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

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, vertical bar B-r vertical bar, 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 vertical bar B-r vertical bar 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 vertical bar B-r vertical bar 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 vertical bar B-r vertical bar and B-t from continuum images follows that from Stokes inversions well. Furthermore, our models can reproduce the nonlinear relationships between I and vertical bar B-r vertical bar 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 vertical bar B-r vertical bar 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.