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Stokes Inversion Techniques with Neural Networks: Analysis of Uncertainty in Parameter Estimation

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Abstract

Magnetic fields are responsible for a multitude of solar phenomena, including potentially destructive events such as solar flares and coronal mass ejections, with the number of such events rising as we approach the peak of the 11-year solar cycle in approximately 2025. High-precision spectropolarimetric observations are necessary to understand the variability of the Sun. The field of quantitative inference of magnetic field vectors and related solar atmospheric parameters from such observations has been investigated for a long time. In recent years, very sophisticated codes for spectropolarimetric observations have been developed. Over the past two decades, neural networks have been shown to be a fast and accurate alternative to classic inversion methods. However, most of these codes can be used to obtain point estimates of the parameters, so ambiguities, degeneracies, and uncertainties of each parameter remain uncovered. In this paper, we provide end-to-end inversion codes based on the simple Milne-Eddington model of the stellar atmosphere and deep neural networks to both parameter estimation and their uncertainty intervals. The proposed framework is designed in such a way that it can be expanded and adapted to other atmospheric models or combinations of them. Additional information can also be incorporated directly into the model. It is demonstrated that the proposed architecture provides high accuracy results, including a reliable uncertainty estimation, even in the multidimensional case. The models are tested using simulations and real data samples.

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Data Availability

In the current study, we used a collection of the Level 1 calibrated Stokes spectra (comprised by images stored in FITS format) and a collection of the Level 2 data sets (obtained from the MERLIN spectral line inversion of the Level 1 calibrated spectra) produced by the Spectropolarimeter (SP) on board the Hinode, since its launch in 2006 (collected in the Community Spectropolarimetric Analysis Center (CSAC) at HAO/NCAR). Hinode is a Japanese mission, developed and launched by ISAS/JAXA, with NAOJ as a domestic partner and NASA and STFC (UK) as international partners. It is operated by these agencies in cooperation with ESA and NSC (Norway). The Hinode has an open data policy, allowing anyone to access the data and data products. Level 1 and 2 data are available by following the data link.

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Acknowledgments

Denis Derkach, Lukia Mistryukova, Aleksandr Khizhik, and Mikhail Hushchyn are grateful to the HSE basic research program. This research was supported in part through computational resources of HPC facilities at HSE University (Kostenetskiy, Chulkevich, and Kozyrev 2021).

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Authors and Affiliations

  1. HSE University, Myasnitskaya Street 20, 101000, Moscow, Russia

    Lukia Mistryukova, Aleksandr Khizhik, Mikhail Hushchyn & Denis Derkach

  2. Central Astronomical Observatory of the Russian Academy of Sciences at Pulkovo, Pulkovskoye Shosse 65/1, 196140, Saint-Petersburg, Russia

    Andrey Plotnikov & Irina Knyazeva

  3. Crimean Astrophysical Observatory, Russian Academy of Sciences, Nauchny, 298409, Crimea

    Andrey Plotnikov

  4. N.P. Bechtereva Institute of the Human Brain, Academica Pavlova Street 9, 197376, Saint-Petersburg, Russia

    Irina Knyazeva

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  1. Lukia Mistryukova
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  5. Mikhail Hushchyn
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Contributions

D.D. conceived and led the research; L.M. and A.K. performed calculations and processed the results; A.P., I.K., M.H. and D.D. analyzed and discussed the results; L.M., I.K. and D.D. wrote the main manuscript text; A.P. and I.K. processed data samples. All authors reviewed the manuscript.

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Correspondence to Lukia Mistryukova.

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Mistryukova, L., Plotnikov, A., Khizhik, A. et al. Stokes Inversion Techniques with Neural Networks: Analysis of Uncertainty in Parameter Estimation. Sol Phys 298, 98 (2023). https://doi.org/10.1007/s11207-023-02189-4

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