• [1]

    A. Krizhevsky, I. Sutskever, and G. E. Hinton, Advances in neural information processing systems,1097-1105 (2016)

  • [2]

    J. Redmon, S. Divvala, R. Girshick et al., IEEE Conference on Computer Vision and Pattern Recognition (CVPR), (Las Vegas, NV, 2016), 779-788

  • [3]

    S. Ren, K. He, R. Girshick et al., IEEE Transactions on Pattern Analysis and Machine Intelligence, 39: 1137-1149 (2017)

  • [4]

    M. T. Luong, H. Pham, and C. D. Manning, the Conference on Emprirical Methods in Natural Language Processing, 1412-1421 (2015)

  • [5]

    Y. Wu, M. Schuster, Z. Chem et al., arXiv: 1609.08144

  • [6]

    G. Hinton, L. Deng, D. Yu et al., IEEE Signal processing magazine, 29: 82-97 (2012)

  • [7]

    A. Hannun, C. Case, J. Casper et al., arXiv: 1412.5567

  • [8]

    D. Amodei, S. Ananthanarayanan, R. Anubhai et al., International conference on machine learning,173-182 (2016)

  • [9]

    Y. LeCun and Y. Bengio, Convolutional networks for images, speech, and time series. The handbook of brain theory and neural networks, 1995, 3361(10): 1995

  • [10]

    K. He, X. Zhang, S. Ren et al., Proceedings of the IEEE conference on computer vision and pattern recognition, 770-778 (2016)

  • [11]

    D. E. Rumerlhar, Nature, 323: 533-536 (1986)

  • [12]

    S. Hochreiter and J. Schmidhuber, Neural computation, 9(8): 1735-1780 (1997)

  • [13]

    K. Cho, B. Van Merrinboer, C. Gulcehre et al., arXiv: 1406.1078

  • [14]

    R. Berg, T. N. Kipf, and M. Welling, arXiv: 1706.02263

  • [15]

    F. Monti, M. Bronstein, X. Bresson, Advances in Neural Information Processing Systems,3697-3707 (2017)

  • [16]

    J. Gilmer, S. S. Schoenholz, P. F. Riley et al., Proceedings of the 34th International Conference on Machine Learning, 70: 1263-1272 (2017)

  • [17]

    N. Choma, F. Monti, L. Gerhardt, et al., 2018 17th IEEE International Conference on Machine Learning and Applications (ICMLA), 386-391 (2018)

  • [18]

    M. Abdughani, J. Ren, L. Wu et al., arXiv: 1807.09088

  • [19]

    J. Arjona Martinez, J. R. Vlimant, M. Spiropulu, et al., arXiv: 1810.07988

  • [20]

    G. V. Kulikov and G. B. Khristiansen, Sov. Phys. JETP, 35(8): 441-444 (1959)

  • [21]

    C. Jin, L. Q. Yin, S. Chen et al., Radiation Detection Technology and Methods, 3(3): 19 (2019)

  • [22]

    B. Bartoli, P. Bernardini, X. J. Bi et al., Physical Review D, 92(9): 092005 (2015)

  • [23]

    M. Amenomori, S. Ayabe, D. Chen et al., Physics Letters B, 632(1): 58-64 (2006)

  • [24]

    M. Bertaina, W. D. Apel, J. C. Arteaga-Velazquez et al., Nuclear Physics B-Proceedings Supplements, 256: 149-160 (2014)

  • [25]

    W. D. Apel, J. C. Arteaga-Velazquez, K. Bekk et al., Physical Review Letters, 107(17): 171104 (2011)

  • [26]

    H. H. He, LHAASO collaboration, Radiation Detection Technology and Methods, 2(1): 7 (2018)

  • [27]

    L. Yin, Z. Cao, S. S. Zhang et al., Accurate Measurement of the Cosmic Ray Proton Spectrum from 100 TeV to 10 PeV with LHAASO, PoS,508 (2017)

  • [28]

    L. Q. Yin, S. S. Zhang, Z. Cao et al., arXiv: 1904.09130

  • [29]

    P. K. Grieder, Extensive air showers, Berlin: Springer, 2010

  • [30]

    A. Haungs, Journal of Physics G: Nuclear and Particle Physics, 29(5): 809 (2003)

  • [31]

    Z. Wu, S. Pan, F. Chen et al., arXiv: 1901.00596

  • [32]

    D. I. Shuman, S. K. Narang, P. Frossard et al., arXiv: 1211.0053

  • [33]

    F. R. K. Chung and F. C. Graham, Spectral graph theory, American Mathematical Soc., (1997)

  • [34]

    J. Bruna, W. Zaremba, A. Szlam et al., arXiv: 1312.6203

  • [35]

    M. Defferrard, X. Bresson, and P. Vandergheynst, dvances in neural information processing systems,3844-3852 (2016)

  • [36]

    T. N. Kipf and M. Welling, arXiv: 1609.02907

  • [37]

    J. Masci, D. Boscaini, M. Bronstein et al., Proceedings of the IEEE international conference on computer vision workshops. 37-45 (2015)

  • [38]

    D. Boscaini, J. Masci, E. Rodola et al., Advances in Neural Information Processing Systems,3189-3197 (2016)

  • [39]

    F. Monti, D. Boscaini, J. Masci et al., Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 5115-5124 (2017)

  • [40]

    K. Greisen, Annual Review of Nuclear Science, 10(1): 63-108 (1960)

  • [41]

    K. Kamata and J. Nishimura, Progress of Theoretical Physics Supplement, 6: 93-155 (1958)

  • [42]

    D. Heck, G. Schatz, J. Knapp et al., CORSIKA: a Monte Carlo code to simulate extensive air showers, (1998)

  • [43]

    S. Z. Chen, J. Zhao, Y. Liu et al., Nuclear Electronics & Detection Technology, 37(11): 1101 (2017)

  • [44]

    S. Agostinelli, J. Allison, K. Amako et al., GEANT4: a simulation toolkit, Nuclear instruments and methods in physics research section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 506(3): 250-303 (2003)

  • [45]

    D. P. Kingma and J. Ba, arXiv: 1412.6980

  • [46]

    J. R. Hoerandel, Astroparticle Physics, 19(2): 193-220 (2003)

  • [47]

    S. Ter-Antonyan, Physical Review D, 89(12): 123003 (2014)

  • [48]

    C. Jin, W. Liu, H. B. Hu and Y. Q. Guo, Physical Review D, 97: 123005 (2018)

  • [49]

    C. Li, H. H. He, G. Xiao et al., Physical Review D, 98(4): 042001 (2018)