We introduce a physics-informed Bayesian Neural Network (BNN) with flow approximated posteriors using multiplicative normalizing flows (MNF) for detailed uncertainty quantification (UQ) at the physics event-level. Our method is capable of identifying both heteroskedastic aleatoric and epistemic uncertainties, providing granular physical insights. Applied to Deep Inelastic Scattering (DIS) events, our model effectively extracts the kinematic variables $x$, $Q^2$, and $y$, matching the performance of recent deep learning regression techniques but with the critical enhancement of event-level UQ. This detailed description of the underlying uncertainty proves invaluable for decision-making, especially in tasks like event filtering. It also allows for the reduction of true inaccuracies without directly accessing the ground truth. A thorough DIS simulation using the H1 detector at HERA indicates possible applications for the future EIC. Additionally, this paves the way for related tasks such as data quality monitoring and anomaly detection. Remarkably, our approach effectively processes large samples at high rates.

翻译：我们提出了一种物理信息贝叶斯神经网络（BNN），其采用乘法归一化流（MNF）来近似后验分布，旨在实现物理事件级别的精细不确定性量化（UQ）。该方法能够同时识别异方差偶然不确定性和认知不确定性，提供粒度化的物理洞察。在深度非弹性散射（DIS）事件的应用中，我们的模型有效提取了运动学变量 $x$、$Q^2$ 和 $y$，性能媲美近期深度学习回归技术，但关键改进在于实现了事件级的不确定性量化。这种对潜在不确定性的详细描述对决策制定具有不可估量的价值，尤其是在事件过滤等任务中。它还允许在没有直接访问真实值的情况下减少实际误差。利用HERA上H1探测器的全面DIS模拟表明，该方法对未来EIC可能具有应用前景。此外，这为数据质量监测和异常检测等相关任务铺平了道路。值得注意的是，我们的方法能够高效处理大批量样本。