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.

We propose a curvature-based approach for choosing a good value for the time-delay parameter τ in delay reconstructions. The idea is based on the effects of the delay on the geometry of the reconstructions. If the delay is too small, the reconstructed dynamics are flattened along the main diagonal of the embedding space; too-large delays, on the other hand, can overfold the dynamics. Calculating the curvature of a two-dimensional delay reconstruction is an effective way to identify these extremes and to find a middle ground between them: both the sharp reversals at the extremes of an insufficiently unfolded reconstruction and the bends in an overfolded one create spikes in the curvature. We operationalize this observation by computing the mean Menger curvature of a trajectory segment on 2D reconstructions as a function of time delay. We show that the minimum of these values gives an effective heuristic for choosing the time delay. In addition, we show that this curvature-based heuristic is useful even in cases where the customary approach, which uses average mutual information, fails—e.g., noisy or filtered data.

A hybrid two-stage machine-learning architecture that addresses the problem of excessive false positives (false alarms) in solar flare prediction systems is investigated. The first stage is a convolutional neural network (CNN) model based on the VGG-16 architecture that extracts features from a temporal stack of consecutive Solar Dynamics Observatory Helioseismic and Magnetic Imager magnetogram images to produce a flaring probability. The probability of flaring is added to a feature vector derived from the magnetograms to train an extremely randomized trees (ERT) model in the second stage to produce a binary deterministic prediction (flare/no-flare) in a 12 hr forecast window. To tune the hyperparameters of the architecture, a new evaluation metric is introduced: the “scaled True Skill Statistic.” It specifically addresses the large discrepancy between the true positive rate and the false positive rate in the highly unbalanced solar flare event training data sets. Through hyperparameter tuning to maximize this new metric, our two-stage architecture drastically reduces false positives by ≈48% without significantly affecting the true positives (reduction by ≈12%), when compared with predictions from the first-stage CNN alone. This, in turn, improves various traditional binary classification metrics sensitive to false positives, such as the precision, F1, and the Heidke Skill Score. The end result is a more robust 12 hr flare prediction system that could be combined with current operational flare-forecasting methods. Additionally, using the ERT-based feature-ranking mechanism, we show that the CNN output probability is highly ranked in terms of flare prediction relevance.

Context. Machine-learning methods for predicting solar flares typically employ physics-based features that have been carefully chosen by experts in order to capture the salient features of the photospheric magnetic fields of the Sun. Aims. Though the sophistication and complexity of these models have grown over time, there has been little evolution in the choice of feature sets, or any systematic study of whether the additional model complexity leads to higher predictive skill. Methods. This study compares the relative prediction performance of four different machine-learning based flare prediction models with increasing degrees of complexity. It evaluates three different feature sets as input to each model: a “traditional” physics-based feature set, a novel “shape-based” feature set derived from topological data analysis (TDA) of the solar magnetic field, and a combination of these two sets. A systematic hyperparameter tuning framework is employed in order to assure fair comparisons of the models across different feature sets. Finally, principal component analysis is used to study the effects of dimensionality reduction on these feature sets. Results. It is shown that simpler models with fewer free parameters perform better than the more complicated models on the canonical 24-h flare forecasting problem. In other words, more complex machine-learning architectures do not necessarily guarantee better prediction performance. In addition, it is found that shape-based feature sets contain just as much useful information as physics-based feature sets for the purpose of flare prediction, and that the dimension of these feature sets – particularly the shape-based one – can be greatly reduced without impacting predictive accuracy.

Solar flares are caused by magnetic eruptions in active regions (ARs) on the surface of the sun. These events can have significant impacts on human activity, many of which can be mitigated with enough advance warning from good forecasts. To date, machine learning-based flare-prediction methods have employed physics-based attributes of the AR images as features; more recently, there has been some work that uses features deduced automatically by deep learning methods (such as convolutional neural networks). We describe a suite of novel shape-based features extracted from magnetogram images of the Sun using the tools of computational topology and computational geometry. We evaluate these features in the context of a multi-layer perceptron (MLP) neural network and compare their performance against the traditional physics-based attributes. We show that these abstract shape-based features outperform the features chosen by the human experts, and that a combination of the two feature sets improves the forecasting capability even further.

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Scaling regions—intervals on a graph where the dependent variable depends linearly on the independent variable—abound in dynamical systems, notably in calculations of invariants like the correlation dimension or a Lyapunov exponent. In these applications, scaling regions are generally selected by hand, a process that is subjective and often challenging due to noise, algorithmic effects, and confirmation bias. In this paper, we propose an automated technique for extracting and characterizing such regions. Starting with a two-dimensional plot—e.g., the values of the correlation integral, calculated using the Grassberger–Procaccia algorithm over a range of scales—we create an ensemble of intervals by considering all possible combinations of end points, generating a distribution of slopes from least squares fits weighted by the length of the fitting line and the inverse square of the fit error. The mode of this distribution gives an estimate of the slope of the scaling region (if it exists). The end points of the intervals that correspond to the mode provide an estimate for the extent of that region. When there is no scaling region, the distributions will be wide and the resulting error estimates for the slope will be large. We demonstrate this method for computations of dimension and Lyapunov exponent for several dynamical systems and show that it can be useful in selecting values for the parameters in time-delay reconstructions.

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