ELUQuant: Event-Level Uncertainty Quantification in Deep Inelastic Scattering

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.