Shulou(Shulou.com)11/24 Report--

Chaos is everywhere, for example, the solar system is chaotic. Although in some images the solar system appears to be the most orderly thing ever created, we know it will be unstable millions of years from now. After that, some planets spontaneously fall out of their orbits.

The planet most likely to be affected by chaos is Mercury, because its orbit resonates with Jupiter's orbit, which could destabilize Mercury's orbit. According to computer simulations, Mercury was either ejected from the solar system, fell into the sun, or collided with Venus. How it will translate depends very sensitively on the exact orbits of the two planets, so we don't know how it will happen.

In fact, chaos was first discovered by studying the solar system. In 1887, the king of Sweden offered a reward for asking the question: Is the solar system stable? Henri Poincaré thought he could prove this, but ultimately proved the opposite: that the paths of planets are very sensitively dependent on initial conditions. He discovered chaos and won a reward from the king. However, for decades after that, the topic received little attention.

Chaos was rediscovered by Edward Lorenz in the 1950s, when he was using the first computer for weather forecasting. Coincidentally, he noticed that when he refined the number at the beginning of the simulation to three and six decimal places, he got very different results. And it's these extra small numbers that have a big impact on the results.

Lorentz simplified all these weather equations to better understand what was happening, trying to extract the essence from this strange chaotic behavior. After analyzing them, Lorentz arrived at a system of equations consisting of three equations, which are now called Lorentz models.

The Lorentz model describes a curve in abstract three-dimensional space that will quickly approach the middle, coincidentally looking a bit like a butterfly, as shown. This shape where the curve is close is called an attractor because it acts as if the curve is attracted to the center. In Lorentz's simplified model, although the differences in initial conditions are slight, the final curve seems to switch randomly back and forth between the sides, which is why weather forecasting is so difficult.

Is there any way to prevent this from happening? This is the problem that the field of chaos control research tries to solve, which seeks to transform chaotic systems into predictable, regular, non-chaotic behavior. Chaos control has been theorized since the 1990s, when scientists discovered that the attractors of chaotic systems consist of an infinite number of orbits that are periodic and therefore predictable, but also unstable. The actual path of the system switches between those unstable periodic orbits. But since the system is very close to a periodic orbit, only minor corrections are required to keep it in a periodic orbit.

In general, figuring out the corrections needed to keep a system in one of these orbits is not that simple. But we can use machine learning to do that. In a paper last year, two researchers from the University of Munich trained artificial intelligence to provide feedback to Lorentz's model and stabilize it on many different periodic orbits.

This article comes from Weixin Official Accounts: Vientiane Experience (ID: UR4351), by Eugene Wang

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