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

2025-10-05

AI Summary

Conventional solar flare prediction models predominantly employ binary classification (flare/no-flare), neglecting the intrinsic ordinal relationship among C-, M-, and X-class flares. This omission leads to high misclassification rates near decision thresholds (e.g., between M1.0 and M9.9). Method: We propose an ordinal-aware loss function that extends binary cross-entropy with a data-driven ordinal weighting scheme, serving as a structured regularization term to explicitly penalize misclassifications between adjacent intensity classes. The method requires no architectural modifications and supports end-to-end training. Contribution/Results: Experiments demonstrate that our approach significantly reduces misclassification in threshold-sensitive regions, improving both accuracy and robustness for C/M/X-class flare prediction. It validates the effectiveness and generalizability of ordinal regularization in solar physics forecasting tasks, offering a principled way to incorporate physical intensity hierarchies into machine learning models.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Computer Vision: Multi-modal Vision

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Large pretrained models with web data
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Addresses misclassification near solar flare prediction thresholds
• Incorporates ordinal relationships into binary classification framework
• Proposes ordinal-weighted loss function to improve model performance

Innovation

• Ordinal encoding regularizes binary loss function
• Penalizes misclassifications near prediction threshold more heavily
• Integrates ordinal sub-class information into cross-entropy loss