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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. 

Solar flare prediction is a central problem in space weather forecasting. Existing solar flare prediction tools are mainly dependent on the GOES classification system, and models commonly use a proxy of maximum (peak) X-ray flux measurement over a particular prediction window to label instances. However, the background X-ray flux dramatically fluctuates over a solar cycle and often misleads both flare detection and flare prediction models during solar minimum, leading to an increase in false alarms. We aim to enhance the accuracy of flare prediction methods by introducing novel labeling regimes that integrate relative increases and cumulative measurements over prediction windows. Our results show that the data-driven labels can offer more precise prediction capabilities and complement the existing efforts.