[Paper Review] Calorimeter shower superresolution

Ian Pang, J. A. Raine+1 more|arXiv (Cornell University)|Aug 22, 2023

Particle physics theoretical and experimental studies86 references4 citations

TL;DR

SuperCalo introduces a flow-based super-resolution model that efficiently upsamples coarse-grained calorimeter showers to high-resolution, fine-grained showers, significantly reducing computational cost and generation time while preserving high-fidelity and diversity. The method achieves state-of-the-art performance on the CaloChallenge 2022 Dataset 2 by learning a conditional density over fine voxels given coarse voxel inputs with improved scalability and fidelity.

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.

Motivation & Objective

• To address the computational bottleneck in high-energy physics simulations by accelerating calorimeter shower generation.
• To develop a scalable, differentiable super-resolution framework that upsampled coarse showers to fine-grained resolutions without training end-to-end on high-dimensional data.
• To reduce memory and generation time by learning a conditional super-resolution function from fewer coarse showers while maintaining high fidelity.
• To enable high-variation, high-fidelity generation of fine-grained showers from a limited number of coarse inputs through probabilistic modeling.
• To demonstrate the feasibility and superiority of super-resolution over direct generative modeling in high-dimensional calorimeter shower simulation.

Proposed method

• SuperCalo employs normalizing flows to model the conditional probability $ p(\vec{E}_{\text{fine}}|\vec{E}_{\text{coarse}}) $, learning a bijective transformation from a simple prior to the complex distribution of fine shower energies.
• The model conditions on coarse voxel energies, their spatial locations, and neighboring coarse energies, enabling localized, independent upsampling per coarse voxel.
• A key innovation is the use of coarse-grained representations as input, with fine-grained outputs generated via a flow-based model conditioned on coarse features, avoiding direct high-dimensional modeling.
• Preprocessing includes logit transformations and noise injection to stabilize training on sparse, zero-dominated energy distributions.
• The model uses one-hot encoded coarse layer and r-bin labels as conditional inputs to improve spatial generalization.
• During inference, the model generates multiple diverse fine-grained showers from a single coarse input by sampling from the learned conditional distribution.

Figure 3: 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 pre

Experimental results

Research questions

• RQ1 Can super-resolution techniques based on normalizing flows effectively upsample coarse calorimeter showers to high-resolution, fine-grained showers with high fidelity?
• RQ2 Does the proposed SuperCalo framework reduce computational cost and generation time compared to direct, end-to-end generative modeling of high-dimensional showers?
• RQ3 To what extent can a small number of coarse showers be used to generate a large number of high-fidelity fine-grained showers through probabilistic upsampling?
• RQ4 How does the choice of coarse voxelization affect the performance and generalization of the super-resolution model?
• RQ5 Can the model preserve realistic shower morphology and energy deposition patterns while enabling fast, scalable inference?

Key findings

• SuperCalo achieves high-fidelity reconstruction of fine-grained calorimeter showers from coarse inputs, with classifier-based metrics indicating strong distributional similarity to reference GEANT4 simulations.
• The model enables generation of diverse, high-fidelity showers from a single coarse input, reducing the need for large-scale coarse training data.
• Generation time is significantly reduced compared to direct high-dimensional generative models, with inference speedups enabled by the coarse-to-fine paradigm.
• The use of flow-based modeling ensures exact likelihood computation and stable training, even on sparse, zero-inflated energy distributions.
• Performance is robust across different coarse voxelization schemes, with the model showing strong generalization to unseen incident energies and shower topologies.
• The classifier-based evaluation shows that generated showers are statistically indistinguishable from reference showers in terms of low- and high-level features, confirming high-fidelity output.

Figure 4: Histograms of the $\rho$ distribution for inner, middle and outer coarse radial bins (from left to right). Distribution of Geant 4 data is shown in gray, and that of SuperCalo $A$ ( $B$ ) as red (blue) lines. See text for definition of $\rho$ .