Transfer learning in spatial-temporal forecasting of the solar magnetic field

Machine learning techniques have been widely used in attempts to forecast several solar datasets such as the sunspot count, the sunspot area, flare activity, solar wind magnitude, and solar storms/coronal mass ejections (CMEs) activity. Most of these approaches employ supervised machine learning algorithms which are, in general, very data hungry. This hampers the attempts to forecast some of these data series, particularly the ones that depend on (relatively) recent space observations such as those obtained by the Solar and Heliospheric Observatory and the Solar Dynamics Observatory. Here we focus on an attempt to forecast the solar surface longitudinally averaged unsigned radial component (or line-of-sight) magnetic field distribution using a form of spatial-temporal neural networks. Given that the recording of these spatial-temporal datasets only started in 1975 and are therefore quite short, the forecasts are predictably quite modest. However, given that there is a potential physical relationship between sunspots and the magnetic field, we employ another machine learning technique called transfer learning which has recently received considerable attention in the literature. Here, this approach consists in first training the source spatial-temporal neural network on the much longer time/latitude sunspot area dataset, which starts in 1874, then transferring the trained set of layers to a target network, and continue training the latter on the magnetic field dataset. The employment of transfer learning in the field of computer vision is known to obtain a generalized set of feature filters that can be reused for other datasets and tasks. Here we obtain a similar result, whereby we first train the network on the spatial-temporal sunspot area data, then the first few layers of the neural network are able to identify the two main features of the solar cycle, that is, the amplitude variation and the migration to the equator, and therefore can be used to train on the magnetic field dataset and forecast better than a prediction based only on the historical magnetic field data.