Bayesian Stokes inversion with normalizing flows

Stokes inversion techniques are very powerful methods for obtaining information on the thermodynamic and magnetic properties of solar stellar atmospheres. In recent years, highly sophisticated codes have been developed that now routinely applied to spectro-polarimetric observations. Most these designed find an optimum solution nonlinear inverse problem. However, obtain location potentially multimodal cases (ambiguities), degeneracies uncertainties each parameter inferred from inversions algorithms – such as Markov chain Monte Carlo (MCMC) require evaluation likelihood model thousand times computationally costly. Variational a quick alternative methods, approximate posterior distribution by parametrized distribution. this study, we introduce flexible variational inference method perform fast Bayesian inference, known normalizing flows. Normalizing flows set invertible, differentiable, parametric transformations convert simple into approximation any other complex If conditioned observations, can be trained return probability estimates observation. We illustrate ability using Milne-Eddington non-local equilibrium (NLTE) inversion. The is extremely general more forward models applied. training procedure need only performed once given prior space resulting network then generate samples describing several orders magnitude faster than existing techniques.