Precise Simulation of Electromagnetic Calorimeter Showers Using a Wasserstein Generative Adversarial Network


Simulations of particle showers in calorimeters are computationally time-consuming, as they have to reproduce both energy depositions and their considerable fluctuations. A new approach to ultra-fast simulations is generative models where all calorimeter energy depositions are generated simultaneously. We use GEANT4 simulations of an electron beam impinging on a multi-layer electromagnetic calorimeter for adversarial training of a generator network and a critic network guided by the Wasserstein distance. The generator is constrained during the training such that the generated showers show the expected dependency on the initial energy and the impact position. It produces realistic calorimeter energy depositions, fluctuations and correlations which we demonstrate in distributions of typical calorimeter observables. In most aspects, we observe that generated calorimeter showers reach the level of showers as simulated with the GEANT4 program.

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  1. 1.

    Agostinelli S, GEANT4 Collaboration (2003) GEANT4: a simulation toolkit. Nucl Instrum Meth A 506:250.

    ADS  Article  Google Scholar 

  2. 2.

    Allison J (2006) Geant4 developments and applications. IEEE Trans Nucl Sci 53:270.

    ADS  Article  Google Scholar 

  3. 3.

    Allison J (2016) Recent developments in Geant4. Nucl Instrum Meth A 835:186.

    ADS  Article  Google Scholar 

  4. 4.

    Goodfellow I et al (2014) Generative adversarial networks. arXiv:1406.2661 [stat.ML]

  5. 5.

    Shrivastava A et al (2016) Learning from simulated and unsupervised images through adversarial training. arXiv:1612.07828 [cs.CV]

  6. 6.

    Hooberman B et al (2017) Calorimetry with deep learning: particle classification, energy regression, and simulation for high-energy physics. In: Proc. deep learning for physical sciences workshop at the 31st conf. neural information processing systems (NIPS), Long Beach

  7. 7.

    Paganini M, de Oliveira L, Nachman B (2018) Accelerating science with generative adversarial networks: an application to 3D particle showers in multilayer calorimeters. Phys Rev Lett 120(4):042003

    ADS  Article  Google Scholar 

  8. 8.

    Paganini M, de Oliveira L, Nachman B (2018) CaloGAN. Phys Rev D 97:014021

    ADS  Article  Google Scholar 

  9. 9.

    Erdmann M, Geiger L, Glombitza J, Schmidt D (2018) Generating and refining particle detector simulations using the Wasserstein distance in adversarial networks. Comput Softw Big Sci 2:4.

    Article  Google Scholar 

  10. 10.

    Arjovsky M, Chintala S, Bottou L (2017) Wasserstein GAN. arXiv:1701.07875 [stat.ML]

  11. 11.

    Gulrajani I et al (2017) Improved training of Wasserstein GANs. arXiv:1704.00028 [cs.LG]

  12. 12.

    Odena A, Olah C, Shlens J (2016) Conditional image synthesis with auxiliary classifier GANs. arXiv:1610.09585 [stat.ML]

  13. 13.

    Abadi M et al. TensorFlow: large-scale machine learning on heterogeneous systems. arxiv:1603.04467 [cs.DC]

  14. 14.

    Apollinari G et al (2015) High-luminosity large hadron collider, technical design report CERN-2015-005. Accessed 30 Nov 2016

  15. 15.

    The CMS Collaboration (2008) The CMS experiment at the CERN LHC. JINST 3:S08004

    Google Scholar 

  16. 16.

    Contardo D et al (2018) The phase-2 upgrade of the CMS endcap calorimeter, technical design report CERN-LHCC-2017-023. CMS-TDR-019 (ISBN 978-92-9083-459-5). Accessed 14 Mar 2018

  17. 17.

    Martelli A (2018) The CMS HGCal detector for HL-LHC upgrade. arXiv:1708.08234v1 [physics.ins-det]

  18. 18.

    Jain S (2017) Construction and first beam-tests of silicon-tungsten prototype modules for the CMS High Granularity Calorimeter for HL-LHC. JINST 12:C03011

    Article  Google Scholar 

  19. 19.

    Quast T (2018) Construction and beam-tests of silicon-tungsten prototype modules for the CMS High Granularity Calorimeter for HL-LHC. JINST 13:C02044

    Article  Google Scholar 

  20. 20.

    Spanggaard J (1998) Delay wire chambers—a users guide, SL-Note-98-023. Accessed 09 May 2017

  21. 21.

    Banerjee T (2017) Validation of physics models of GEANT4 using data from CMS experiment. J Phys Conf Ser 898:042005

    Article  Google Scholar 

  22. 22. Accessed 15 Jan 2018

  23. 23.

    Colas J, ATLAS Collaboration (2005) Position resolution and particle identification with the ATLAS EM calorimeter. Nucl Instrum Methods Phys Res Sect A 550:96–115

    ADS  Article  Google Scholar 

  24. 24.

    Jun SY (2011) Gflash as a parameterized calorimeter simulation for the CMS experiment. J Phys Conf Ser 293:012023

    Article  Google Scholar 

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For valuable discussions and comments on the manuscript we wish to thank Lucie Linssen, Eva Sicking and Florian Pitters from the EP-LCD group at CERN, and Yannik Rath from the Aachen group. We gratefully acknowledge permission to apply the geometry files provided by the CMS HGCAL group for simulating data needed for this study. This work is supported by the Ministry of Innovation, Science and Research of the State of North Rhine-Westphalia, and the Federal Ministry of Education and Research (BMBF). Thorben Quast gratefully acknowledges the grant of the Wolfgang Gentner scholarship.

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Correspondence to Thorben Quast.

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See Tables 2, 3 and 4.

Table 2 Critic network as used in the adversarial framework
Table 3 Generator network as used in the framework to generate electromagnetic calorimeter showers
Table 4 Constrainer network as used in the framework for energy (position) regression

See Figs. 10 and 11.

Fig. 10

Analogous to Fig. 5. The noise threshold is set to 10 MIPs instead of 2 MIPs

Fig. 11

Analogous to Figs. 7, 8 and 9. The noise threshold is set to 10 MIPs instead of 2 MIPs

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Erdmann, M., Glombitza, J. & Quast, T. Precise Simulation of Electromagnetic Calorimeter Showers Using a Wasserstein Generative Adversarial Network. Comput Softw Big Sci 3, 4 (2019).

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  • Deep learning
  • Adversarial networks
  • Wasserstein distance
  • Detector
  • Simulation