Skip to main content

Deep learning to classify ultra-high-energy cosmic rays by means of PMT signals

Neural Computing and Applications volume 33, pages 9153–9169 (2021)Cite this article

Abstract

One of the most captivating problems being faced nowadays in Physics are ultra-high energy cosmic rays. They are high-energy radiations coming mainly from outside the Solar System, and when they enter Earth’s atmosphere, they produce a cascade of particles. This cascade of particles, named as extensive air shower, can be recorded by means of photomultiplier tubes in surface detectors, obtaining different recordings of the energy signal (since the air shower can hit one or more detectors). Based on these signals, different features can be obtained that might give an insight into which particle has caused the extensive air shower, which is of utmost importance for physicists. Therefore, this work presents a supervised learning algorithm to determine that the particle is a photon or a hadron. Convolutional neural networks and feed forward neural networks are compared in order to analyze the importance of spatial information for the classification. Then, a comparison between using the information of each surface detector separately and integrating the information from them for the classification is studied, showing that the integration improves the results compared to using each surface detector’s trace independently. Furthermore, a comparison between manually extracted features from the signal and the automatically extracted features by the convolutional neural network is done, showing the classification potential of the latter. Finally, the addition of particle shower features which are external to the surface detector measurements is assessed, showing that the combination of automatically extracted features and external variables is able to predict the particle that has produced the air shower with an accuracy of 98.87%.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Notes

  1. https://github.com/pacocp/spocu-pytorch.

References

  1. Ulrich R, Engel R, Unger M (2011) Hadronic multiparticle production at ultrahigh energies and extensive air showers. Phys Rev D 83(5):054026

    Article  Google Scholar 

  2. Auger P, Ehrenfest P, Maze R, Daudin J, Fréon RA (1939) Extensive cosmic-ray showers. Rev Mod Phys 11(3–4):288

    Article  Google Scholar 

  3. Observatory TPACR (2015) Nuclear instruments and methods in physics research section A: accelerators, spectrometers, detectors and associated equipment. Nucl Instrum Methods Phys Res A 798:172–213

    Article  Google Scholar 

  4. Banan A, Nasiri A, Taheri-Garavand A (2020) Deep learning-based appearance features extraction for automated carp species identification. Aquacult Eng 89:102053

    Article  Google Scholar 

  5. Fan Y, Kangkang X, Hui W, Zheng Y, Tao B (2020) Spatiotemporal modeling for nonlinear distributed thermal processes based on KL decomposition, MLP and LSTM network. IEEE Access 8:25111–25121

    Article  Google Scholar 

  6. Shamshirband S, Rabczuk T, Chau K-W (2019) A survey of deep learning techniques: application in wind and solar energy resources. IEEE Access 7:164650–164666

    Article  Google Scholar 

  7. Ardabili SF, Najafi B, Shamshirband S, Bidgoli BM, Deo RC, Chau K (2018) Computational intelligence approach for modeling hydrogen production: a review. Eng Appl Comput Fluid Mech 12(1):438–458

    Google Scholar 

  8. Taormina R, Chau K-W (2015) ANN-based interval forecasting of streamflow discharges using the LUBE method and MOFIPS. Eng Appl Artif Intell 45:429–440

    Article  Google Scholar 

  9. Wu CL, Chau K-W (2013) Prediction of rainfall time series using modular soft computing methods. Eng Appl Artif Intell 26(3):997–1007

    Article  Google Scholar 

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

    Article  Google Scholar 

  11. Erdmann M, Schlüter F, Šmída R (2019) Classification and recovery of radio signals from cosmic ray induced air showers with deep learning. J Instrum 14(04):P04005

    Article  Google Scholar 

  12. Huennefeld M (2017) Deep learning in physics exemplified by the reconstruction of muon-neutrino events in icecube. PoS ICRC2017, pp 1057. https://doi.org/10.22323/1.301.1057

  13. Guillén A, Bueno A, Carceller JM, Martínez-Velázquez JC, Rubio G, Todero Peixoto CJ, Sanchez-Lucas P (2019) Deep learning techniques applied to the physics of extensive air showers. Astropart Phys 111:12–22

    Article  Google Scholar 

  14. Velinov PIY (2016) Expanded classification of solar cosmic ray events causing ground level enhancements (GLEs). Types and groups of GLEs. Comptes Rendus de l’Académie Bulgare des Sciences 69(10):1341–1351

    Google Scholar 

  15. Glombitza J (2019) Air-shower reconstruction at the Pierre Auger observatory based on deep learning. In: ICRC, vol 36, p 270

  16. Herrera LJ, Peixoto CJT, Baños O, Carceller JM, Carrillo F, Guillén A (2020) Composition classification of ultra-high energy cosmic rays. Entropy 22(9):998

    Article  Google Scholar 

  17. Carrillo-Perez F, Herrera LJ, Carceller JM, Guillén A (2019) Improving classification of ultra-high energy cosmic rays using spacial locality by means of a convolutional DNN. In: International work-conference on artificial neural networks. Springer, pp 222–232

  18. Ostapchenko S (2011) Monte Carlo treatment of hadronic interactions in enhanced Pomeron scheme: Qgsjet-II model. Phys Rev D 83(1):014018

    Article  Google Scholar 

  19. Heck D, Knapp J, Capdevielle JN, Schatz G, Thouw T (1998) CORSIKA: A Monte Carlo code to simulate extensive air showers. Report fzka 6019(11)

  20. Argiro S, Barroso SLC, Gonzalez J, Nellen L, Paul T, Porter TA, Prado L Jr, Roth M, Ulrich R, Veberič D (2007) The offline software framework of the Pierre Auger observatory. Nucl Instrum Methods Phys Res Sect A Accel Spectrom Detect Assoc Equip 580(3):1485–1496

    Article  Google Scholar 

  21. Gonzalez JG, IceCube Collaboration et al (2016) Measurement of the muon content of air showers with icetop. In: Journal of physics: conference series, vol 718. IOP Publishing, p 052017

  22. Kégl B (2013) Measurement of the muon signal using the temporal and spectral structure of the signals in surface detectors of the Pierre Auger observatory. In: 33rd international cosmic ray conference (ICRC2013)

  23. Garcia-Gamez D (2013) Measurement of atmospheric production depths of muons with the Pierre Auger observatory. In: EPJ web of conferences, vol 53. EDP Sciences, p 04008

  24. Valiño I, Pierre Auger Collaboration et al (2015) Measurements of the muon content of air showers at the Pierre Auger observatory. In: Journal of physics: conference series, vol 632. IOP Publishing, p 012103

  25. Aab A, Abreu P, Aglietta M, Ahn EJ, Samarai IA, Albuquerque IFM, Allekotte I, Allen J, Allison P, Almela A et al (2015) Muons in air showers at the Pierre Auger observatory: mean number in highly inclined events. Phys Rev D 91(3):032003

    Article  Google Scholar 

  26. LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521(7553):436

    Article  Google Scholar 

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

    MATH  Google Scholar 

  28. Schmidhuber J (2015) Deep learning in neural networks: an overview. Neural Netw 61:85–117

    Article  Google Scholar 

  29. Fernández-Redondo M, Hernández-Espinosa C (2001) Weight initialization methods for multilayer feedforward. In: ESANN, pp 119–124

  30. Glorot X, Bengio Y (2010) Understanding the difficulty of training deep feedforward neural networks. In: Proceedings of the thirteenth international conference on artificial intelligence and statistics, pp 249–256

  31. LeCun Y, Boser B, Denker JS, Henderson D, Howard RE, Hubbard W, Jackel LD (1989) Backpropagation applied to handwritten zip code recognition. Neural Comput 1(4):541–551

    Article  Google Scholar 

  32. Krizhevsky A, Sutskever I, Hinton GE (2012) Imagenet classification with deep convolutional neural networks. In: Advances in neural information processing systems, pp 1097–1105

  33. Aznan Nik KN, Bonner S, Connolly J, Moubayed NA, Breckon T (2018) On the classification of SSVEP-based dry-EEG signals via convolutional neural networks. In: 2018 IEEE international conference on systems, man, and cybernetics (SMC). IEEE, pp 3726–3731

  34. Ioffe S, Szegedy C (2015) Batch normalization: accelerating deep network training by reducing internal covariate shift. arXiv preprint arXiv:1502.03167

  35. Towards Data Science (2014) Applied deep learning part 4. https://towardsdatascience.com/applied-deep-learning-part-4-convolutional-neural-networks-584bc134c1e2. Accessed 18 Jun 2019

  36. Andrej K (2017) CS231n convolutional neural networks for visual recognition. https://cs231n.github.io/convolutional-networks/. Accessed 18 Jun 2019

  37. Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20(3):273–297

    MATH  Google Scholar 

  38. Abu-Mostafa YS, Magdon-Ismail M, Lin H-T (2012) Learning from data, vol 4. AMLBook, New York

    Google Scholar 

  39. Keerthi SS, Lin C-J (2003) Asymptotic behaviors of support vector machines with Gaussian kernel. Neural Comput 15(7):1667–1689

    Article  MATH  Google Scholar 

  40. Paszke A, Gross S, Massa F, Lerer A, Bradbury J, Chanan G et al (2019) Pytorch: an imperative style, high-performance deep learning library. arXiv preprint arXiv:1912.01703

  41. Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, Prettenhofer P, Weiss R, Dubourg V, Vanderplas J, Passos A, Cournapeau D, Brucher M, Perrot M, Duchesnay E (2011) Scikit-learn: machine learning in python. J Mach Learn Res 12:2825–2830

    MathSciNet  MATH  Google Scholar 

  42. Chang C-C, Lin C-J (2011) LIBSVM: a library for support vector machines. ACM Trans Intell Syst Technol 2:27:1–27:27

    Article  Google Scholar 

  43. McKinney W (2010) Data structures for statistical computing in python. In: van der Walt S, Millman J (eds) Proceedings of the 9th python in science conference, pp 51–56

  44. van der Walt S, Colbert SC, Varoquaux G (2011) The NumPy array: a structure for efficient numerical computation. Comput Sci Eng 13(2):22–30

    Article  Google Scholar 

  45. Hunter JD (2007) Matplotlib: a 2D graphics environment. Comput Sci Eng 9(3):90–95

    Article  Google Scholar 

  46. Kisel’ák J, Lu Y, Švihra J, Szépe P, Stehlík M (2020) “SPOCU”: scaled polynomial constant unit activation function. Neural Comput Appl. https://doi.org/10.1007/s00521-020-05182-1

  47. Khessiba S, Blaiech AG, Khalifa KB, Abdallah AB, Hédi BM (2020) Innovative deep learning models for EEG-based vigilance detection. Neural Comput Appl. https://doi.org/10.1007/s00521-020-05467-5

  48. Nair V, Hinton GE (2010) Rectified linear units improve restricted Boltzmann machines. In: Proceedings of the 27th international conference on machine learning (ICML-10), pp 807–814

  49. Glorot X, Bordes A, Bengio Y (2011) Deep sparse rectifier neural networks. In: Proceedings of the fourteenth international conference on artificial intelligence and statistics, pp 315–323

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

  51. Hinz T, Navarro-Guerrero N, Magg S, Wermter S (2018) Speeding up the hyperparameter optimization of deep convolutional neural networks. Int J Comput Intell Appl 17(02):1850008

    Article  Google Scholar 

  52. Bergstra JS, Bardenet R, Bengio Y, Kégl B (2011) Algorithms for hyper-parameter optimization. In: Advances in neural information processing systems, pp 2546–2554

  53. Robbins H, Monro S (1951) A stochastic approximation method. Ann Math Stat 22:400–407

    Article  MathSciNet  MATH  Google Scholar 

  54. Scholkopf B, Smola AJ (2018) Learning with kernels: support vector machines, regularization, optimization, and beyond. Adaptive computation and machine learning series. MIT Press, Cambridge

    Book  Google Scholar 

  55. Zhang Z, Zhang Y, Li Z (2018) Removing the feature correlation effect of multiplicative noise. In: Advances in neural information processing systems, pp 627–636

  56. Bengio Y, Bergstra JS (2009) Slow, decorrelated features for pretraining complex cell-like networks. In: Advances in neural information processing systems, pp 99–107

  57. Cogswell M, Ahmed F, Girshick R, Zitnick L, Batra D (2015) Reducing overfitting in deep networks by decorrelating representations. arXiv preprint arXiv:1511.06068

  58. Rodríguez P, Gonzalez J, Cucurull G, Gonfaus JM, Roca X (2016) Regularizing CNNs with locally constrained decorrelations. arXiv preprint arXiv:1611.01967

Download references

Acknowledgements

This research has been possible thanks to the support of projects: FPA2017-85197-P and RTI2018-101674-B-I00 (Spanish Ministry of Economy and Competitiveness—MINECO—and the European Regional Development Fund. –ERDF). We thank the Pierre Auger Collaboration for letting us use the simulated event samples that are at the core of this study, and to Professor Antonio Bueno for his helpful advice and careful explanations.

Author information

Author notes

  1. L. J. Herrera and A. Guillén have contributed equally to this work.

Authors and Affiliations

  1. Computer Architecture and Technology Department, University of Granada, Granada, Spain

    F. Carrillo-Perez, L. J. Herrera & A. Guillén

  2. Theoretical and Cosmos Physics Department, University of Granada, Granada, Spain

    J. M. Carceller

Authors
  1. F. Carrillo-Perez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. J. Herrera
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. M. Carceller
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Guillén
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. Carrillo-Perez.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Carrillo-Perez, F., Herrera, L.J., Carceller, J.M. et al. Deep learning to classify ultra-high-energy cosmic rays by means of PMT signals. Neural Comput & Applic 33, 9153–9169 (2021). https://doi.org/10.1007/s00521-020-05679-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-020-05679-9

Keywords

  • Ultra-high-energy cosmic rays
  • Convolutional neural network
  • Support vector machines
  • Deep learning