Spectral classification of young stars using conditional invertible neural networks

Aims. We introduce an updated version of our deep learning tool that predicts effective temperature, surface gravity, extinction, and veiling from the optical spectra of young low-mass stars with intermediate spectral resolution. We determine the stellar parameters of 2051 stars in Trumpler 14 (Tr14) in the Carina Nebula Complex observed with VLT/MUSE. Methods. We adopted a conditional invertible neural network (cINN) architecture to infer the posterior distribution of stellar parameters and train our cINN on two Phoenix stellar atmosphere model libraries (Settl and Dusty). Compared to the cINNs presented in our first study, the updated cINN considers the influence of the relative flux error on the parameter estimation and predicts an additional fourth parameter, veiling. We tested the prediction performance of cINN on synthetic test models to quantify the intrinsic error of the cINN as a function of relative flux error and on 36 class III template stars to validate the performance on real spectra. Using our cINN, we estimated the stellar parameters of young stars in Tr14 and compared them with those derived using the classical template fitting method applied to the same data in a previous study. Results. We provide Teff, log g, AV, and rveil values of 2051 stars in Tr14 measured by our cINN as well as stellar ages and masses derived from the Hertzsprung–Russell diagram based on the measured parameters. Our parameter estimates generally agree well with those measured by template fitting. However, for K- and G-type stars, the Teff derived from template fitting is, on average, two to three subclasses hotter than the cINN estimates, while the corresponding veiling values from template fitting appear to be underestimated compared to the cINN predictions. We obtained an average age of 0.7−0.6+3.2 Myr for the Tr14 stars. By examining the impact of veiling on the equivalent width-based classification, we demonstrate that the main cause of temperature overestimation for K- and G-type stars in the previous study is that veiling and effective temperature are not considered simultaneously in their process. Conclusions. Our cINN performs comparably to the multi-dimensional template fitting method while being significantly faster and capable of consistently analysing stars across a wide temperature range (2600–7000 K).