A deep learning method to estimate magnetic fields in solar active regions from photospheric continuum images^⋆

¹ Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Sciences, 20 Datun Road, Beijing 100101, PR China
² School of Astronomy and Space Science, University of Chinese Academy of Sciences, No. 19(A) Yuquan Road, Beijing 100049, PR China
³ Yunnan Observatories, Chinese Academy of Sciences, Kunming, 650011 Yunnan, PR China
e-mail: jkf@ynao.ac.cn
⁴ School of Space and Environment, Beihang University, Beijing, PR China
⁵ College of Computer Science, Sichuan University, Chengdu 610065, PR China
⁶ Big Bear Solar Observatory, New Jersey Institute of Technology, Big Bear City, CA 92314-9672, USA

Received: 19 January 2021
Accepted: 5 June 2021

Abstract

Context. The magnetic field is the underlying cause of solar activities. Spectropolarimetric Stokes inversions have been routinely used to extract the vector magnetic field from observations for about 40 years. In contrast, the photospheric continuum images have an observational history of more than 100 years.

Aims. We suggest a new method to quickly estimate the unsigned radial component of the magnetic field, |B_r|, and the transverse field, B_t, just from photospheric continuum images (I) using deep convolutional neural networks (CNN).

Methods. Two independent models, that is, I versus |B_r| and I versus B_t, are trained by the CNN with a residual architecture. A total of 7800 sets of data (I, B_r and B_t) covering 17 active region patches from 2011 to 2015 from the Helioseismic and Magnetic Imager are used to train and validate the models.

Results. The CNN models can successfully estimate |B_r| as well as B_t maps in sunspot umbra, penumbra, pore, and strong network regions based on the evaluation of four active regions (test datasets). From a series of continuum images, we can also detect the emergence of a transverse magnetic field quantitatively with the trained CNN model. The three-day evolution of the averaged value of the estimated |B_r| and B_t from continuum images follows that from Stokes inversions well. Furthermore, our models can reproduce the nonlinear relationships between I and |B_r| as well as B_t, explaining why we can estimate these relationships just from continuum images.

Conclusions. Our method provides an effective way to quickly estimate |B_r| and B_t maps from photospheric continuum images. The method can be applied to the reconstruction of the historical magnetic fields and to future observations for providing the quick look data of the magnetic fields.