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 $\geq$M-class flares by utilizing the shape-based features of magnetograms of active region (AR) patches spanning from $-$90$^{\circ}$ to $+$90$^{\circ}$ 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 $\sim$7%, $\sim$4%, and $\sim$3% for AR patches within $\pm$30$^\circ$, $\pm$60$^\circ$, and $\pm$90$^\circ$ 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 $\pm$60$^{\circ}$ to $\pm$90$^{\circ}$) 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.

翻译：本文提出一种新颖的损失函数，旨在通过将太阳耀斑固有的序数特性嵌入二元交叉熵损失函数，以优化二元耀斑预测问题。该改进旨在根据数据的序数特性为模型提供更好的指导，从而提升模型的整体性能。在实验中，我们采用基于ResNet34的迁移学习模型，以活动区磁图在太阳经度-90°至+90°范围内的形态特征作为输入数据，预测≥M级耀斑。我们采用复合技能评分作为评估指标，该指标通过真技巧评分与海德克技巧评分的几何平均值计算，用于对模型性能进行排序和比较。本研究的主要贡献如下：(i) 提出一种将序数性编码至二元损失函数的新方法，并展示了其在太阳耀斑预测中的应用；(ii) 通过实现对整个日面所有活动区的耀斑预测（无任何经度限制）来提升预报能力，并评估比较性能；(iii) 使用所提损失函数优化的候选模型，在复合技能评分指标上，相较于标准二元交叉熵损失函数，对太阳经度±30°、±60°和±90°范围内的活动区磁图分别实现了约7%、4%和3%的性能提升。此外，我们展示了在日面边缘区域（±60°至±90°区间）发布耀斑预报的能力，其复合技能评分达到0.34（真技巧评分=0.50，海德克技巧评分=0.23），从而拓展了基于活动区的太阳耀斑预测模型的应用范围。这一进展提升了太阳耀斑预报的可靠性，使其具备更有效的预测能力。