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.
KeywordsDeep learning Adversarial networks Wasserstein distance Detector Simulation
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.
Compliance with Ethical Standards
Conflict of Interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
- 4.Goodfellow I et al (2014) Generative adversarial networks. arXiv:1406.2661 [stat.ML]
- 5.Shrivastava A et al (2016) Learning from simulated and unsupervised images through adversarial training. arXiv:1612.07828 [cs.CV]
- 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 BeachGoogle Scholar
- 10.Arjovsky M, Chintala S, Bottou L (2017) Wasserstein GAN. arXiv:1701.07875 [stat.ML]
- 11.Gulrajani I et al (2017) Improved training of Wasserstein GANs. arXiv:1704.00028 [cs.LG]
- 12.Odena A, Olah C, Shlens J (2016) Conditional image synthesis with auxiliary classifier GANs. arXiv:1610.09585 [stat.ML]
- 13.Abadi M et al. TensorFlow: large-scale machine learning on heterogeneous systems. arxiv:1603.04467 [cs.DC]
- 14.Apollinari G et al (2015) High-luminosity large hadron collider, technical design report CERN-2015-005. https://cds.cern.ch/record/2116337. Accessed 30 Nov 2016
- 15.The CMS Collaboration (2008) The CMS experiment at the CERN LHC. JINST 3:S08004Google Scholar
- 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). https://cds.cern.ch/record/2293646. Accessed 14 Mar 2018
- 17.Martelli A (2018) The CMS HGCal detector for HL-LHC upgrade. arXiv:1708.08234v1 [physics.ins-det]
- 20.Spanggaard J (1998) Delay wire chambers—a users guide, SL-Note-98-023. http://cds.cern.ch/record/702443/files/sl-note-98-023.pdf. Accessed 09 May 2017
- 22.https://github.com/cms-sw/cmssw/tree/CMSSW_10_0_X. Accessed 15 Jan 2018