Machine learning that predicts chaotic evolution

In a series of results reported in the journals Physical Review Letters and Chaos, scientists have used machine learning — the same computational technique behind recent successes in artificial intelligence — to predict the future evolution of chaotic systems out to stunningly distant horizons. The approach is being lauded by outside experts as groundbreaking and likely to find wide application.

The Lyapunov time represents how long it takes for two almost-identical states of a chaotic system to exponentially diverge. As such, it typically sets the horizon of predictability.

The algorithm knows nothing about the Kuramoto-Sivashinsky equation itself; it only sees data recorded about the evolving solution to the equation. This makes the machine-learning approach powerful; in many cases, the equations describing a chaotic system aren’t known, crippling dynamicists’ efforts to model and predict them. Ott and company’s results suggest you don’t need the equations — only data.

They employed a machine-learning algorithm called reservoir computing to “learn” the dynamics of an archetypal chaotic system called the Kuramoto-Sivashinsky equation. The evolving solution to this equation behaves like a flame front, flickering as it advances through a combustible medium. 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.

https://www.quantamagazine.org/machine-learnings-amazing-ability-to-predict-chaos-20180418/