“The machine-learning technique is almost as good as knowing the truth, so to say.” “This is really very good,” Holger Kantz, a chaos theorist at the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany, said of the eight-Lyapunov-time prediction.
As such, it typically sets the horizon of predictability. The Lyapunov time represents how long it takes for two almost-identical states of a chaotic system to exponentially diverge. After training itself on data from the past evolution of the Kuramoto-Sivashinsky equation, the researchers’ reservoir computer could then closely predict how the flamelike system would continue to evolve out to eight “Lyapunov times” into the future, eight times further ahead than previous methods allowed, loosely speaking.
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