Neural Network Forecast of the Sunspot Butterfly Diagram

Using neural networks as a prediction method, we attempt to demonstrate that forecasting of the Sun's sunspot time series can be extended to the spatial-temporal case. We employ this machine learning methodology to forecast not only in time but also in space (in this case the latitude) on a spatial-temporal dataset representing the solar sunspot diagram extending to a total of 142 years. The analysis shows that this approach seems to be able to reconstruct the overall qualitative aspects of the spatial-temporal series, namely the overall shape and amplitude of the latitude and time pattern of sunspots. This is, as far as we are aware, the first time neural networks have been used to forecast the Sun's sunspot butterfly diagram, and although the results are limited in the quantitative prediction aspects, it points the way to use the full spatial-temporal series as opposed to just the time series for machine learning approaches to forecasting. Further to that, we use the method to predict that the upcoming Cycle 25 maximum sunspot number will be around $R_{25}=57 \pm 17$. This implies a very weak cycle and that it will be the weakest cycle on record.