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CaloClouds: Fast Geometry-Independent Highly-Granular Calorimeter Simulation

Erik Buhmann, Sascha Diefenbacher, Engin Eren, Frank Gaede, Gregor Kasieczka, Anatolii Korol, William Korcari, Katja Krüger, Peter McKeown

TL;DR

This work achieves a major breakthrough in this task by directly generating a point cloud of a few thousand space points with energy depositions in the detector in 3D space without relying on a fixed-grid structure.

Abstract

Simulating showers of particles in highly-granular detectors is a key frontier in the application of machine learning to particle physics. Achieving high accuracy and speed with generative machine learning models would enable them to augment traditional simulations and alleviate a major computing constraint. This work achieves a major breakthrough in this task by, for the first time, directly generating a point cloud of a few thousand space points with energy depositions in the detector in 3D space without relying on a fixed-grid structure. This is made possible by two key innovations: i) Using recent improvements in generative modeling we apply a diffusion model to generate photon showers as high-cardinality point clouds. ii) These point clouds of up to $6,000$ space points are largely geometry-independent as they are down-sampled from initial even higher-resolution point clouds of up to $40,000$ so-called Geant4 steps. We showcase the performance of this approach using the specific example of simulating photon showers in the planned electromagnetic calorimeter of the International Large Detector (ILD) and achieve overall good modeling of physically relevant distributions.

CaloClouds: Fast Geometry-Independent Highly-Granular Calorimeter Simulation

TL;DR

This work achieves a major breakthrough in this task by directly generating a point cloud of a few thousand space points with energy depositions in the detector in 3D space without relying on a fixed-grid structure.

Abstract

Simulating showers of particles in highly-granular detectors is a key frontier in the application of machine learning to particle physics. Achieving high accuracy and speed with generative machine learning models would enable them to augment traditional simulations and alleviate a major computing constraint. This work achieves a major breakthrough in this task by, for the first time, directly generating a point cloud of a few thousand space points with energy depositions in the detector in 3D space without relying on a fixed-grid structure. This is made possible by two key innovations: i) Using recent improvements in generative modeling we apply a diffusion model to generate photon showers as high-cardinality point clouds. ii) These point clouds of up to space points are largely geometry-independent as they are down-sampled from initial even higher-resolution point clouds of up to so-called Geant4 steps. We showcase the performance of this approach using the specific example of simulating photon showers in the planned electromagnetic calorimeter of the International Large Detector (ILD) and achieve overall good modeling of physically relevant distributions.
Paper Structure (12 sections, 7 equations, 11 figures, 2 tables)

This paper contains 12 sections, 7 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Data Samples
  3. Model
  4. Diffusion Point Cloud Generator
  5. Encoder & Latent Flow
  6. Shower Flow & Post-Diffusion Calibration
  7. Results
  8. Physics Performance
  9. Shower Translation
  10. Timing
  11. Conclusions
  12. Effects of the Pre-Clustering

Figures (11)

  • Figure 1: Illustration of the data preprocessing pipeline.
  • Figure 2: Illustration of the training and sampling procedure of the CaloClouds architecture. The separate training of the Shower Flow and the Latent Flow is not shown.
  • Figure 3: Illustration of the CaloClouds' PointWise Net (a) consisting of multiple ConcatSquash layers (b). The number of hidden dimensions is indicated. MLP denotes a multi-layer perceptron. $^*$No activation function is applied in the last layer of the PointWise Net.
  • Figure 4: Illustration of the reverse diffusion process. Starting from the initial noise. The color scale corresponds to the point energy.
  • Figure 5: Histograms of the cell energies (left), radial shower profile (center), and longitudinal shower profile (right) for both Geant4 and CaloClouds. In the per-cell energy distribution, the region below 0.1 MeV is grayed out (see main text for details). All distributions are calculated for a uniform distribution of incident particle energies.
  • ...and 6 more figures