Bayesian Stokes inversion with Normalizing flows

Abstract

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

11 pages, 7 figures, accepted for publication in A&A

References in corpus (19)

• NICE: Non-linear Independent Components Estimation
• CRISP Spectropolarimetric Imaging of Penumbral Fine Structure
• Real-time gravitational-wave science with neural posterior estimation
• Inversion of the radiative transfer equation for polarized light
• Non-LTE inversions of the Mg II h&k and UV triplet lines
• Radiative diagnostics in the solar photosphere and chromosphere
• Recovering Thermodynamics from Spectral Profiles observed by IRIS: A Machine and Deep Learning Approach
• Stokes Inversion based on Convolutional Neural Networks
• High-Dimensional Probability Estimation with Deep Density Models
• Inference of the chromospheric magnetic field orientation in the Ca II 8542 A line fibrils
• Dissecting bombs and bursts: non-LTE inversions of low-atmosphere reconnection in SST and IRIS observations
• An observationally-constrained model of strong magnetic reconnection in the solar chromosphere. Atmospheric stratification and estimates of heating rates
• Bayesian Coronal Seismology
• Spectropolarimetric analysis of an active region filament. I. Magnetic and dynamical properties from single component inversions
• RADYNVERSION: Learning to Invert a Solar Flare Atmosphere with Invertible Neural Networks
• Nested sampling with any prior you like
• Benchmarking Simulation-Based Inference
• Approximate Bayesian Neural Doppler Imaging
• Fully probabilistic quasar continua predictions near Lyman-α with conditional neural spline flows

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