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.

翻译：利用先进的机器学习技术，我们开发了一种方法，能够从地面射电探测器阵列记录的电压波形中精确重建超高能宇宙射线的到达方向与能量。在我们的方法中，触发天线被表示为图结构，作为图神经网络（GNN）的输入。通过将物理知识融入GNN架构与输入数据中，相较于完全数据驱动的方法，我们提高了重建精度并减少了所需训练集的规模。该方法在模拟真实噪声条件的数据上实现了0.092°的角度分辨率和16.4%的电磁能量重建分辨率。我们还采用不确定性估计方法来提升预测的可靠性，量化GNN输出的置信度，并为方向与能量重建提供置信区间。最后，我们研究了验证模型在现实变化下一致性与鲁棒性的策略，旨在识别在仿真与现实之间存在域偏移时预测仍保持可靠的场景。