Leveraging the mathematics of shape for solar magnetic eruption prediction

Abstract

Current operational forecasts of solar eruptions are made by human experts using a combination of qualitative shape-based classification systems and historical data about flaring frequencies. In the past decade, there has been a great deal of interest in crafting machine-learning (ML) flareprediction methods to extract underlying patterns from a training set-e.g., a set of solar magnetogram images, each characterized by features derived from the magnetic field and labeled as to whether it was an eruption precursor. These patterns, captured by various methods (neural nets, support vector machines, etc.), can then be used to classify new images. A major challenge with any ML method is the featurization of the data: pre-processing the raw images to extract higherlevel properties, such as characteristics of the magnetic field, that can streamline the training and use of these methods. It is key to choose features that are informative, from the standpoint of the task at hand. To date, the majority of ML-based solar eruption methods have used physics-based magnetic and electric field features such as the total unsigned magnetic flux, the gradients of the fields, the vertical current density, etc. In this paper, we extend the relevant feature set to include characteristics of the magnetic field that are based purely on the geometry and topology of 2D magnetogram images and show that this improves the prediction accuracy of a neural-net based flare-prediction method.

Decreasing False Alarm Rates in ML-based Solar Flare Prediction using SDO/HMI Data

“…To complement the physics-based features, we also include some shape-based features extracted using topological data analysis (TDA), as proposed in Deshmukh et al (2020). TDA is an approach to characterize the shape of data in terms of its homology, i.e.…”

“…Since we are dealing with a 2-dimensional image for extracting the features, our Betti numbers are restricted to {β 0 , β 1 }. As in Deshmukh et al (2020), we choose β 1 for our topology-based feature set. On an image, TDA counts holes by first performing sub-level thresholding, i.e.…”

“…The first is a set of physics-based features -called SHARPs -that are available in the SHARPs HMI data set as metadata (Bobra et al 2014a). The second source is a set of features extracted using topological data analysis (TDA) (Zomorodian 2011), as applied to sunspot magnetograms in Deshmukh et al (2020); Deshmukh et al (2021). Concatenating the VGG-16 probability output, 20 SHARPs features and 14 TDA-based features, we have a complete feature set of 35 features which combines information from deep learning-based and feature engineered approaches.…”

“…Recently, the full-disk vector (i.e., three-dimensional) magnetograms from NASA's Solar Dynamics Observatory (SDO, Chamberlin et al 2012) Helioseismic andMagnetic Imager (HMI, Scherrer et al 2012) instrument have enabled the creation of a large database of derived AR magnetic field quantities called the SHARP parameters (Bobra et al 2014a). Since 2015, many ML solar flare prediction systems have used the SHARP parameters, or a subset of parameters, as the primary feature vector input to supervised learning architectures (e.g., Bobra & Couvidat 2015;Bobra & Ilonidis 2016;Florios et al 2018;Chen et al 2019;Deshmukh et al 2020). The SHARP AR image cutout and feature set has recently been expanded to include data from the predecessor instrument to SDO/HMI, the SOHO/Michelson Doppler Imager (MDI; Scherrer et al 1995), to create the SMARPs dataset (Bobra et al 2021).…”

Operational solar flare prediction model using Deep Flare Net

“…However, there is insufficient discussion on how to develop the methods available to real-time operations in space weather forecasting offices, including the methods for validation and verification of the models. Currently, new physical and geometrical (topological) features are applied to flare prediction using machine learning (e.g., Wang et al 2020a;Deshmukh et al 2020), and it has been noted that training sets may be sensitive to which period in the solar cycle they are drawn from. (Wang et al 2020b).…”