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

Chetraj Pandey, Jinsu Hong, Anli Ji, Rafal A. Angryk, Berkay Aydin

TL;DR

This work addresses the limitation of binary solar flare prediction by incorporating ordinal information among flare sub-classes into the training loss. It introduces BCE-PP, a proximity-penalty based on subclass ordinality with per-sample weights $\beta_i$ and a tunable scale $\alpha$, modifying the standard BCE to emphasize boundary errors near the M threshold. Experiments on SHARP/HMI AR patches using a lightweight MobileNet show that BCE-PP yields modest improvements in the Composite Skill Score ($\text{CSS}$) and reduces false positives, though gains vary with data setup, highlighting boundary-focused regularization as a practical tool for space-weather forecasting. The approach provides a simple, data-driven regularizer that leverages ordinal structure without extra model complexity, potentially enhancing real-time flare risk assessment when combined with more balanced data or multimodal observations.

Abstract

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.

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

TL;DR

This work addresses the limitation of binary solar flare prediction by incorporating ordinal information among flare sub-classes into the training loss. It introduces BCE-PP, a proximity-penalty based on subclass ordinality with per-sample weights and a tunable scale , modifying the standard BCE to emphasize boundary errors near the M threshold. Experiments on SHARP/HMI AR patches using a lightweight MobileNet show that BCE-PP yields modest improvements in the Composite Skill Score () and reduces false positives, though gains vary with data setup, highlighting boundary-focused regularization as a practical tool for space-weather forecasting. The approach provides a simple, data-driven regularizer that leverages ordinal structure without extra model complexity, potentially enhancing real-time flare risk assessment when combined with more balanced data or multimodal observations.

Abstract

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.

Paper Structure

This paper contains 8 sections, 6 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Data and Model
  3. Proximity-Penalized Binary Loss (BCE-PP)
  4. Experimental Evaluation
  5. Experimental Settings
  6. Evaluation Metrics
  7. Evaluation
  8. Conclusion and Future Work

Figures (2)

  • Figure 1: An illustrative example showing: (a) the original raw HMI active region (AR) magnetogram corresponding to HARP 4781 at timestamp 2014-11-08T00:00:00 UTC; (b) the associated bitmap of the AR patch in (a), where white pixels indicate the region of interest; and (c) the final preprocessed AR image from (a), cropped to 512$\times$512, which is used for model training.
  • Figure 2: An illustrative plot depicting: (a) the standard binary cross-entropy (BCE) loss; and (b–c) the BCE with proximity penalty (BCE-PP) used for solar flare prediction, which incorporates ordinal flare characteristics through a loss-weighting mechanism with $\alpha = 0.25$ and $\alpha = 1$, respectively. Note: the FL class corresponds to target 1, and the NF class corresponds to target 0.