A new artificially intelligent system can independently formulate natural laws on the basis of measurement data. In this way, ‘AI-Descartes’ rediscovered, among other things, Kepler’s description of planetary orbits.
An artificially intelligent system has rediscovered Kepler’s third law. This law shows the relationship between the orbital period of two celestial bodies and their distance from each other. The system called AI-Descartes, combines data analysis with existing theories. In addition to Kepler’s law, it also found formulas about sticky gas particles and moving clocks.
Physicists strive to capture all natural phenomena in laws. They do that in two ways. First, they try to discover patterns in observations. Second, they derive new formulas by combining existing laws.
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However, the most important laws of nature, described in, among other things, the standard models of particle physics and cosmology, have barely improved for decades. This is partly because many experiments nowadays yield a confusing mess of data; think of the countless particle collisions in the Large Hadron Collider.
Outliers
Artificial intelligence (AI) may be able to help break this physics impasse. There are already several AIs that look for patterns in large amounts of experimental data.
That data is often quite messy. They contain weird outliers, resulting from measurement errors or one-time events. For example, a planet that orbits around a star can wobble for a while because another planet comes close to it.
In their search for patterns, AIs include all those random outliers. As a result, they often provide extremely complex formulas that say little about the underlying laws of nature. Systems also often find so many different formulas that it makes you as a researcher go wild.
Mathematical Laws
With AI-Descartes, physicists hope to circumvent these problems. The system was developed by a team led by Cristina Cornelio, researcher at Samsung AI in Cambridge (UK). The AI is named after the seventeenth-century philosopher and mathematician René Descartes, known for the saying ‘I think, therefore I am’. He had the then pioneering view that nature is governed by mathematical laws that follow logically from each other.
AI-Descartes, like previous systems, derives formulas from experimental data. The system then chooses the one that best fits the existing theories from all possible formulas. “We are combining an approach that has been used by scientists for centuries – deriving new formulas from existing background theories – with a data-driven approach that is more common in this age of machine learning,” says Cornelio.
Exoplanets and binary stars
The researchers gave AI-Descartes NASA data of the movement of the planets in the solar system. They also showed the system how some planets outside the solar system move around their star, and how some binary stars orbit each other.
Based on that data, AI-Descartes rediscovered Kepler’s third law from 1619. This law shows how two celestial bodies, for example a planet and a star, revolve around each other. The duration of an orbit depends on the distance between the two objects and their masses (see Kepler frame).
Kepler’s third law isn’t the most complicated formula in physics – you can learn it in high school. Still, it is remarkable that an AI has derived the law from observations. With the planets in the solar system, the connection is difficult to recognize. Because they are much less massive than the sun, these planets satisfy an even simpler formula. Measurements of exoplanets and binary stars, on the other hand, are less accurate, so they contain more crazy outliers. Nevertheless, the data from binary stars put AI-Descartes on the right track.
Theory of relativity
The researchers also unleashed AI-Descartes on two more complex physical phenomena. Thus, the system rediscovered a formula of the American chemist Irving Langmuir from 1918. That formula describes how gas particles stick to a solid surface.
AI-Descartes was also allowed to search for a formula from Albert Einstein’s special theory of relativity (1905). The formula describes how a moving clock runs a tiny bit slower than a stationary clock. Because this effect is hardly measurable, AI-Descartes was unable to draw up the exact formula. However, the system did find some formulas that come quite close. Based on the data entered, the AI also concluded that the speed of light must be constant, one of the pillars of Einstein’s theory of relativity.
Lean backwards
The current results are mainly proof that an AI can formulate useful physical laws based on measurement data. The ultimate goal is to have AI-Descartes discover new laws.
To do this, the AI must first know more existing theories. Because all background knowledge has to be fed to the system in the correct computer terms, this still takes a lot of time. In addition, an incorrect entry or a missing part immediately destroys the results.
The researchers therefore want to train AI-Descartes to read scientific articles themselves and to derive the well-known formulas from them. If they succeed, theoretical physicists can sit back and see whether computers help their field further. “One of the most exciting aspects of our work is the opportunity to make significant advances in scientific research,” says Cornelio.
Kepler frame
Kepler’s third law was published in 1619 by the German astronomer Johannes Kepler. The law shows how fast two celestial bodies revolve around each other. It can be written as a formula in different ways. For example, you can assume the time in which both objects complete a round, as below.
The orbital period (p) depends on the distance between the two celestial bodies (d) and the masses of both objects (m1 and m2). Furthermore, the formula contains Newton’s gravitational constant (G), an unchanging number that indicates how strong gravity is.
With this formula you can, for example, calculate how long it takes the earth to go around the sun. You then fill in d the distance between the Earth and the Sun (1.5 ∙ 1011 m) and before m1 and m2 the masses of both objects (6.0 ∙ 1024 kg and 2.0 ∙ 1030 kilograms). This results in a value of more than 31.5 million seconds, or more than 365 days.
In this case, you can even omit the mass of the Earth from the formula, because it is negligible compared to the mass of the Sun. That means that the orbital period of a planet in the solar system depends only on its distance from the sun. Even if the Earth had been ten times as heavy, a year would have lasted 365 days.