Multivariate Probabilistic Forecasting of Solar Indices and Proxies with Neural Network Ensembles

Space weather indices and proxies are used commonly to drive forecasts of thermosphere density, which
directly affects objects in low-Earth orbit (LEO) through atmospheric drag. Several of the most common indices/proxies include F10.7, S10.7, M10.7, and Y10.7. These indices/proxies correlate well with solar extreme ultra-violet (EUV) energy deposition into the thermosphere and are used as drivers for the operational high accuracy satellite drag model (HASDM) used by the USAF. Currently, the USAF contracts Space Environment Technologies (SET), which uses a linear algorithm to provide forecasted driver values for HASDM. In this work, we introduce methods using neural network ensembles to improve over the SET algorithm. We make short term forecasts of the indices/proxies as well as provide robust and reliable uncertainty estimates. Predictions are made only using historical proxy and index data by leveraging multi-layer long-short term memory (LSTM) neural network model ensembles. We investigate input data manipulation methods, ensemble diversity methods, various weighting schemes, and model validation methods. Previous work has shown an improvement over the SET method when univariate forecasting F10.7 is performed. The best univariate ensemble methods provided an improved relative mean squared error (MSE), with respect to persistence, of between 48% and 59% when forecasting F10.7. Our work has also found model ensembles produce less biased predictions at higher solar activity levels through the evaluation of the calibration error score (CES) metric. We explore univariate forecasting of F10.7, S10.7, M10.7, and Y10.7; and also forecasting multiple indices/proxies simultaneously using LSTMs. This work investigates the advantages and/or disadvantages associated with simultaneous multivariate forecasting. We aim to leverage neural network model ensembles which provide a distribution of predicted values; allowing an investigation into forecast uncertainty and can be sampled during operation. With more robust and reliable model driver forecasts and uncertainty estimates, we are able to provide more realistic inputs for HASDM and generate robust and reliable output of model and driver uncertainty estimates in prediction.