Solar flare forecasting utilizing deep survival analysis

Context. Solar flares and their associated particle ejections can have adverse effects on technology on Earth. Solar flare forecasting, the prediction of such high-energy outbursts on the Sun, is becoming increasingly important as space missions and infrastructure expand. To enhance the prediction of flare timing, we combined survival analysis, traditionally used in medicine, with deep learning. Aims. Our objective is to improve flare prediction by eliminating fixed time decision boundaries during model training. This allows the model to capture the evolving flare risks within solar active regions. The aim is to further integrate a discrete classifier that triggers warning systems based on the underlying continuous time-to-event predictions. Methods. We employed deep survival analyses to estimate the likelihood and timing of a flare using photospheric vector magnetogram data from solar active regions. Deep survival analysis estimates the probability of an event occurring over time, in our case the next flare. A subsequent step utilizes a support vector machine (SVM) to provide discrete warning classifications on a flexible time decision boundary. Results. Our survival model effectively predicts time-to-event survival probabilities, following the evolution of active regions and capturing temporal data patterns. With an averaged true skill statistic (TSS) of 0.71 across classes, the SVM distinguishes between low-risk, future, and imminent flare events. Nonflaring regions are well separated with a TSS of 0.84, while differentiating between short- and long-term flare predictions is more challenging, with TSS scores ranging from 0.3 to 0.7 depending on warning thresholds of 8 to 60 hours. Conclusions. By removing rigid time boundaries, our continuous-time survival analysis approach enhances real-time forecasting capabilities and addresses the limitations of traditional models. Future studies may further refine and optimize these techniques.