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

Modern spectroscopic surveys obtain spectra for millions of stars. However, classical spectroscopic methods can often be computationally expensive, rendering them impractical for the analysis of large datasets. We introduce a novel simulation-based deep-learning approach for the efficient analysis of high-resolution stellar spectra to be obtained with the upcoming high-resolution 4MOST spectrograph. We used a suite of synthetic non-local thermodynamic equilibrium (NLTE) spectra generated with Turbospectrum to mimic 4MOST observations and trained a conditional invertible neural network (cINN) for the purpose of predicting self-consistently stellar surface parameters and chemical abundances. The cINN is a neural network architecture that estimates full posterior distributions for the target stellar properties, providing an intrinsic uncertainty estimate. We evaluated the predictive performance of the trained cINN model on both synthetic data and observed spectra of stars. We found that our new cINN trained on NLTE synthetic spectra is capable of recovering stellar parameters with average errors ($\sigma$) of $33$ K for $T_\mathrm{eff}$, $0.16$ dex for $\log(g)$, and $0.12$ dex for [Fe/H], $0.1$ dex for [Ca/Fe], $0.11$ for [Mg/Fe], and $0.51$ dex for [Li/Fe], respectively, at a signal to noise ratio of 250 per Angstrom. From the analysis of the observed spectra of Gaia-ESO / 4MOST / PLATO benchmark stars, we verified that our NLTE estimates for stellar parameters and abundances are consistent with results obtained with the independent code TSFitPy. We conclude that the NLTE cINN is robust and can, theoretically, evaluate 4 million high-resolution 4MOST spectra in less than a day, using GPU acceleration.