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

Abstract

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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Acknowledgements

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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Appendix

Appendix

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
figure10

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

Fig. 11
figure11

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). https://doi.org/10.1007/s41781-018-0019-7

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Keywords

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