# Embedding Ordinality to Binary Loss Function for Improving Solar Flare Forecasting

arXiv: https://arxiv.org/abs/2408.11768 · HTML: https://mlsanity.com/paper/2408.11768/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 47 references that are in the map.
- First posted on arXiv 21 Aug 2024.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [How to Train Your Flare Prediction Model: Revisiting Robust Sampling of Rare Events](https://mlsanity.com/paper/2103.07542/) (2021)
- [Towards Coupling Full-disk and Active Region-based Flare Prediction for Operational Space Weather Forecasting](https://mlsanity.com/paper/2209.07406/) (2022)
- [All-Clear Flare Prediction Using Interval-based Time Series Classifiers](https://mlsanity.com/paper/2105.01202/) (2021)
- [Explaining Full-disk Deep Learning Model for Solar Flare Prediction using Attribution Methods](https://mlsanity.com/paper/2307.15878/) (2023)
- [Challenges with Extreme Class-Imbalance and Temporal Coherence: A Study on Solar Flare Data](https://mlsanity.com/paper/1911.09061/) (2019)
- [Towards Interpretable Solar Flare Prediction with Attention-based Deep Neural Networks](https://mlsanity.com/paper/2309.04558/) (2023)
- [Exploring Deep Learning for Full-disk Solar Flare Prediction with Empirical Insights from Guided Grad-CAM Explanations](https://mlsanity.com/paper/2308.15712/) (2023)
- [Advancing Solar Flare Prediction using Deep Learning with Active Region Patches](https://mlsanity.com/paper/2406.11054/) (2024)
- [Unveiling the Potential of Deep Learning Models for Solar Flare Prediction in Near-Limb Regions](https://mlsanity.com/paper/2309.14483/) (2023)

## Built on by (most cited first, 4 of 4)

- [Surya: Foundation Model for Heliophysics](https://mlsanity.com/paper/2508.14112/) (2025)
- [Uncertainty-Aware Solar Flare Regression](https://mlsanity.com/paper/2603.06712/) (2026)
- [Ordinal Encoding as a Regularizer in Binary Loss for Solar Flare Prediction](https://mlsanity.com/paper/2510.04063/) (2025)
- [Enhancing Explainability in Solar Energetic Particle Event Prediction: A Global Feature Mapping Approach](https://mlsanity.com/paper/2511.09475/) (2025)

## Abstract (arXiv)

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 ≥M-class flares by utilizing the shape-based features of magnetograms of active region (AR) patches spanning from -90circ to +90circ 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 ~7%, ~4%, and ~3% for AR patches within ±30^circ, ±60^circ, and ±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 ±60circ to ±90circ) 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.