Xin Huang^{1}, Huaning Wang^{1}, Long Xu^{1}, Jinfu Liu^{2}, Rong Li^{3}, & Xinghua Dai^{1}

1. Key Laboratory of Solar Activity, National Astronomical Observatories of Chinese Academy of Sciences, Beijing, People’s Republic of China

2. Harbin Institute of Technology, Harbin, People’s Republic of China

3. Beijing Wuzi University, Beijing, People’s Republic of China

Conventional solar flare forecasting models rely mainly on morphological or physical parameters extracted from active regions, however, most of these parameters are strongly correlated with each other, and none of them significantly outperformed the others^{[1]}. Instead of extracting the man-made physical parameters from active regions, we try to apply a deep-learning method^{[2]} to automatically dig out forecasting patterns hidden in the data.

We collect all active regions within ±30° of the central meridian for line-of-sight magnetograms observed by the SOHO/MDI and the SDO/HMI from 1996 April to 2015 October, and combine the HMI data with the MDI data^{[3]} to generate a big data set. Supported by this data set, we develop a solar flare forecasting model by using the convolutional neural network (Figure 1), which is one of many deep-learning methods. The network consists of convolutional layer, nonlinear layer, pooling layer, and fully connected layer. The convolutional layer is used to extract forecasting patterns from input magnetograms. The nonlinear layer adds a nonlinear transform into the forecasting model. The pooling layer reduces dimensionality of parameters in the network. And finally, the fully connected layer can provide a high-level reasoning for the solar flare forecasting. As the most important part of the solar flare forecasting model, filter weights in the convolutional layer are initialized by random numbers. In the training phase, these weights are iteratively adjusted to minimize forecasting errors on the training data. The stable filter weights are considered as the forecasting patterns learned form the data.

Figure 1|Structure of convolutional neural network for solar flare forecasting.

Taking the first convolutional layer in the neural network as an example (Figure 2), the 64 11 × 11 filters are initialized by random values (Figure 2a). During the training process, the filter weights become more and more orderly, as shown in Figures 2b and 2c, and finally these weights stabilize after an iteration of 3000 steps (Figure 2d). As shown in Figure 2d, we found that the weights in most filters tend to be 0, and they are useless for the flare forecasting. By contrast, the stable nonzero filter weights are considered to be useful forecasting patterns, for example, the 44th and the 62nd filters in Figure 2d.

Figure 2|Variations of convolutional kernels in the first convolutional layer during different training iterations. (a) Initial random filter weights. (b) Filter weights after 1000 training iterations. (c) Filter weights after 2000 training iterations. (d) Filter weights after 3000 training iterations.

In order to analyze the physical implications of these forecasting patterns, we select line-of-sight magnetograms from two flare-productive active regions (AR 11158 and AR 10720) as the input data. The input data is convolved with a filter to generate a feature map, and the feature map can be mapped into the same size as the input image to get the projected feature map. The highlighted area in a projected feature map is the region of interest in active regions determined by the convolutional neural network, which is considered as a potential flaring area (Figure 3). We can find that the region of interest determined by the convolutional neural network is consistent with the physical potential flaring area^{[4]}. This result implicates reasonability of the deep-learning-based solar flare forecasting model. Essential to the deep learning based solar flare forecasting model is that the magnetic flux distribution in the region of interest is nonlinearly transformed and finally obtains some statistical relationship with solar flares.

Figure 3|Magnetograms, feature maps, and projected feature maps for active regions 11158 and 10720. (a) Magnetogram of AR 11158 overlaid with contours of its 44th projected feature map. (b) 44th feature map of AR 11158. (c) 44th projected feature map of AR 11158. (d) Magnetogram of AR 11158 overlaid with contours of its 62nd projected feature map. (e) 62nd feature map of AR 11158. (f) 62nd projected feature map of AR 11158. (g) Magnetogram of AR 10720 overlaid with contours of its 44th projected feature map. (h) 44th feature map of AR 10720. (i) 44th projected feature map of AR 10720. (j) Magnetogram of AR 10720 overlaid with contours of its 62nd projected feature map. (k) 62nd feature map of AR 10720. (l) 62nd projected feature map of AR 10720.

The built forecasting model can be used to forecast solar flares with the threshold of C-, M-, or X-levels within the forecasting period of 6, 12, 24, or 48 hr. The testing results of the forecasting model show that the performance of the proposed forecasting model is comparable to the state-of-the-art flare forecasting models^{[5]}.

### References

[1] Leka, K. D., & Barnes, G. 2007, *ApJ*, **656**, 1173

[2] Hinton, G. E., & Salakhutdinov, R. R. 2006, *Science*, **313**, 504

[3] Liu, Y., Hoeksema, J. T., Scherrer, P. H,. et al. 2012, *Solar Phys*, **279**, 295

[4] Schrijver, C. J. 2009, *Adv. Space Res.*, **43**, 739

[5] Bobra, M. G., & Couvidat, S. 2015, *ApJ*, **798**, 135