用图神经网络精准重建宇宙射线方向与能量，提升可靠性与小样本表现。
Deep ensemble graph neural networks for probabilistic cosmic-ray direction and energy reconstruction in autonomous radio arrays
- 将天线信号建模为图结构，融合物理知识优化GNN架构与输入数据
- 在模拟噪声下实现0.092°角分辨率和16.4%能量分辨率
- 引入不确定性估计，可量化预测置信度并验证模型鲁棒性
我们开发了一种基于机器学习的方法，利用地面无线电探测阵列记录的电压波形，精确重建超高能宇宙射线的入射方向与能量。该方法将触发天线表示为图结构，输入图神经网络（GNN）。通过在GNN架构和输入数据中融入物理先验知识，提升了精度并减少了对训练数据量的需求。在含真实噪声的模拟数据上，该方法实现了0.092°的角分辨率和16.4%的电磁能量重建分辨率。同时，采用不确定性估计方法，量化了模型输出的置信度，并提供方向与能量重建的置信区间。最后，研究了模型在现实环境变化下的一致性与鲁棒性策略，旨在识别模拟与真实场景差异下的可靠预测情形。
原文摘要 · Abstract (English)
Using advanced machine learning techniques, we developed a method for reconstructing precisely the arrival direction and energy of ultra-high-energy cosmic rays from the voltage traces they induced on ground-based radio detector arrays. In our approach, triggered antennas are represented as a graph structure, which serves as input for a graph neural network (GNN). By incorporating physical knowledge into both the GNN architecture and the input data, we improve the precision and reduce the required size of the training set with respect to a fully data-driven approach. This method achieves an angular resolution of 0.092° and an electromagnetic energy reconstruction resolution of 16.4% on simulated data with realistic noise conditions. We also employ uncertainty estimation methods to enhance the reliability of our predictions, quantifying the confidence of the GNN's outputs and providing confidence intervals for both direction and energy reconstruction. Finally, we investigate strategies to verify the model's consistency and robustness under real life variations, with the goal of identifying scenarios in which predictions remain reliable despite domain shifts between simulation and reality.
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