Several natural phenomena, such as floods, earth-quakes, volcanic eruptions, or extreme space weather events often come with severity indexes. While these indexes, whether linear or logarithmic are vital, data-driven predictive models for these events rather use a fixed threshold. In this paper, we explore encoding this ordinality to enhance the performance of data-driven models, with specific application in solar flare forecasting. The prediction of solar flares is commonly approached as a binary forecasting problem, categorizing events as either Flare (FL) or No-Flare (NF) based on a chosen threshold (e.g., >C-class, > M-class, or >X-class). However, this binary formulation overlooks the inherent ordinality between the sub-classes within each binary class (FL and NF). In this paper, we propose a novel loss function aimed at optimizing the binary flare prediction problem by embedding the intrinsic ordinal flare characteristics into the binary cross-entropy (BCE) loss function. This modification is intended to provide the model with better guidance based on the ordinal characteristics of the data and improve the overall performance of the models. For our experiments, we employ a ResNet34-based model with transfer learning to predict 2:M-class flares by utilizing the shape-based features of magnetograms of active region (AR) patches spanning from -90° to +90°of solar longitude as our input data. We use a composite skill score (CSS) as our evaluation metric, which is calculated as the geometric mean of the True Skill Score (TSS) and the Heidke Skill Score (HSS) to rank and compare our models' performance. The primary contributions of this work are as follows: (i) We introduce a novel approach to encode ordinality into a binary loss function showing an application to solar flare prediction, (ii) We enhance solar flare forecasting by enabling flare predictions for each AR across the entire solar disk, without any longitudinal restrictions, and evaluate and compare performance. (iii) Our candidate model, optimized with the proposed loss function, shows an improvement of (~17%, (~14%, and (~13% for AR patches within ±30°, ±60°, and ±90° of solar longitude, respectively in terms of CSS, when compared with standard BCE. Additionally, we demonstrate the ability to issue flare forecasts for ARs in near-limb regions (regions between ±60° to ±90°) with a CSS=0.34 (TSS=0.50 and HSS=0.23), expanding the scope of AR-based models for solar flare prediction. This advances the reliability of solar flare forecasts, leading to more effective prediction capabilities.

Recently, the synergy of physics-based feature engineering and data-intensive methods, including machine learning and deep learning, has ushered in a new era in the analysis and prediction of space weather forecasting, specifically for solar flare prediction. These sophisticated approaches play a pivotal role in understanding the complex mechanisms leading to solar flares, with a primary focus on forecasting these events and mitigating potential risks they pose to our planet. While current methodologies have made substantial advancements, they are not without limitations, and one particularly glaring limitation is the neglect of temporal evolution characteristics within the active regions from which solar flares originate. This oversight impairs the capacity of these methods to capture the intricate relationships among high-dimensional features of these active regions, thereby constraining their practical utility. Our study focuses on two key objectives: the development of interpretable classifiers for multivariate time series data and the introduction of an innovative feature ranking method using sliding window-based sub-interval ranking. The central contribution of our work lies in bridging the gap between complex, less interpretable “black-box” models typically employed for high-dimensional data and the exploration of pertinent sub-intervals within multivariate time series data, with a specific emphasis on solar flare forecasting. Our findings underscore the efficacy of our sliding-window time series forest classifier in solar flare prediction, achieving a True Skill Statistic of over 85%. Our approach is capable of pinpointing the most critical features and sub-intervals relevant to any given learning task. These results indicate significant progress toward improving the interpretability and accuracy of flare prediction models, further advancing our understanding of these impactful events.

This study progresses solar flare prediction research by presenting a full-disk deep-learning model to forecast $\geq\mathrm{M}$-class solar flares and evaluating its efficacy on both central (within ±70°) and near-limb beyond ±70°) events, showcasing qualitative assessment of post hoc explanations for the model’s predictions, and providing empirical findings fro human-centered quantitative assessments of these explanations. Our model is trained using hourly full-disk line-of-sight magnetogram images to predict $\geq{\mathrm{M}}$-class solar flares within the subsequent 24-hour prediction window. Additionally, we apply the Guided Gradient-weighted Class Activation Mapping (Guided Grad-CAM) attribution method to interpret our model’s predictions and evaluate the explanations. Our analysis unveils that full-disk solar flare predictions correspond with active region characteristics. The following points represent the most important findings of our study: ❨1❩ Our deep learning models achieved an average true skill statistic (TSS) of $\sim 0.51$ and a Heidke skill score (HSS) of $\sim.38$, exhibiting skill to predict solar flares where for central locations the average recall is $\sim 0.75$ (recall values for X- and M-class are 0.95 and 0.73 respectively) and for the near-limb flares the average recall is $\sim 0.52$ (recall values for X- and M- class are 0.74 and 0.50 respectively); ❨2❩ qualitative examination of the model’s explanations reveals that it discerns and leverages features linked to active regions in both central and near-limb locations within full-disk magnetograms to produce respective predictions. In essence, our models grasp the shape and texture-based properties of flaring active regions, even in proximity to limb areas—a novel and essential capability with considerable significance for operational forecasting systems.

Magnetic polarity inversion line (PIL) in solar active regions have been recognized as essential features for the occurrence of solar flares and the prediction of the flaring phenomenon. In this work, we provide a software framework that detects PILs from the line-of-sight (LoS) or the radial component of the magnetic field vector in active region magnetogram patches. The PIL detection procedure is based on an edge detection technique along with magnetic field strength and PIL size filter. First, we identify positive and negative polarity regions with a magnetic field strength threshold. Then, we utilize the Canny edge detector and morphological operations to both positive and negative regions to identify coarse PILs. Finally, we generate PILs by applying magnetic field strength and PIL size filter to the coarse PILs as mentioned above. Moreover, we provide feature extraction functions to obtain the properties of PILs (i.e., PIL size, the area of polarity inversion, the masked unsigned flux of enclosing PIL, convexity, eigenvalues, fractal dimension, and Hu moments of PIL shape), and produce three PIL-related binary masks (i.e., PIL, the region of polarity inversion, and the convex hull of PIL) for each Longitudinal magnetogram patch. We also provide a qualitative evaluation of our module. The detection results for a well known active region (NOAA AR 11158) are shown as proof of concept.

Outlier detection has become one of the core tasks in spatio-temporal data mining. It plays an essential role in data quality improvement for the machine learning models and recognizing the anomalous patterns, which may remarkably deviate from expected patterns among the trajectory datasets. In this work, we propose a clustering-based technique to detect local outliers in trajectory datasets by utilizing spatial and temporal attributes of moving objects. This local outlier detection involves three phases. In the first phase, we apply a temporal partition procedure to divide the raw trajectory into multiple trajectory segments and extract trajectory features from spatial and temporal attributes for each trajectory segment. Then, we generate template features of trajectory segments by applying a clustering schema in the second phase. Finally, we use the abnormal score - a novel dissimilarity measure, which quantifies the disparity among the query and template trajectory segments in terms of trajectory features and hence determines the local outliers based on the distribution of abnormal score. To demonstrate the effectiveness of our method, we conduct three case studies on the real-life spatio-temporal trajectory datasets from the solar astroinformatics domain (i.e., solar active regions, coronal mass ejections, polarity inversion lines (PIL)). Our experimental results show that our local outlier detection approach can effectively discover the erroneous reports from the reporting module and abnormal phenomenon in various spatio-temporal trajectory datasets.

Forecasting the occurrence of solar flares is a typical 21st century rare-event classification task. Over the past two decades, many studies have implemented various techniques and approaches for classification of strong and weak solar flares. The release of the recent flare forecasting benchmark dataset, named SWAN-SF, has opened the door for taking advantage of multivariate time series (MVTS) of pre-flare magnetic fields’ activity in order to potentially achieve higher performance and increase the robustness of the new forecasting models. In this study, we take a new approach and explore the effectiveness of imaging algorithms on the time series. We convert MVTS data into multi-channel image data using Gramian Angular Fields (GAF) and Markov Transition Fields (MTF) to explore the proven strength of deep neural networks in the Image Processing domain, on flares’ MVTS data. Inspired by GAF, we propose another imaging matrix that our experiments show that it significantly improves the performance of the CNN, by 120% in terms of TSS and 440% in terms of HSS2. Finally, we juxtapose two approaches to tackle the flare forecasting problem: one, to utilize a time-series specific Support Vector Classifier for classification of flares, and the other, to train a Convolutional Neural Network (CNN) on the derived images using GAF, MTF, and our modified GAF.

An all-clear flare prediction is a type of solar flare forecasting that puts more emphasis on predicting non-flaring instances (often relatively small flares and flare quiet regions) with high precision while still maintaining valuable predictive results. While many flare prediction studies do not address this problem directly, all-clear predictions can be useful in operational context. However, in all-clear predictions, finding the right balance between avoiding false negatives (misses) and reducing the false positives (false alarms) is often challenging. Our study focuses on training and testing a set of interval-based time series named Time Series Forest (TSF). These classifiers will be used towards building an all-clear flare prediction system by utilizing multivariate time series data. Throughout this paper, we demonstrate our data collection, predictive model building and evaluation processes, and compare our time series classification models with baselines using our benchmark datasets. Our results show that time series classifiers provide better forecasting results in terms of skill scores, precision and recall metrics, and they can be further improved for more precise all-clear forecasts by tuning model hyperparameters.