It is 300 years since Isaac Newton formulated the laws that allow us to know exactly where a planet or any celestial object will be at any given time, which makes it possible, for example, to send rockets to Mars or probes to Pluto. Newton was, indeed, the first to discover how two bodies endowed with mass interact thanks to gravity, and that was the key to understanding how things move and relate to each other in the Universe in which we live. What the great English physicist never achieved was to calculate how not two, but three objects that orbit each other would be related. It has been three centuries since Newton raised what is known as the “three-body problem,” a difficult mathematical question that neither he nor anyone else has been able to solve so far, and which inspired the Chinese writer Cixin Liu to write a of the most successful science fiction works of recent years.
The three-body problem is difficult because it is a chaotic system, which means that you need extremely precise knowledge of the initial position of the three bodies in question in order to make any reliable predictions. In these systems the “butterfly effect” becomes tremendously real, and even the slightest error results in a completely different orbit than anticipated. There is no equation on the face of the Earth that is capable of predicting how objects will move, or of determining whether or not their orbits will be stable in time.
An Artificial Intelligence to solve it
Today, to approach the problem, mathematicians have to meticulously test every possible scenario, either by hand or using computers, which are slow to respond and are resource intensive. Now, physicist Philip Breen, from the University of Edinburgh, has devised together with his colleagues a new way to approach the problem using Artificial Intelligence, specifically a neural network that can be up to 100 million times faster than the best solvers computerized. The work has just been published on “arXiv.org”.
The researchers trained their AI in 9,900 different three-body scenarios generated by a state-of-the-art system called Brutus. To test his method and make sure the AI worked, Bren and his team first used 100 Brutus scenarios and then tested the AI with another 5,000 already solved, but without giving him the solutions. The AI quickly solved them, and its results matched almost exactly Brutus’ examples, showing that the neural network could provide fast and accurate answers to the three-body problem.
Understand the collision of black holes
According to Bren, that ability could, for example, improve our understanding of how black holes collide and form gravitational waves. In fact, many of these complex dynamic systems could be studied as a series of three-body interactions, and thus resolved by the neural network.
The system, however, has a limitation. Because AI only works for a finite period of time, and if a particular three-body problem has not been studied before, from the beginning, it is impossible to know in advance how long it will take to find the solution. To solve the question, the researchers come up with a “trick”: Instead of using AI to do all the computation, the idea is to give it only the hardest bits, when the three bodies come close to each other. Then, with that computational bottleneck resolved, the problem is returned to Brutus.
The idea, according to Christopher Foley of the University of Cambridge and a co-author of the study, could very quickly provide any number of solutions, even without a clear equation. “It is not so much about elegance – says Foley – as it is about progressing and advancing in our understanding of the basic components of our physical environment. If I can get the solutions that way, it doesn’t matter how I get to them, as long as they are valid.