Calorimeter shower superresolution

TL;DR

Calorimeter shower simulation at the LHC is computationally bottlenecked; this paper introduces SuperCalo, a flow-based superresolution method that upscales coarse, lower-dimensional calorimeter representations into high-dimensional fine showers by learning $p(\vec{E}_{\rm fine}|\vec{E}_{\rm coarse})$. The approach combines two conditional normalizing flows (Flow-1 and Flow-2) with a coarse-to-fine upsampling step (SuperCalo A or B) to produce fast, probabilistic reconstructions of $p(\vec{E}_{\rm fine}|E_{\rm inc})$, reducing computation and memory while preserving shower variability. Results on CaloChallenge Dataset 2 show good fidelity across layer and voxel-energy distributions, with classifier-based metrics indicating high realism and substantial speedups (~10^3×) relative to Geant4, and potential further gains using alternative architectures like IAF. The framework is architecture-agnostic, scalable to higher granularity, and offers a practical pathway to accelerate fast calorimeter simulation in high-energy physics.

Abstract

Calorimeter shower simulation is a major bottleneck in the Large Hadron Collider computational pipeline. There have been recent efforts to employ deep-generative surrogate models to overcome this challenge. However, many of best performing models have training and generation times that do not scale well to high-dimensional calorimeter showers. In this work, we introduce SuperCalo, a flow-based superresolution model, and demonstrate that high-dimensional fine-grained calorimeter showers can be quickly upsampled from coarse-grained showers. This novel approach presents a way to reduce computational cost, memory requirements and generation time associated with fast calorimeter simulation models. Additionally, we show that the showers upsampled by SuperCalo possess a high degree of variation. This allows a large number of high-dimensional calorimeter showers to be upsampled from much fewer coarse showers with high-fidelity, which results in additional reduction in generation time.

Figures (13)

• Figure 1: Schematic of full generation chain where the coarse voxel model (comprising of Flow-1 and Flow-2) and SuperCalo are applied sequentially.
• Figure 2: 3-D calorimeter voxel geometry for Dataset 2 showing fine voxelization (gray) and representative coarse voxels for SuperCalo$A$ (red) and SuperCalo$B$ (green).
• Figure 3: Histograms of total energy deposited in a layer $i$ ($E_{{\rm layer},i}$), for $i=1$, 10, 20, and 45 (from left to right). Distribution of Geant4 data is shown in gray, and that of SuperCalo$A$ ($B$) as red (blue) lines.
• Figure 4: Plot of AUC scores for classifier trained on voxel energies from single layer (blue), two adjacent layers (red) and three adjacent layers (green). The horizontal axis indicates the layer number of the first layer's voxels that the classifier was trained on. For the final layer (45) the preceding adjacent layers are taken, otherwise subsequent adjacent layers are taken.
• Figure 5: Histograms of the $\rho$ distribution for inner, middle and outer coarse radial bins (from left to right). Distribution of Geant4 data is shown in gray, and that of SuperCalo$A$ ($B$) as red (blue) lines. See text for definition of $\rho$.