Using Transformers to Integrate Irregular Data for Improved Ionospheric Modeling

The ionosphere has important impacts on many different systems, such as communications, thus modeling it is a crucial task. The influence of the ionosphere is closely linked to its electron density, but this is difficult to measure adequately. Because of this, modeling requires the use of additional correlated values, such as solar activity metrics. These measures do not capture enough to reproduce small-scale changes in electron density, so we have developed a technique to expand our input space to include sparse measurements of Total Electron Content (TEC), or the integral of electron density.

TEC data is measured more densely than electron density, although it is still not consistent spatially, with many gaps in measurement coverage. Despite this, it is collected very consistently throughout time so it presents itself as a good candidate for an input to an ionospheric model. Even so, TEC has not been used as an input to such models, especially Machine Learning (ML) models, as the irregular coverage of the measurements makes it difficult to deal with.

We have developed a technique to use transformer-like architectures to move from an irregular domain to a fixed size embedded domain to facilitate further usage of the TEC data. This approach has enabled us to use TEC as a direct input to electron density models, noticeably improving performance. Our technique also enables the use of a variety of irregular inputs all at once, enabling a wider range of possible model inputs. Lastly, as a byproduct of the process, we can use the inverse of our embedding technique (which is also how we train the model) to perform TEC map completion, where we can predict TEC values even where no measurements have been taken.