https://doi.org/10.1007/s41781-026-00166-7
Research
Uncertainty Quantification for a Cramér Generative Adversarial Network-Based Simulation of the Ring-Imaging Cherenkov Particle Detector Using Feature Densities
1
Instituto Tecnológico de Costa Rica, Cartago, Costa Rica
2
INFN Sezione di Firenze, Sesto Fiorentino
, Italy
3
CERN, European Organization for Nuclear Research, Geneva, Switzerland
a
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Received:
6
October
2025
Accepted:
18
May
2026
Published online:
30
June
2026
Abstract
The simulation of particle collisions and of the subsequent detection process is by far the most computationally expensive task for the experiments at the Large Hadron Collider. Generative machine learning has been investigated for the last decade to replace the interaction-level computations implemented in the Geant4 libraries with deep neural networks. Using neural networks to approximate the outcome of a Geant4 simulation is fast, computationally efficient and ready for hardware acceleration, but introduces an additional approximation error that must be modeled and controlled. In this work, we consider the simulation of the particle identification features obtained with the RICH detectors of the LHCb experiment at CERN, which has been extensively studied in the literature as an example of parametrization of the detector response with generative models, and in particular with Cramér generative adversarial networks. We propose the usage of the feature densities (FD) method to provide a computationally sustainable uncertainty quantification algorithm. This method computes a density estimation of the embeddings obtained from projected training data. In the reported studies, the proposed method is proved to predict uncertainty scores comparable to the previously implemented Monte Carlo dropout method, with a computational cost reduced by one order of magnitude. And we propose evolutions in the generative models that may result in a further reduction of the computational cost. The usage of different embedding layers and the possibility of evaluating the training data as many times as possible makes the density estimation very flexible to estimate the feature densities. Author names: Please confirm if the author names are presented accurately and in the correct sequence (given name, middle name/initial, family name). Author 1 Given name: Fernando Ugalde Last name: Green, Author 2 Given name: José Arce Last name: Morales, Author 3 Given name: Jonathan David Pastor Last name: Barrientos, Author 4 Given name: Sergio Arguedas Last name: Cuendis Author 1 Given name: Fernando Last name: Ugalde Green, Author 2 Given name: José Last name: Arce Morales, Author 3 Given name: Jonathan David Last name: Pastor Barrientos, Author 4 Given name: Sergio Last name: Arguedas Cuendis
Key words: Deep learning / Generative adversarial networks / Feature densities / Monte Carlo dropout / Uncertainty quantification / Out of distribution detection
© The Author(s) 2026
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