  Stellar feedback, the energetic interaction between young stars and their
birthplace, plays an important role in the star formation history of the
universe and the evolution of the interstellar medium (ISM). Correctly
interpreting the observations of star-forming regions is essential to
understand stellar feedback, but it is a non-trivial task due to the complexity
of the feedback processes and degeneracy in observations. In our recent paper,
we introduced a conditional invertible neural network (cINN) that predicts
seven physical properties of star-forming regions from the luminosity of 12
optical emission lines as a novel method to analyze degenerate observations. We
demonstrated that our network, trained on synthetic star-forming region models
produced by the WARPFIELD-Emission predictor (WARPFIELD-EMP), could predict
physical properties accurately and precisely. In this paper, we present a new
updated version of the cINN that takes into account the observational
uncertainties during network training. Our new network named Noise-Net reflects
the influence of the uncertainty on the parameter prediction by using both
emission-line luminosity and corresponding uncertainties as the necessary input
information of the network. We examine the performance of the Noise-Net as a
function of the uncertainty and compare it with the previous version of the
cINN, which does not learn uncertainties during the training. We confirm that
the Noise-Net outperforms the previous network for the typical observational
uncertainty range and maintains high accuracy even when subject to large
uncertainties.
