利用水库计算机学习混沌吸引子及其在混沌同步和密码学中的应用
Using a reservoir computer to learn chaotic attractors, with applications to chaos synchronisation and cryptography
摘要：
使用被称为储备池计算的机器学习方法，可以训练一个动态系统来模拟另一个动态系统。我们表明，这种训练有素的水库计算机再现混沌系统的吸引子的属性，以及充分表现出混沌同步。也就是说，由混沌系统弱驱动的训练的水库计算机将与混沌系统同步。相反，混沌系统，由一个训练有素的水库计算机弱驱动，将与水库计算机同步。我们说明这种行为的麦基玻璃和洛伦兹系统。然后，我们表明，训练有素的水库计算机可以用来破解混沌密码学，并说明这一点的Mackey-Glass系统的基础上的混沌密码系统。最后，我们讨论了为什么水库计算机是如此善于模拟混沌系统。
英文摘要：
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.
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