Emission-line diagnostics of HII regions using conditional Invertible
  Neural Networks
  Young massive stars play an important role in the evolution of the
interstellar medium (ISM) and the self-regulation of star formation in giant
molecular clouds (GMCs) by injecting energy, momentum, and radiation (stellar
feedback) into surrounding environments, disrupting the parental clouds, and
regulating further star formation. Information of the stellar feedback inheres
in the emission we observe, however inferring the physical properties from
photometric and spectroscopic measurements is difficult, because stellar
feedback is a highly complex and non-linear process, so that the observational
data are highly degenerate. On this account, we introduce a novel method that
couples a conditional invertible neural network (cINN) with the
WARPFIELD-emission predictor (WARPFIELD-EMP) to estimate the physical
properties of star-forming regions from spectral observations. We present a
cINN that predicts the posterior distribution of seven physical parameters
(cloud mass, star formation efficiency, cloud density, cloud age which means
age of the first generation stars, age of the youngest cluster, the number of
clusters, and the evolutionary phase of the cloud) from the luminosity of 12
optical emission lines, and test our network with synthetic models that are not
used during training. Our network is a powerful and time-efficient tool that
can accurately predict each parameter, although degeneracy sometimes remains in
the posterior estimates of the number of clusters. We validate the posteriors
estimated by the network and confirm that they are consistent with the input
observations. We also evaluate the influence of observational uncertainties on
the network performance.
