Bayesian Stokes inversion with Normalizing flows
arXiv:2108.07089 · doi:10.1051/0004-6361/202142018
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.
arXiv comment11 pages, 7 figures, accepted for publication in A&A
References in corpus (40)
- Adam: A Method for Stochastic Optimization
- emcee: The MCMC Hammer
- Deep Residual Learning for Image Recognition
- NICE: Non-linear Independent Components Estimation
- Normalizing Flows: An Introduction and Review of Current Methods
- The frontier of simulation-based inference
- CRISP Spectropolarimetric Imaging of Penumbral Fine Structure
- Spectroscopy Made Easy: Evolution
- Normalizing Flows for Probabilistic Modeling and Inference
- Real-time gravitational-wave science with neural posterior estimation
- STiC -- A multi-atom non-LTE PRD inversion code for full-Stokes solar observations
- Inversion of the radiative transfer equation for polarized light
- Non-LTE inversions of the Mg II h&k and UV triplet lines
- DELO-Bezier formal solutions of the polarized radiative transfer equation
- 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
- A method for global inversion of multi-resolution solar data
- BayesCLUMPY: Bayesian Inference with Clumpy Dusty Torus Models
- 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
- On chromospheric heating during flux emergence in the solar atmosphere
- An observationally-constrained model of strong magnetic reconnection in the solar chromosphere. Atmospheric stratification and estimates of heating rates
- Bayesian Coronal Seismology
- Solar image denoising with convolutional neural networks
- Stratification of physical parameters in a C-class solar flare using multi-line observations
- Strategies for Spectral Profile Inversion using Artificial Neural Networks
- Observationally based models of penumbral microjets
- Spectropolarimetric analysis of an active region filament. I. Magnetic and dynamical properties from single component inversions
- Overview of Approximate Bayesian Computation
- Neural Spline Flows
- Physical properties of bright Ca II K fibrils in the solar chromosphere
- 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
- Mapping the Sun's upper photosphere with artificial neural networks
- Modeling the Gaia Color-Magnitude Diagram with Bayesian Neural Flows to Constrain Distance Estimates