Ordinal Encoding as a Regularizer in Binary Loss for Solar Flare Prediction

The prediction of solar flares is typically formulated as a binary classification task, distinguishing events as either Flare (FL) or No-Flare (NF) according to a specified threshold (for example, greater than or equal to C-class, M-class, or X-class). However, this binary framework neglects the inherent ordinal relationships among the sub-classes contained within each category (FL and NF). Several studies on solar flare prediction have empirically shown that the most frequent misclassifications occur near this prediction threshold. This suggests that the models struggle to differentiate events that are similar in intensity but fall on opposite sides of the binary threshold. To mitigate this limitation, we propose a modified loss function that integrates the ordinal information among the sub-classes of the binarized flare labels into the conventional binary cross-entropy (BCE) loss. This approach serves as an ordinality-aware, data-driven regularization method that penalizes the incorrect predictions of flare events in close proximity to the prediction threshold more heavily than those away from the boundary during model optimization. By incorporating ordinal weighting into the loss function, we aim to enhance the model's learning process by leveraging the ordinal characteristics of the data, thereby improving its overall performance.