Photonic Reservoir Computer with Output Feedback

  • Piotr AntonikEmail author
Part of the Springer Theses book series (Springer Theses)


This chapter describes, arguably, the most important experiment of my PhD. Not because I worked on it for a long time, but because it brought the most interesting, novel and even unexpected results. Here, we present a photonic reservoir computer with output feedback, and we demonstrate its capacity to generate periodic time series and to emulate chaotic systems. We study in detail the effect of experimental noise on system performance. In the case of chaotic systems, we introduce several metrics, based on standard signal-processing techniques, to evaluate the quality of the emulation.


  1. 1.
    Smerieri, Anteo, François Duport, Yvan Paquot, Benjamin Schrauwen, Marc Haelterman, and Serge Massar. 2012. Analog readout for opticalreservoir computers. In Advances in neural information processing systems, 944–952.Google Scholar
  2. 2.
    Duport, François, Anteo Smerieri, Akram Akrout, Marc Haelterman, and Serge Massar. 2016. Fully analogue photonic reservoir computer. Scientific Report 6: 22381.Google Scholar
  3. 3.
    Vinckier, Quentin, Arno Bouwens, Marc Haelterman, and Serge Massar. 2016. Autonomous all-photonic processor based on reservoir computingparadigm. In Conference on lasers and electro-optics. Optical Societyof America. SF1F.1.Google Scholar
  4. 4.
    Antonik, Piotr, Marc Haelterman, and Serge Massar. 2017. Brain-inspiredphotonic signal processor for generating periodic patterns and emulatingchaotic systems. Physical Review Applied 7: 054014.ADSCrossRefGoogle Scholar
  5. 5.
    Antonik, Piotr, Michiel Hermans, Marc Haelterman, and Serge Massar. 2017. Random pattern and frequency generation using a photonic reservoircomputer with output feedback. Neural Processing Letters: 1–14.Google Scholar
  6. 6.
    Zhang, G. Peter. 2012. Neural networks for time-series forecasting. In Handbook of natural computing, ed. Grzegorz Rozenberg, ThomasBack, and Joost N. Kok, 461–477. Berlin: Springer.CrossRefGoogle Scholar
  7. 7.
    Wyffels, Francis and Benjamin Schrauwen. 2010. A comparative study of Reservoir Computing strategies for monthly time series prediction. Neurocomputing 73 (10–12): 1958–1964.CrossRefGoogle Scholar
  8. 8.
    Antonik, Piotr, Michiel Hermans, François Duport, Marc Haelterman, and Serge Massar. 2016. Towards pattern generation and chaotic series predictionwith photonic reservoir computers. In SPIE’s 2016 laser technology and industrial laser conference, vol. 9732, 97320B.Google Scholar
  9. 9.
    Xu, Meiling, Min Han, and Shunshoku Kanae. 2016. L1/2 norm regularizedecho state network for chaotic time series prediction. In APNNS’s 23th international conference on neural information processing (ICONIP), vol. 9886. LNCS, 12–19.CrossRefGoogle Scholar
  10. 10.
    The 2006/07 forecasting competition for neural networks and computational intelligence.
  11. 11.
    Jaeger, Herbert, and Harald Haas. 2004. Harnessing nonlinearity: Predictingchaotic systems and saving energy in wireless communication. Science 304: 78–80.ADSCrossRefGoogle Scholar
  12. 12.
    Wyffels, Francis, Benjamin Schrauwen, and Dirk Stroobandt. 2008. Stableoutput feedback in reservoir computing using ridge regression. In International conference on artificial neural networks, 808–817. Berlin: Springer.Google Scholar
  13. 13.
    Caluwaerts, Ken, Michiel D’Haene, David Verstraeten, and Benjamin Schrauwen. 2013. Locomotion without a brain: Physical reservoir computing in tensegrity structures. Artificial Life 19 (1): 35–66.CrossRefGoogle Scholar
  14. 14.
    Reinhart, Rene Felix, and Jochen Jakob Steil. 2012. Regularization and stabilityin reservoir networks with output feedback. Neurocomputing 90: 96–105.CrossRefGoogle Scholar
  15. 15.
    Wyffels, Francis, Jiwen Li, Tim Waegeman, Benjamin Schrauwen, and Herbert Jaeger., 2014. Frequency modulation of large oscillatory neural networks. Biological Cybernetics 108 (2): 145–157.MathSciNetCrossRefGoogle Scholar
  16. 16.
    Antonik, Piotr, Michiel Hermans, Marc Haelterman, and Serge Massar. 2016. Towards adjustable signal generation with photonic reservoir computers. In 25th international conference on artificial neural networks, vol. 9886.CrossRefGoogle Scholar
  17. 17.
    Jaeger, Herbert. 2007. Echo state network. Scholarpedia 2 (9): 2330.ADSCrossRefGoogle Scholar
  18. 18.
    Maass, Wolfgang, Thomas Natschlager, and Henry Markram. 2002. Realtimecomputing without stable states: A new framework for neural computation based on perturbations. Neural computation 14: 2531–2560.CrossRefGoogle Scholar
  19. 19.
    Yamazaki, Tadashi, and Shigeru Tanaka. 2007. The cerebellum as a liquid state machine. Neural Networks 20 (3): 290–297.CrossRefGoogle Scholar
  20. 20.
    Rossert, Christian, Paul Dean, and John Porrill. 2015. At the edge of chaos: How cerebellar granular layer network dynamics can provide the basis for temporal filters. PLOS Computational Biology 11 (10): 1–28. Oct.ADSCrossRefGoogle Scholar
  21. 21.
    Appeltant, Lennert, Miguel Cornelles Soriano, Guy Van der Sande, Serge Massar, JanDanckaert, Joni Dambre, Benjamin Schrauwen, Claudio R. Mirasso, and Ingo Fischer. 2011. Information processing using a single dynamical node as complex system. Nature Communications 2: 468.ADSCrossRefGoogle Scholar
  22. 22.
    Paquot, Yvan, François Duport, Anteo Smerieri, Joni Dambre, Marc Haelterman BenjaminSchrauwen, and Serge Massar. 2012. Optoelectronic reservoir computing. Scientific Reports 2: 287.Google Scholar
  23. 23.
    Larger, Laurent, M.C. Soriano, Daniel Brunner, L Appeltant, Jose M Gutierrez, Luis Pesquera, Claudio R Mirasso, and Ingo Fischer. 2012. Photonicinformation processing beyond Turing: An optoelectronic implementation of reservoir computing. Optics Express 20: 3241–3249.ADSCrossRefGoogle Scholar
  24. 24.
    Mackey, Michael C., and Leon Glass. 1977. Oscillation and chaos in physiologicalcontrol systems. Science 197 (4300): 287–289.ADSCrossRefGoogle Scholar
  25. 25.
    Lorenz, Edward N. 1963. Deterministic nonperiodic flow. Journal of the atmospheric sciences 20 (2): 130–141.ADSCrossRefGoogle Scholar
  26. 26.
    Antonik, Piotr, François Duport, Michiel Hermans, Anteo Smerieri, Marc Haelterman, and Serge Massar. 2016. Online training of an Opto- electronic reservoir computer applied to Real-Time channel equalization. IEEE Transactions on Neural Networks and Learning Systems 28 (11): 2686–2698.Google Scholar
  27. 27.
    Farmer, Doyne J. 1982. Chaotic attractors of an infinite-dimensional dynamicalsystem. Physica D: Nonlinear Phenomena 4 (3): 366–393.ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    Atkinson, Kendall E. 2008. An introduction to numerical analysis. Wiley.Google Scholar
  29. 29.
    Hirsch, Morris W., Stephen Smale, and Robert L. Devaney. 2003. Differential equations, dynamical systems, and an introduction to chaos. Boston: Academic press.zbMATHGoogle Scholar
  30. 30.
    Horowitz, Paul, and Winfield Hill. 1980. 1980. The art of electronics: Cambridge University Press.Google Scholar
  31. 31.
    Oppenheim, A.V., and R.W. Schafer. 1989. Discrete-time signal processing. Prentice-Hall signal processing series: Prentice Hall. ISBN 9780132162920.
  32. 32.
    Vinckier, Quentin, François Duport, Anteo Smerieri, Kristof Vandoorne, Peter Bienstman, Marc Haelterman, and Serge Massar. 2015. High-performancephotonic reservoir computer based on a coherently driven passive cavity. Optica 2 (5): 438–446.Google Scholar
  33. 33.
    Walker, John. ENT program.
  34. 34.
    Marsaglia, George. The Marsaglia random number CDROM including the Diehard Battery of Tests of Randomness.
  35. 35.
    Rukhin, Andrew, Juan Soto, James Nechvatal, Miles Smid, and Elaine Barker. 2001. A statistical test suite for random and pseudorandom number generators for cryptographic applications. National Institute of Standards and Technology: Technical report.Google Scholar
  36. 36.
    Martinenghi, Romain, Sergei Rybalko, Maxime Jacquot, Yanne Kouomou Chembo, and Laurent Larger. 2012. Photonic nonlinear transient computingwith multiple-delay wavelength dynamics. Physical Review Letters 108: 244101.Google Scholar
  37. 37.
    Jaeger, Herbert. 2014. Conceptors: An easy introduction. In CoRR abs/1406.2671.Google Scholar
  38. 38.
    Jaeger, Herbert. 2014. Controlling recurrent neural networks by conceptors. In CoRR abs/1403.3369.Google Scholar
  39. 39.
    Kovac, André David, Maximilian Koall, Gordon Pipa, and Hazem Toutounji. 2016. Persistent memory in single node delay-coupled reservoir computing. PLOS ONE 11 (10): 1–15.CrossRefGoogle Scholar
  40. 40.
    Sussillo, David, and L.F. Abbott. 2009. Generating coherent patterns ofactivity from chaotic neural networks. Neuron 63 (4): 544–557.CrossRefGoogle Scholar
  41. 41.
    Antonik, Piotr, Marc Haelterman, and Serge Massar. 2017. Online trainingfor high-performance analogue readout layers in photonic reservoir computers. Cognitive Computation 9: 297–306.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CentraleSupélecMetzFrance

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