Integrating Physics-Informed Neural Networks with Convolutional Neural Networks for Solar Flare Prediction

Accurate forecasting of extreme solar flares is essential for mitigating space weather impacts on critical infrastructure, yet current deep learning approaches face fundamental limitations in operational reliability. Models often lack physical interpretability and may fail to generalize to configurations under-represented in training data, which are critical weaknesses
when forecasting rare extreme events. We take steps toward addressing these gaps by developing physics-informed architectures that embed magnetohydrodynamic (MHD) constraints directly into neural network training.

Using SDO/HMI SHARP vector magnetograms (2010–2021, 13,298 observations), we compare three approaches for 24-hour multi-class flare forecasting: (1) a ResNet34 baseline, (2) a reconstruction-physics hybrid enforcing MHD constraints through magnetic field reconstruction, and (3) a probability-physics hybrid coupling physics-derived features to classification probabilities. The probability-physics model achieves macro-averaged True Skill Statistic (TSS) of 0.389 [95% CI: 0.355–0.425] versus baseline 0.338 [0.301–0.375], a statistically significant 15% improvement (p < 0.001). Critically, physics-constrained models reduce divergence violations by two orders of magnitude, ensuring predictions satisfy fundamental conservation laws and remain physically interpretable across a broader range of magnetic configurations, including those under-represented in training data.

Feature space analysis reveals that intermediate C-class flares occupy transitional magnetic states with extensive overlap between non-flaring and extreme configurations, highlighting an intrinsic forecasting challenge that persists across architectures. M+ (M- and X-class) events maintain strong discrimination (AUC > 0.87) despite severe class imbalance, indicating that physically meaningful features can aid identification of extreme events even when training samples are scarce.

Our results suggest that embedding first-principles MHD constraints—divergence-free conditions, force-free equilibrium, and energy conservation—enhances both forecast skill and physical plausibility without increasing computational cost. The integration of physics-informed learning with CNN-based flare prediction offers a pathway toward improving operationally deployed systems with enhanced reliability for extreme event forecasting. For operational forecasters, improved physical interpretability may provide greater confidence in model predictions during critical decision-making, while reduced false alarm rates minimize unnecessary protective actions for satellite operators and power grid managers.

Keywords: extreme space weather, solar flare forecasting, physics-informed neural net-
works, operational reliability, magnetohydrodynamics, infrastructure risk mitigation