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Parallel information processing using a reservoir computing system based on mutually coupled semiconductor lasers

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Abstract

Via the nonlinear channel equalization and the Santa-Fe time series prediction, the parallel processing capability of a reservoir computing (RC) system based on two mutually coupled semiconductor lasers is demonstrated numerically. The results show that, for parallel processing the prediction tasks of two Santa-Fe time series with rates of 0.25 GSa/s, the minimum prediction errors are 3.8 × 10−5 and 4.4 × 10−5, respectively. For parallel processing two nonlinear channel equalization tasks, the minimum symbol error rates (SERs) are 3.3 × 10−4 for both tasks. For parallel processing a nonlinear channel equalization and a Santa-Fe time series prediction, the minimum SER is 6.7 × 10−4 for nonlinear channel equalization, and the minimum prediction error is 4.6 × 10−5 for Santa-Fe time series prediction.

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References

  1. 1.

    S.M. Yu, Y. Wu, R. Jeyasingh, D. Kuzum, H.-S. Philip Wong, An electronic synapse device based on metal oxide resistive switching memory for neuromorphic computation. IEEE Trans. Electron. Devices 58(8), 2729–2737 (2018)

  2. 2.

    J.J. Steil, Backpropagation-decorrelation: online recurrent learning with O(N) complexity. In Proceedings of IEEE IJCNN (2004), pp. 843–848

  3. 3.

    H. Jaeger, The ‘echo state’ approach to analyzing and training recurrent neural networks. Technical Report GMD Report 148, German National Research Center for Information Technology (2001)

  4. 4.

    W. Maass, T. Natschlager, H. Markram, Real-time computing without stable states: a new framework for neural computation based on perturbations. Neural Comput. 14(11), 2531–2560 (2002)

  5. 5.

    D. Verstraeten, B. Schrauwen, M. D’Haene, D. Stroobandt, An experimental unification of reservoir computing methods. Neural Netw. 20(3), 391–403 (2007)

  6. 6.

    E.A. Antonelo, B. Schrauwen, D. Stroobandt, Event detection and localization for small mobile robots using reservoir computing. Neural Netw. 21(6), 862–871 (2008)

  7. 7.

    M. Lukoševičius, H. Jaeger, Reservoir computing approaches to recurrent neural network training. Comput. Sci. Rev. 3(3), 127–149 (2009)

  8. 8.

    F. Triefenbach, A. Jalal, B. Schrauwen, J.-P. Martens, Phoneme recognition with large hierarchical reservoirs. Adv. Neural Inf. Process. Syst. 23, 2307–2315 (2010)

  9. 9.

    L. Boccato, A. Lopes, R. Attux, F.J. Von Zuben, An echo state network architecture based on Volterra filtering and PCA with application to the channel equalization problem. In International Joint Conference on Neural Networks, IEEE (2011), pp. 580–587

  10. 10.

    P. Buteneers, D. Verstraeten, P. Van Mierlo, T. Wyckhuys, D. Stroobandt, R. Raedt, H. Hallez, B. Schrauwen, Automatic detection of epileptic seizures on the intra-cranial electroencephalogram of rats using reservoir computing. Artif. Intell. Med. 53(3), 215–223 (2011)

  11. 11.

    L. Boccato, A. Lopes, R. Attux, F.J. Von Zuben, An extended echo state network using Volterra filtering and principal component analysis. Neural Netw. 32(2), 292–302 (2012)

  12. 12.

    P. Antonik, M. Gulina, J. Pauwels, S. Massar, Using a reservoir computer to learn chaotic attractors, with applications to chaos synchronization and cryptography. Phys. Rev. E 98(1), 012215 (2018)

  13. 13.

    L. Appeltant, M.C. Soriano, G. Van der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C.R. Mirasso, I. Fischer, Information processing using a single dynamical node as complex system. Nat. Commun. 2, 468–472 (2011)

  14. 14.

    G. Dion, S. Mejaouri, J. Sylvestre, Reservoir computing with a single delay-coupled nonlinear mechanical oscillator. J. Appl. Phys. 124(15), 152132 (2018)

  15. 15.

    K. Caluwaerts, M. D’Haene, D. Verstraeten, B. Schrauwen, Locomotion without a brain: physical reservoir computing in tensegrity structures. Artif. Life 19(1), 35–66 (2013)

  16. 16.

    J. Degrave, K. Caluwaerts, J. Dambre, F. Wyffels, Developing an embodied gait on a compliant quadrupedal robot. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE (2015), pp. 4486–4491

  17. 17.

    L. Larger, M.C. Soriano, D. Brunner, L. Appeltant, J.M. Gutierrez, L. Pesquera, C.R. Mirasso, I. Fischer, Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing. Opt. Express 20(3), 3241–3249 (2012)

  18. 18.

    R. Martinenghi, S. Rybalko, M. Jacquot, Y.K. Chembo, L. Larger, Photonic nonlinear transient computing with multiple-delay wavelength dynamics. Phys. Rev. Lett. 108(24), 244101 (2012)

  19. 19.

    P. Antonik, M. Haelterman, S. Massar, Brain-inspired photonic signal processor for generating periodic patterns and emulating chaotic systems. Phys. Rev. Appl. 7(5), 054014 (2017)

  20. 20.

    M. Tezuka, K. Kanno, M. Bunsen, Reservoir computing with a slowly modulated mask signal for preprocessing using a mutually coupled optoelectronic system. Jpn. J. Appl. Phys. 55(8), 08RE06 (2016)

  21. 21.

    J. Qin, Q.C. Zhao, H.X. Yin, C. Liu, Numerical simulation and experiment on optical packet header recognition utilizing reservoir computing based on optoelectronic feedback. IEEE Photon. J. 9(1), 7901311 (2017)

  22. 22.

    F. Duport, B. Schneider, A. Smerieri, M. Haelterman, S. Massar, All-optical reservoir computing. Opt. Express 20(20), 22783–22795 (2012)

  23. 23.

    D. Brunner, M.C. Soriano, C.R. Mirasso, I. Fischer, Parallel photonic information processing at gigabyte per second data rates using transient states. Nat. Commun. 4, 1364 (2013)

  24. 24.

    H. Zhang, X. Feng, B.X. Li, Y. Wang, K.Y. Cui, F. Liu, W.B. Dou, Y.D. Huang, Integrated photonic reservoir computing based on hierarchical time-multiplexing structure. Opt. Express 22(25), 31356–31370 (2014)

  25. 25.

    R.M. Nguimdo, G. Verschaffelt, J. Danckaert, G. Van der Sande, Fast photonic information processing using semiconductor lasers with delayed optical feedback: role of phase dynamics. Opt. Express 22(7), 8672–8686 (2014)

  26. 26.

    J. Nakayama, K. Kanno, A. Uchida, Laser dynamical reservoir computing with consistency: an approach of a chaos mask signal. Opt. Express 24(8), 8679–8692 (2016)

  27. 27.

    J. Bueno, D. Brunner, M.C. Soriano, I. Fischer, Conditions for reservoir computing performance using semiconductor lasers with delayed optical feedback. Opt. Express 25(3), 2401–2412 (2017)

  28. 28.

    Y.S. Hou, G.Q. Xia, W.Y. Yang, D. Wang, E. Jayaprasath, Z.F. Jiang, C.X. Hu, Z.M. Wu, Prediction performance of reservoir computing system based on a semiconductor laser subject to double optical feedback and optical injection. Opt. Express 26(8), 10211–10219 (2018)

  29. 29.

    Y. Kuriki, J. Nakayama, K. Takano, A. Uchida, Impact of input mask signals on delay-based photonic reservoir computing with semiconductor lasers. Opt. Express 26(5), 5777–5788 (2018)

  30. 30.

    J. Vatin, D. Rontani, M. Sciamanna, Enhanced performance of a reservoir computer using polarization dynamics in VCSELs. Opt. Lett. 43(18), 4497–4500 (2018)

  31. 31.

    J. Torrejon, M. Riou, F.A. Araujo, S. Tsunegi, G. Khalsa, D. Querlioz, P. Bortolotti, V. Cros, K. Yakushiji, A. Fukushima, H. Kubota, S. Yuasa, M.D. Stiles, J. Grollier, Neuromorphic computing with nanoscale spintronic oscillators. Nature 547(7664), 428–431 (2017)

  32. 32.

    C. Du, F. Cai, M.A. Zidan, W. Ma, S.H. Lee, W.D. Lu, Reservoir computing using dynamic memristors for temporal information processing. Nat. Commun. 8, 2204 (2017)

  33. 33.

    G. Van der Sande, R.M. Nguimdo, G. Verschaffelt, Parallel processing using an optical delay-based reservoir computer. In Proceedings of SPIE (2016), vol. 9894, 98941P

  34. 34.

    Q.C. Zhao, H.X. Yin, H.G. Zhu, Simultaneous recognition of two channels of optical packet headers utilizing reservoir computing subject to mutual-coupling optoelectronic feedback. Optik 157, 951–956 (2018)

  35. 35.

    X.R. Bao, Q.C. Zhao, H.X. Yin, J. Qin, Recognition of the optical packet header for two channels utilizing the parallel reservoir computing based on a semiconductor ring laser. Mod. Phys. Lett. B 32(14), 1850150 (2018)

  36. 36.

    Y.S. Hou, G.Q. Xia, E. Jayaprasath, D.Z. Yue, W.Y. Yang, Z.M. Wu, Prediction and classification performance of reservoir computing system using mutually delay-coupled semiconductor lasers. Opt. Commun. 433, 215–220 (2019)

  37. 37.

    A. Röhm, K. Lüdge, Multiplexed networks: reservoir computing with virtual and real nodes. J. Phys. Commun. 2(8), 085007 (2018)

  38. 38.

    N.Q. Li, R.M. Nguimdo, A. Locquet, D.S. Citrin, Enhancing optical-feedback-induced chaotic dynamics in semiconductor ring lasers via optical injection. Nonlinear Dyn. 92(2), 315–324 (2018)

  39. 39.

    J.J. Chen, Y.N. Duan, L.F. Li, Z.Q. Zhong, Wideband polarization-resolved chaos with time-delay signature suppression in VCSELs subject to dual chaotic optical injections. IEEE Access 6, 66807–66815 (2018)

  40. 40.

    D.Z. Zhong, Z.Z. Xiao, G.Z. Yang, Criterion of globally complete chaos synchronization for diverse three-node VCSEL networks with coupling delays. Appl. Phys. B 125(2), 26 (2019)

  41. 41.

    Y.H. Hong, X.F. Chen, P.S. Spencer, K.A. Shore, Enhanced flat broadband optical chaos using low-cost VCSEL and fiber ring resonator. IEEE J. Quantum Electron. 51(3), 1200106 (2015)

  42. 42.

    Y.H. Hong, P.S. Spencer, K.A. Shore, Wideband chaos with time-delay concealment in vertical-cavity surface-emitting lasers with optical feedback and injection. IEEE J. Quantum Electron. 50(4), 236–242 (2014)

  43. 43.

    N. Jiang, W. Pan, B. Luo, L.S. Yan, S.Y. Xiang, Simultaneous unidirectional and bidirectional chaos-based optical communication using hybrid coupling semiconductor lasers. Sci. China Inf. Sci. 57(1), 012401 (2014)

  44. 44.

    A.B. Wang, Y.B. Yang, B.J. Wang, B.B. Zhang, L. Li, Y.C. Wang, Generation of wideband chaos with suppressed time-delay signature by delayed self-interference. Opt. Express 21(7), 8701–8710 (2013)

  45. 45.

    Y.S. Hou, L.L. Yi, G.Q. Xia, Z.M. Wu, Exploring high quality chaotic signal generation in a mutually delay coupled semiconductor laser system. IEEE Photon. J. 9(5), 1505110 (2017)

  46. 46.

    T. Heil, I. Fischer, W. Elsasser, J. Muler, C.R. Mirasso, Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers. Phys. Rev. Lett. 86(5), 795–798 (2001)

  47. 47.

    A.S. Weigend, N.A. Gershenfeld, Time series prediction : Forecasting the future and understanding the past, Redwood, Addison-Wesley (1994)

  48. 48.

    L.A. Thiede, U. Parlitz, Gradient based hyperparameter optimization in echo state networks. Neural Netw. 115, 23–29 (2019)

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 61575163, Grant 61775184, and Grant 61875167, in part by the Natural Science Foundation of Inner Mongolia Autonomous Region of china under Grant 2019MS06022, and in part by the Postgraduate Research and Innovation Project of Chongqing Municipality under Grant CYB19087.

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Correspondence to G. Q. Xia or Z. M. Wu.

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Hou, Y.S., Xia, G.Q., Jayaprasath, E. et al. Parallel information processing using a reservoir computing system based on mutually coupled semiconductor lasers. Appl. Phys. B 126, 40 (2020). https://doi.org/10.1007/s00340-019-7351-4

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