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 language | English |
|---|---|
| Article number | 012215 |
| Number of pages | 9 |
| Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |
| Volume | 98 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 24 Jul 2018 |
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Keywords
- reservoir computer
- recurrent neurral network
- echo state network
- chaos based cryptography
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Using a reservoir computer to learn chaotic attractors, with applications to chaos synchronization and cryptography. / Antonik, Piotr; Gulina, Marvyn; Pauwels, Jael ; Massar, Serge.
In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 98, No. 1, 012215, 24.07.2018.Research output: Contribution to journal › Article
TY - JOUR
T1 - Using a reservoir computer to learn chaotic attractors, with applications to chaos synchronization and cryptography
AU - Antonik, Piotr
AU - Gulina, Marvyn
AU - Pauwels, Jael
AU - Massar, Serge
PY - 2018/7/24
Y1 - 2018/7/24
N2 - 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.
AB - 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.
KW - Ordinateur réservoir
KW - Réseau de neurones récurrents
KW - Réseau d'état d'écho
KW - Cryptographie par chaos
KW - reservoir computer
KW - recurrent neurral network
KW - echo state network
KW - chaos based cryptography
UR - http://www.scopus.com/inward/record.url?scp=85050553440&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.98.012215
DO - 10.1103/PhysRevE.98.012215
M3 - Article
VL - 98
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
SN - 1539-3755
IS - 1
M1 - 012215
ER -