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

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 synchronisation. That is, the trained reservoir computer, weakly driven by the chaotic system, will synchronise with the chaotic system. Conversely, the chaotic system, weakly driven by a trained reservoir computer, will synchronise with the reservoir computer. We illustrate this behaviour 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.

arXiv comment10 pages, 6 figures

References in corpus (8)

• Optoelectronic Reservoir Computing
• Using Machine Learning to Replicate Chaotic Attractors and Calculate Lyapunov Exponents from Data
• Breaking projective chaos synchronization secure communication using filtering and generalized synchronization
• Brain-inspired photonic signal processor for periodic pattern generation and chaotic system emulation
• Error Function Attack of chaos synchronization based encryption schemes
• Cryptanalyzing a discrete-time chaos synchronization secure communication system
• The difference between memory and prediction in linear recurrent networks
• Breaking a chaos-noise-based secure communication scheme

Cited by in corpus (30)

• On Explaining the Surprising Success of Reservoir Computing Forecaster of Chaos? The Universal Machine Learning Dynamical System with Contrasts to VAR and DMD
• Optical Reservoir Computing using multiple light scattering for chaotic systems prediction
• 0.75 Gbit/s high-speed classical key distribution with mode-shift keying chaos synchronization of Fabry-Perot lasers
• Using reservoir computers to distinguish chaotic signals
• Network Structure Effects in Reservoir Computers
• Machine-learning inference of fluid variables from data using reservoir computing
• Good and bad predictions: Assessing and improving the replication of chaotic attractors by means of reservoir computing
• Do Reservoir Computers Work Best at the Edge of Chaos?
• Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systems
• Optimizing Memory in Reservoir Computers
• Using Machine Learning to Assess Short Term Causal Dependence and Infer Network Links
• Data-driven Reconstruction of Nonlinear Dynamics from Sparse Observation
• Catch-22s of reservoir computing
• Dimension of Reservoir Computers
• Reducing network size and improving prediction stability of reservoir computing
• Dynamical system analysis of a data-driven model constructed by reservoir computing
• Time Shifts to Reduce the Size of Reservoir Computers
• Dynamical Component Analysis (DyCA): Dimensionality Reduction For High-Dimensional Deterministic Time-Series
• Chaotic attractor reconstruction using small reservoirs -- the influence of topology
• Stability Analysis of Reservoir Computers Dynamics via Lyapunov Functions
• Deep Photonic Reservoir Computer for Speech Recognition
• Two methods to approximate the Koopman operator with a reservoir computer
• Reservoir Computers with Random and Optimized Time-Shifts
• Reservoir Computing meets Recurrent Kernels and Structured Transforms
• Machine-learning construction of a model for a macroscopic fluid variable using the delay-coordinate of a scalar observable
• Synchronizing Chaos using Reservoir Computing
• Stochastic Reservoir Computers
• Improving the Performance of Echo State Networks Through State Feedback
• Reservoir Computers Modal Decomposition and Optimization
• Reservoir observer enhanced with residual calibration and attention mechanism