Using a reservoir computer to learn chaotic attractors, with applications to chaos synchronization and cryptography

Piotr Antonik, Marvyn Gulina, Jael Pauwels, Serge Massar

Research output: Contribution to journalArticle

Abstract

Using the machine learning approach known as reservoir computing, it is possible to train one dynamical system to emulate another. We show that such trained reservoir computers reproduce the properties of the attractor of the chaotic system sufficiently well to exhibit chaos synchronization. That is, the trained reservoir computer, weakly driven by the chaotic system, will synchronize with the chaotic system. Conversely, the chaotic system, weakly driven by a trained reservoir computer, will synchronize with the reservoir computer. We illustrate this behavior on the Mackey-Glass and Lorenz systems. We then show that trained reservoir computers can be used to crack chaos based cryptography and illustrate this on a chaos cryptosystem based on the Mackey-Glass system. We conclude by discussing why reservoir computers are so good at emulating chaotic systems.

Original languageEnglish
Article number012215
Number of pages9
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume98
Issue number1
DOIs
Publication statusPublished - 24 Jul 2018

Keywords

  • reservoir computer
  • recurrent neurral network
  • echo state network
  • chaos based cryptography

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