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Probing the solar coronal magnetic field with physics-informed neural networks

Nature Astronomy volume 7, pages 1171–1179 (2023)Cite this article

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Abstract

While the photospheric magnetic field of our Sun is routinely measured, its extent into the upper atmosphere is typically not accessible by direct observations. Here we present an approach for coronal magnetic-field extrapolation, using a neural network that integrates observational data and the physical force-free magnetic-field model. Our method flexibly finds a trade-off between the observation and force-free magnetic-field assumption, improving the understanding of the connection between the observation and the underlying physics. We utilize meta-learning concepts to simulate the evolution of active region NOAA 11158. Our simulation of 5 days of observations at full cadence (12 minutes) requires less than 12 hours of total computation time, allowing for real-time force-free magnetic-field extrapolations. The application to an analytical magnetic-field solution, a systematic analysis of the time evolution of free magnetic energy and magnetic helicity in the coronal volume, as well as comparison with extreme-ultraviolet observations, demonstrates the validity of our approach. The obtained temporal and spatial depletion of free magnetic energy unambiguously relates to the observed flare activity.

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Fig. 1: Overview of the proposed method for force-free magnetic-field extrapolation.
Fig. 2: Evaluation of different parameter settings and trade-off between measurement and physical model, using the vector magnetogram from 15 February 2011 at 00:00 UT.
Fig. 3: Simulated series of active region NOAA 11158 and comparison of extracted parameters with observations.
Fig. 4: Simulated magnetic topology of active region NOAA 11158 and comparison with observations in the EUV.

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Data availability

All our simulation results are publicly available (parameter variation, time series, 66 individual active regions) at https://doi.org/10.6084/m9.figshare.21983486. See also the project page at https://github.com/RobertJaro/NF2. The SDO HMI and AIA data are provided by JSOC (http://jsoc.stanford.edu/). We provide automatic download scripts with SunPy42,43.

Code availability

Our codes are publicly available. We provide Python notebooks that perform simulations for arbitrary regions without any pre-requirements. We provide GPU accelerated code for computing the potential-field solution based on the Green’s function method32 at https://github.com/RobertJaro/NF2.

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Acknowledgements

R.J., A.M.V. and T.P. have received financial support from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 824135 (SOLARNET). J.K.T. and A.M.V. acknowledge the Austrian Science Fund (FWF): P31413-N27. We acknowledge the use of the Skoltech Zhores cluster for obtaining the results presented in this paper44. This research has made use of SunPy v3.0.042,45, AstroPy46, PyTorch47 and Paraview48. We acknowledge M. Gupta for running the optimization-based NLFF models used for comparison with our method in Supplementary Section B.

Author information

Authors and Affiliations

  1. University of Graz, Institute of Physics, Graz, Austria

    R. Jarolim, J. K. Thalmann & A. M. Veronig

  2. University of Graz, Kanzelhöhe Observatory for Solar and Environmental Research, Treffen am Ossiacher See, Austria

    A. M. Veronig

  3. Skolkovo Institute of Science and Technology, Moscow, Russia

    T. Podladchikova

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Contributions

R.J. developed the method and led the writing of the paper. J.K.T. performed the evaluation and comparison to existing NLFF methods, and contributed to the writing of the paper. A.M.V. contributed to the conceptualization of the study and writing of the paper. T.P. contributed to the HPC computations. All authors discussed the results and commented on the paper.

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Correspondence to R. Jarolim.

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Nature Astronomy thanks Michael Wheatland, Yong-Jae Moon and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–5 and Sections A–D.

Supplementary Video 1

Evolution of the active region NOAA 11158. Top row: observations of SDO/AIA 131 Å, SDO/HMI Bz component, and SDO/AIA 1,600 Å. Bottom row: maps of vertically integrated current density, free magnetic energy and running difference of released free magnetic energy computed from the magnetic-field extrapolations.

Supplementary Data 1

Full set of performance metrics for the λ = 1 series shown in Supplementary Fig. 3.

Supplementary Data 2

Full set of performance metrics for the λ = 0.1 series shown in Supplementary Fig. 3.

Supplementary Data 3

Full set of performance metrics for the λ = 0.1 extrapolations from scratch shown in Supplementary Fig. 3.

Supplementary Data 4

Full set of performance metrics for the series from ref. 10 using wd = 1, shown in Supplementary Fig. 3.

Supplementary Data 5

Full set of performance metrics for the series from ref. 10 using wd = 2, shown in Supplementary Fig. 3.

Supplementary Data 6

Full evaluation and extended information for quality evaluation of 66 extrapolated active regions, shown in Supplementary Fig. 5.

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Jarolim, R., Thalmann, J.K., Veronig, A.M. et al. Probing the solar coronal magnetic field with physics-informed neural networks. Nat Astron 7, 1171–1179 (2023). https://doi.org/10.1038/s41550-023-02030-9

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