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Generating and Refining Particle Detector Simulations Using the Wasserstein Distance in Adversarial Networks

Abstract

We use adversarial network architectures together with the Wasserstein distance to generate or refine simulated detector data. The data reflect two-dimensional projections of spatially distributed signal patterns with a broad spectrum of applications. As an example, we use an observatory to detect cosmic ray-induced air showers with a ground-based array of particle detectors. First we investigate a method of generating detector patterns with variable signal strengths while constraining the primary particle energy. We then present a technique to refine simulated time traces of detectors to match corresponding data distributions. With this method we demonstrate that training a deep network with refined data-like signal traces leads to a more precise energy reconstruction of data events compared to training with the originally simulated traces.

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References

  1. 1.

    Hinton GE, Osindero S, Teh YW (2006) A fast learning algorithm for deep belief nets. Neural Comput 18(7):1527–1554

  2. 2.

    Ciresan DC, Meier U, Schmidhuber J (2012) Multi-column deep neural networks for image classification. arXiv:1202.2745

  3. 3.

    Yu D, Deng L (2014) Automatic speech recognition: a deep learning approach. Springer, London

  4. 4.

    Russakovsky O et al (2015) Imagenet large scale visual recognition challenge. Int J Comput Vis 115(3):211–252

  5. 5.

    He K, Zhang X, Ren S, Sun J (2015) Deep residual learning for image recognition. arXiv:1512.03385

  6. 6.

    Silver D et al (2016) Mastering the game of Go with deep neural networks and tree search. Nature 529:7578

  7. 7.

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

  8. 8.

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

  9. 9.

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

  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.

    Goodfellow I, Bengio Y, Courville A (2016) Deep learning. MIT Press, Cambridge

  13. 13.

    Aurisano A et al (2016) A convolutional neural network neutrino event classifier. JINST 11(09):P09001

  14. 14.

    Baldi P et al (2014) Searching for exotic particles in high-energy physics with deep learning. Nat Commun 5:4308

  15. 15.

    Baldi P et al (2015) Enhanced Higgs to \(\tau ^+\tau ^-\) searches with deep learning. Phys Rev Lett 114:111801

  16. 16.

    Adam-Bourdarios C et al (2015) The Higgs boson machine learning challenge. In: Cowan G et al (eds) Proceedings of the NIPS 2014 workshop on high-energy physics and machine learning, Proceedings of machine learning research, vol 42. PMLR, Montreal, pp 19–55

  17. 17.

    Guest D et al (2016) Jet flavor classification in high-energy physics with deep neural networks. Phys Rev D 94(11):112002

  18. 18.

    Baldi P et al (2016) Jet substructure classification in high-energy physics with deep neural networks. Phys Rev D 93(9):094034

  19. 19.

    Erdmann M, Fischer B, Rieger M (2017) Jet-parton assignment in \(t\bar{t}\)H events using deep learning. JINST 12(08):P08020

  20. 20.

    Erdmann M, Glombitza J, Walz D (2018) A deep learning-based reconstruction of cosmic ray-induced air showers. Astropart Phys 97:46–53

  21. 21.

    de Oliveira L, Paganini M, Nachman B (2017) Learning particle physics by example: location-aware generative adversarial networks for physics synthesis. Comput Softw Big Sci 1(1):4

  22. 22.

    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

  23. 23.

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

  24. 24.

    Carminati F et al (2017) Calorimetry with deep learning: particle classification, energy regression, and simulation for high-energy physics. In: Workshop on deep learning for physical sciences (DLPS 2017), NIPS 2017, Long Beach

  25. 25.

    Shimmin C et al (2017) Decorrelated jet substructure tagging using adversarial neural networks. Phys Rev D 96(7):074034

  26. 26.

    Villani C (2008) Optimal transport: old and new. Grundlehren der mathematischen Wissenschaften. Springer, Berlin

  27. 27.

    Radford A, Metz L, Chintala S (2015) Unsupervised representation learning with deep convolutional generative adversarial networks. arXiv:1511.06434

  28. 28.

    Kingma DP, Ba J (2014) Adam: a method for stochastic optimization. arXiv:1412.6980

  29. 29.

    Chollet F et al (2015) Keras. https://github.com/keras-team/keras

  30. 30.

    Abadi M et al (2015) TensorFlow: large-scale machine learning on heterogeneous systems. https://www.tensorflow.org

  31. 31.

    Erdmann M et al (2017) The VISPA internet-platform in deep learning applications. In: Proc. 18th int. workshop on advanced computing and analysis techniques in physics research (ACAT), Washington

  32. 32.

    Aab A et al (2015) The Pierre Auger cosmic ray observatory. Nucl Instrum Methods A 798:172–213

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Acknowledgements

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). We wish to thank Thorben Quast for his valuable comments on the manuscript.

Author information

Correspondence to Martin Erdmann.

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Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Appendix

Appendix

See Tables 1, 2 and 3.

Table 1 Generator network as used in the WGAN to generate signal patterns
Table 2 Critic network as used in the WGAN to generate signal patterns
Table 3 Refiner network as used in the WGAN to refine signal traces. Residual shortcut connections are added after every pair of convolutions

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Erdmann, M., Geiger, L., Glombitza, J. et al. Generating and Refining Particle Detector Simulations Using the Wasserstein Distance in Adversarial Networks. Comput Softw Big Sci 2, 4 (2018). https://doi.org/10.1007/s41781-018-0008-x

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Keywords

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