of magnitude. The network accurately reproduces astrophysical relationships both on the scale of the Milky Way and within smaller star clusters. We created a table containing the new parameters generated by our cINN. Conclusion: This neural network represents a compelling proposition for future astronomical surveys. These coherent derived uncertainties make it possible to reuse these estimates in other works as Bayesian priors and thus present a solid basis for future work.