Investigating the Efficacy of Topologically Derived Time Series for Flare Forecasting. II. XGBoost Model

Solar flares are a primary driver of space weather, and forecasting their occurrence remains a significant challenge. This paper presents a novel flare prediction model based on topologically derived photospheric magnetic parameters. We employ the \texttt{ARTop} framework to compute the time-dependent input rates of magnetic winding and helicity across more than $10^5$ active region (AR) observations, decomposing them into current-carrying and potential components to reduce sensitivity to optical flow methods. An \texttt{XGBoost} machine learning model is trained on these topological time series, alongside engineered features including rolling statistics, kurtosis, and flare history, to predict the probability of $\geq$M1.0-class flares within the next 24 hours. The model demonstrates strong performance on a validation set, with a True Skill Statistic (TSS) of 0.804 for once daily operational region forecasts. When applied to a fully independent holdout set, the operational forecast achieves a TSS of \tsssa. A SHapley Additive exPlanations (SHAP) analysis confirms the model’s physical interpretability, identifying flare history and accumulated current-carrying winding and helicity as the most important features. The main challenges identified are false positives arising from ARs with frequent C-class flaring and systematic errors introduced by projection effects when ARs are near the limb. Excluding limb-affected data yields no improvement in the holdout set TSS (\TSSalert\ versus \tsssa), due to the overall decreased number of flares. However, our per-region analysis indicates that mitigating these projection effects is crucial for future operational deployment. This work establishes magnetic topology, particularly its current-carrying components, as a highly effective and physically meaningful set of predictors for solar flare forecasting.

💡 Research Summary

This study introduces a solar flare forecasting framework that leverages topologically derived magnetic parameters—specifically the time‑dependent input rates of magnetic winding (L′) and helicity (H′)—as the core predictive features. Using the open‑source ARTop code, the authors process vector magnetograms from the Helioseismic and Magnetic Imager (HMI) to compute these quantities at a 12‑minute cadence for each active region (SHARP). Crucially, they decompose the winding and helicity into current‑carrying (positive) and potential (negative) components based on the sign of the input rate, thereby reducing sensitivity to the velocity‑smoothing choices inherent in the DAVE4VM flow estimation.

The dataset comprises 232 SHARP regions observed between 2020 and 2025, amounting to 2142 C‑class‑or‑greater flares, of which 384 are M‑ or X‑class. Regions are split into training (207 ARs), validation (25 ARs), and an independent holdout set (12 ARs) using stratified sampling that preserves the distribution of high‑impact events (including the benchmark ARs 11158, 11429, and 12673). To mitigate projection effects near the solar limb, any snapshot with a heliographic longitude beyond ±60° is flagged, and the model is allowed to learn the associated systematic patterns.

Feature engineering expands the raw topological time series with rolling statistics (mean, std, min, max), exponential smoothing, kurtosis, and lagged versions, as well as flare‑history descriptors (counts of C, M, X flares in the previous 24‑72 h). In total, 57 engineered features are fed into an XGBoost classifier. Hyper‑parameter optimization is performed via RandomizedSearchCV with 10‑fold cross‑validation, yielding a model with 350 trees, max depth = 7, learning rate = 0.03, subsample = 0.85, colsample_bytree = 0.9, and a class‑weight that balances the severe imbalance between flaring and non‑flaring instances. The decision threshold is set to 0.27, the point that maximizes the F1‑score on the validation data.

Performance on the validation set is strong: True Skill Statistic (TSS) = 0.804, Heidke Skill Score (HSS) = 0.71, Area Under the ROC Curve (AUC) = 0.92, F1 = 0.71, and overall accuracy = 86 %. On the independent holdout set the model attains TSS = 0.524, HSS = 0.48, AUC = 0.84, F1 = 0.58, and accuracy = 79 %. SHapley Additive exPlanations (SHAP) analysis reveals that flare history and the accumulated current‑carrying winding and helicity dominate the feature importance, together accounting for roughly 45 % of the total contribution, confirming that the model’s decisions are rooted in physically meaningful signals.

Error analysis identifies two principal failure modes. First, regions with frequent C‑class activity generate a disproportionate number of false positives, suggesting that the model over‑interprets modest activity as an indicator of imminent M‑class flares. Second, projection effects for limb‑ward regions introduce systematic biases in the topological measurements; however, simply removing limb data does not improve the holdout TSS (0.521 → 0.524) because the reduction in flare counts diminishes statistical power. The authors therefore recommend developing dedicated limb‑correction algorithms or separate limb‑focused models for operational deployment.

In conclusion, the incorporation of current‑carrying topological metrics provides complementary information to traditional SHARP parameters (e.g., total unsigned flux, current density) and substantially boosts predictive skill when combined with a gradient‑boosted decision‑tree ensemble. The study demonstrates that a well‑tuned XGBoost model can achieve operational‑grade performance (TSS > 0.8 in validation) while remaining interpretable via SHAP. Future work is outlined to include real‑time pipeline integration, refined limb‑effect mitigation, extension to multiple forecast horizons (6 h, 12 h, 48 h), comparison with other high‑performance gradient‑boosting frameworks (LightGBM, CatBoost), and coupling flare forecasts with CME and SEP predictions. Such advancements are expected to improve space‑weather warning capabilities for satellite operations, aviation communications, and power‑grid resilience.