A machine-learning model for estimating the eventual peak of an ongoing solar flare had its lowest reported error in the C-class-and-above group and its highest for X-class flares, according to a preprint. Its error also fell when forecasts were made closer to the flare’s observed peak.
The work focuses on peak soft X-ray flux—the level of X-ray emission reached at a flare’s strongest point—while the event is still unfolding. In practical terms, it estimates how strong an ongoing flare will become.
Forecasts updated as flares develop
The system generated a new estimate every minute, beginning three minutes after cataloged onset and continuing until the observed peak. Each estimate used the preceding 60 minutes of X-ray observations.
The evaluation covered C-, M- and X-class flares observed by GOES-8 through GOES-18 between 1997 and 2024. Its event-level table contained 19,438 flare events, and the sliding-window process yielded 211,552 time-series samples.
The system paired real-time GOES X-ray readings with a sequence-based neural network, which reads recent measurements in order, to estimate peak flux. Researchers assessed it with four-fold cross-validation and reported RMSE, percentage error and Pearson correlation between predicted and observed peaks.
The strongest flares produced the largest errors
For the C-class-and-above group, reported RMSE was 0.26 and percentage error was 3.11%. The corresponding figures were 0.45 and 5.59% for M-class-and-above flares, and 0.87 and 12.76% for X-class flares.
Timing mattered as well. Events with longer rises to their peaks had larger RMSE than shorter-rise events, while both RMSE and percentage error decreased as the prediction time approached the peak.
Using the predicted peak to distinguish C-class from M-class-and-above flares produced a TSS of 0.68 and an F1 score of 0.77, two summary measures of classification skill.
Uncertainty was weakest for X-class events
Coverage here means the share of observed peaks that fell inside the model’s uncertainty ranges. It was 96.1% for the C-class-and-above group, 91.7% for M-class-and-above flares and 83.8% for X-class flares.
The authors say the lower coverage for stronger flares may reflect both their greater prediction difficulty and the limited number of such events. They also report that noise uncertainty made a larger contribution to total uncertainty than model uncertainty.
The evidence stops short of a live test
A separate retrospective archive contained 3,317 events: 2,914 C-class, 379 M-class and 24 X-class flares. The reported results were similar in scale to the main evaluation: RMSE and percentage error were 0.25 and 3.27% for C-class-and-above, 0.45 and 5.87% for M-class-and-above, and 0.84 and 12.53% for X-class; total uncertainty coverage was 96.2%, 91.7% and 84.2%, respectively.
The models were also implemented in a publicly accessible near-real-time flare-nowcasting system.
The evaluation used cross-validation on the studied GOES records and a separate retrospective archive; it did not report an independent external test set or formal prospective validation. The results therefore describe model performance on these data, not downstream space-weather improvements or guaranteed performance on future flares.
The archive’s 24 X-class events also leave that subgroup especially sensitive to the limits of a small sample.
Paper data and sources
Original title: Toward Operational Solar Flare Peak Flux Nowcasting: A Strategy Combining Real-Time Data, Machine Learning, and NOAA Flare Detection Criteria
Authors: Kangwoo Yi, Qin Li, Haodi Jiang et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text