Exploring the Potential of Neural Networks to Predict Statistics of Solar Wind Turbulence. Issue 9 (7th September 2022) - Wrench, Daniel; Parashar, Tulasi N.; Singh, Ritesh K.; Frean, Marcus; Rayudu, Ramesh
Abstract: Time series data sets often have missing or corrupted entries, which need to be handled in subsequent data analysis. For example, in the context of space physics, calibration issues, satellite telemetry issues, and unexpected events can make parts of a time series unusable. This causes problems for understanding the dynamics of the heliosphere and space weather environment. Various approaches exist to tackle this problem, including mean/median imputation, linear interpolation, and autoregressive modeling. Here, we study the utility of artificial neural networks (ANNs) to predict statistics of sparse time series. Our focus is not on time series prediction but on gleaning the best possible information about the statistical behavior of the system. As an example application, we focus on the structure functions of turbulent time series measured in the solar wind. Using a data set with artificial gaps, a neural network is trained to predict second‐order structure functions and then tested on an unseen data set to quantify its performance. A small feedforward ANN, with only 20 hidden neurons, can predict the large‐scale fluctuation amplitudes better than mean imputation or linear interpolation when the percentage of missing data is high. Although they perform worse than the other methods when it comes to capturing both the shape and fluctuation amplitude together, their performance is better in a statistical sense for large fractions of missing data. Caveats regarding their utility, the optimization procedure, and potential future improvements are discussed. Plain Language Summary: We explore the utility of machine learning to predict statistics of a turbulent system such as the solar wind, in cases involving large data gaps. It is shown that simple artificial neural networks (ANNs) are good at estimating large‐scale features of second‐order structure functions even for very large amounts of missing data. However, these simple ANNs are limited in estimating other features of the structure functions, such as inner and outer scales, and the inertial range slope. More sophisticated methods are required to describe such features. Developing such a method is key to improving space weather models (e.g., the functions that couple solar wind parameters to space weather) in the face of incomplete data. Key Points: Small neural networks are able to predict structure functions for sparse solar wind time series in a limited sense A network with only 20 hidden neurons statistically outperforms (in terms of MSE) simple imputation techniques for high (>50%) data loss More work is needed to generalize the model's architecture to improve performance and increase applicability to other systems