Stellar parameter determination from photometry using invertible neural networks

Photometric surveys with the Hubble Space Telescope (HST) remain one of the most efficient tools in astronomy to study stellar clusters with high resolution and deep coverage. Estimating physical parameters of their constituents from photometry alone, however, is not a trivial task. Leveraging sophisticated stellar evolution models one can simulate observations and characterise stars and clusters. Due to observational constraints, such as extinction, photometric uncertainties and low filter coverage, as well as intrinsic effects of stellar evolution, this inverse problem suffers from degenerate mappings between the observable and physical parameter space that are difficult to detect and break. We employ a novel deep learning approach called conditional invertible neural network (cINN) to solve the inverse problem of predicting physical parameters from photometry on an individual star basis. Employing latent variables to encode information otherwise lost in the mapping from physical to observable parameter space, the cINN can predict full posterior distributions for the underlying physical parameters. We build this approach on carefully curated synthetic data sets derived from the PARSEC stellar evolution models. For simplicity we only consider single metallicity populations and neglect all effects except extinction. We benchmark our approach on HST data of two well studied stellar clusters, Westerlund 2 and NGC 6397. On the synthetic data we find overall excellent performance, with age being the most difficult parameter to constrain. For the real observations we retrieve reasonable results and are able to confirm previous findings for Westerlund 2 on cluster age ($1.04_{-0.90}^{+8.48}\,\mathrm{Myr} $), mass segregation, and the stellar initial mass function.