DNN for analysing transiting planets observations
The analysis of transiting planet observations relies often on methods like Markov-Chain-Monte-Carlo methods or similar. While powerful, they are generally time consuming and may not explore the full posterior distribution of planetary parameters, in particular when the posterior distribution is multi-variate. The extensive required computer time results from the necessity to compute millions of time the forward model, in this case the solution of differential equations describing the internal structure of a planet.
We developed a new, simpler, method which is based on the random brute force exploration of the parameter space, replacing the forward model by a Deep Neural Network fitted a priori on millions of similar internal structure models.
We demonstrated in this paper that our our model leads to very accurate planetary radii, the difference between the DNN-based radius and the one obtained by solving differential equations is a fraction of a percent (to be compared with the typical precision of observed radii, of the order of a few %).
Our model was used in numerous papers from the CHEOPS collaboration, and fully described in Leleu et al. 2021. An illustration of the precision of our DNN is displayed on the side.
Difference in percentage between planetary radius computed using our DNN and the one computed by direct numerical simulation. Adapted from Leleu et al. (2021), Astronomy & Astrophysics, Volume 649, id.A26. doi:10.1051/0004-6361/202039767
DNN for accelerating planetary system formation numerical simulations
Numerical simulations of planetary system formation relies on solving sets of differential equations, and can be very time consuming. As an example, the most recent synthetic planetary populations computed using the so-called Bern model, can take up to one millions CPU hours for computing one thousand planetary systems.
An important part of these calculations is the determination of the internal structure of forming planet, an essential step in determining how much gas forming planets can accrete. Equally important is the determination of the so-called critical mass, the mass a planet must reach in order to become a gas giant planet similar to Jupiter.
In this paper, we trained a Deep Neural Network to compute both the critical mass as a function of the relevant parameters, as well as the mass of forming planets. We demonstrated that our models reach an excellent accuracy compared to solving directly differential equations, much better that what was done at the time in the literature using scaling laws.
Predicted critical mass (in Earth masses, logarithmic scale) as a function of the critical mass obtained by solving the internal structure equations (blue), and using scaling laws from the literature (red).
Adapted from Alibert and Venturini., (2019), Astronomy & Astrophysics, Volume 626, id.A21. doi:10.1051/0004-6361/201834942