Planets grow in stellar disks accreting solid material and gas. Whether they become bodies like Earth or Jupiter depends on different factors like the properties of the solids, the pressure and temperature in the disk and the already accumulated material. With computer models the astrophysicists try to simulate the growth process and determine the interior planetary structure. For given boundary conditions they calculate the masses of the gas envelope of a planet. "This requires solving a set of differential equations", explains Yann Alibert, science officer of the NCCR PlanetS at the University of Bern: "Solving these equations has been a specialty of the astrophysicists here in Bern for the past 15 years, but it is a complicated and time consuming process."
To speed up the calculations Yann Alibert and PlanetS associate Julia Venturini of the International Space Science Institute (ISSI) in Bern adopted a method that has already captured many other fields including the smartphone in our hand: deep learning. It is for instance used for face and image recognition. But this branch of artificial intelligence and machine learning has also improved automatic language translation and will be crucial for self-driving cars. "There is a big hype also in astronomy," says Alibert: "Machine learning has already been used to analyze observations, but to my knowledge we are the first to use deep learning for such a purpose." Alibert and Venturini publish their results in the journal Astronomy and Astrophysics (A&A).
Database of millions of planets
First, the researchers had to create a database. They calculated millions of possible interior structures of planets. "It took us three weeks to compute all these test cases using a code developed by Julia Venturini during her PhD in Bern," says Alibert. The next step was to decide the architecture of an artificial neural network, a set of algorithms that passes input data through mathematical operations and has the ability to learn without being explicitly programmed. "Then, we trained this network using our gigantic database," explains the astrophysicist: "Now our network is able to predict the mass of a planet being formed under certain conditions with a very good accuracy and tremendously faster than solving the differential equations."
The deep learning process is much more precise than previously developed methods to replace the solution of differential equations by some analytical formulas. These analytical formulas could predict that a planet should grow up to the mass of Jupiter, while in reality it could not have more mass than Neptune. "We show that our deep neural networks provide a very good approximation at the level of percents," summarizes Alibert. The researchers provide their results on the software development platform GitHub, so that colleagues working in planet formation all around the world benefit from them.