CaloFlow for CaloChallenge Dataset 1

TL;DR

CaloFlow introduces a two-stage normalizing-flow approach to fast calorimeter shower generation conditioned on incident energy, applied to CaloChallenge Dataset 1 for $\gamma$ and $\pi^+$ showers. Using flow-I for layer-energy distributions and flow-II for normalized voxel showers in a teacher–student density-distillation framework, the method achieves Geant4-level fidelity in shower images, energy histograms, and shower shapes while delivering generation times far faster than Geant4. Quantitative classifier metrics and $\chi^2$/NDF comparisons show strong fidelity relative to Geant4, with improved realism over prior GAN-based methods and competitive results against diffusion-based approaches on this dataset. The study highlights the potential of flow-based calorimeter simulations, while outlining future directions such as continuous-energy conditioning and scaling to higher-dimensional datasets (Datasets 2 and 3).

Abstract

CaloFlow is a new and promising approach to fast calorimeter simulation based on normalizing flows. Applying CaloFlow to the photon and charged pion Geant4 showers of Dataset 1 of the Fast Calorimeter Simulation Challenge 2022, we show how it can produce high-fidelity samples with a sampling time that is several orders of magnitude faster than Geant4. We demonstrate the fidelity of the samples using calorimeter shower images, histograms of high-level features, and aggregate metrics such as a classifier trained to distinguish CaloFlow from Geant4 samples.

Figures (21)

• Figure 1: Diagram of coordinate system used in the CaloChallenge datasetcalochallenge.
• Figure 2: Breakdown of incident energies in CaloChallenge Dataset 1.
• Figure 3: Shower averages for $\gamma$ teacher (top), $\gamma$ student (middle) and Geant4 $\gamma$ reference dataset (bottom) respectively.
• Figure 4: Shower averages for $\pi^+$ teacher (top), $\pi^+$ student (middle) and Geant4 $\pi^+$ reference dataset (bottom) respectively.
• Figure 5: Energy distributions for $\gamma$ dataset.