A transformer-based framework for predicting geomagnetic indices with uncertainty quantification

Geomagnetic activities have a crucial impact on Earth, which can affect spacecraft and electrical power grids. Geospace scientists use a geomagnetic index, called the Kp index, to describe the overall level of geomagnetic activity. This index is an important indicator of disturbances in the Earth’s magnetic field and is used by the U.S. Space Weather Prediction Center as an alert and warning service for users who may be affected by the disturbances. Another commonly used index, called the ap index, is converted from the Kp index. Early and accurate prediction of the Kp and ap indices is essential for preparedness and disaster risk management. In this paper, we present a deep learning framework, named GNet, to perform short-term forecasting of the Kp and ap indices. Specifically, GNet takes as input time series of solar wind parameters’ values, provided by NASA’s Space Science Data Coordinated Archive, and predicts as output the Kp and ap indices respectively at time point \(\varvec{t + w}\) hours for a given time point \(\varvec{t}\) where \(\varvec{w}\) ranges from 1 to 9. GNet combines transformer encoder blocks with Bayesian inference, which is capable of quantifying both aleatoric uncertainty (data uncertainty) and epistemic uncertainty (model uncertainty) in making predictions. Experimental results show that GNet outperforms closely related machine learning methods in terms of the root mean square error and R-squared score. Furthermore, GNet can provide both data and model uncertainty quantification results, which the existing methods cannot offer. To our knowledge, this is the first time that Bayesian transformers have been used for geomagnetic activity prediction.